1
|
Sheng D, Wang D, Zhang J, Wang X, Zhai Y. A Time-Varying Mixture Integer-Valued Threshold Autoregressive Process Driven by Explanatory Variables. Entropy (Basel) 2024; 26:140. [PMID: 38392395 PMCID: PMC10887732 DOI: 10.3390/e26020140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2024] [Revised: 02/01/2024] [Accepted: 02/02/2024] [Indexed: 02/24/2024]
Abstract
In this paper, a time-varying first-order mixture integer-valued threshold autoregressive process driven by explanatory variables is introduced. The basic probabilistic and statistical properties of this model are studied in depth. We proceed to derive estimators using the conditional least squares (CLS) and conditional maximum likelihood (CML) methods, while also establishing the asymptotic properties of the CLS estimator. Furthermore, we employed the CLS and CML score functions to infer the threshold parameter. Additionally, three test statistics to detect the existence of the piecewise structure and explanatory variables were utilized. To support our findings, we conducted simulation studies and applied our model to two applications concerning the daily stock trading volumes of VOW.
Collapse
Affiliation(s)
- Danshu Sheng
- School of Mathematics and Statistics, Liaoning University, Shenyang 110031, China
| | - Dehui Wang
- School of Mathematics and Statistics, Liaoning University, Shenyang 110031, China
| | - Jie Zhang
- School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
| | - Xinyang Wang
- School of Mathematics and Statistics, Liaoning University, Shenyang 110031, China
| | - Yiran Zhai
- State Grid Jilin Electric Power Company Limited Information and Telecommunication Company, Changchun 132400, China
| |
Collapse
|
2
|
Zimmer F, Draxler C, Debelak R. Power Analysis for the Wald, LR, Score, and Gradient Tests in a Marginal Maximum Likelihood Framework: Applications in IRT. Psychometrika 2023; 88:1249-1298. [PMID: 36029390 PMCID: PMC10656348 DOI: 10.1007/s11336-022-09883-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2021] [Revised: 01/11/2022] [Indexed: 06/15/2023]
Abstract
The Wald, likelihood ratio, score, and the recently proposed gradient statistics can be used to assess a broad range of hypotheses in item response theory models, for instance, to check the overall model fit or to detect differential item functioning. We introduce new methods for power analysis and sample size planning that can be applied when marginal maximum likelihood estimation is used. This allows the application to a variety of IRT models, which are commonly used in practice, e.g., in large-scale educational assessments. An analytical method utilizes the asymptotic distributions of the statistics under alternative hypotheses. We also provide a sampling-based approach for applications where the analytical approach is computationally infeasible. This can be the case with 20 or more items, since the computational load increases exponentially with the number of items. We performed extensive simulation studies in three practically relevant settings, i.e., testing a Rasch model against a 2PL model, testing for differential item functioning, and testing a partial credit model against a generalized partial credit model. The observed distributions of the test statistics and the power of the tests agreed well with the predictions by the proposed methods in sufficiently large samples. We provide an openly accessible R package that implements the methods for user-supplied hypotheses.
Collapse
Affiliation(s)
| | - Clemens Draxler
- The Health and Life Sciences University, Hall in Tirol, Austria
| | | |
Collapse
|
3
|
Guo X, Li R, Liu J, Zeng M. Statistical inference for linear mediation models with high-dimensional mediators and application to studying stock reaction to COVID-19 pandemic. J Econom 2023; 235:166-179. [PMID: 36568314 PMCID: PMC9759674 DOI: 10.1016/j.jeconom.2022.03.001] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/02/2021] [Revised: 01/31/2022] [Accepted: 03/04/2022] [Indexed: 06/17/2023]
Abstract
Mediation analysis draws increasing attention in many research areas such as economics, finance and social sciences. In this paper, we propose new statistical inference procedures for high dimensional mediation models, in which both the outcome model and the mediator model are linear with high dimensional mediators. Traditional procedures for mediation analysis cannot be used to make statistical inference for high dimensional linear mediation models due to high-dimensionality of the mediators. We propose an estimation procedure for the indirect effects of the models via a partially penalized least squares method, and further establish its theoretical properties. We further develop a partially penalized Wald test on the indirect effects, and prove that the proposed test has a χ 2 limiting null distribution. We also propose an F -type test for direct effects and show that the proposed test asymptotically follows a χ 2 -distribution under null hypothesis and a noncentral χ 2 -distribution under local alternatives. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed tests and compare their performance with existing ones. We further apply the newly proposed statistical inference procedures to study stock reaction to COVID-19 pandemic via an empirical analysis of studying the mediation effects of financial metrics that bridge company's sector and stock return.
Collapse
Affiliation(s)
- Xu Guo
- School of Statistics, Beijing Normal University, Beijing, 100875, China
| | - Runze Li
- Department of Statistics, The Pennsylvania State University, University Park, PA 16802, USA
| | - Jingyuan Liu
- MOE Key Laboratory of Econometrics, Department of Statistics, School of Economics, Wang Yanan Institute for Studies in Economics and Fujian Key Lab of Statistics, Xiamen University, Xiamen, 361000, China
| | - Mudong Zeng
- Department of Statistics, The Pennsylvania State University, University Park, PA 16802, USA
| |
Collapse
|
4
|
Gu J, Fan Y, Yin G. Omnibus test for restricted mean survival time based on influence function. Stat Methods Med Res 2023; 32:1082-1099. [PMID: 37015346 PMCID: PMC10331519 DOI: 10.1177/09622802231158735] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/06/2023]
Abstract
The restricted mean survival time (RMST), which evaluates the expected survival time up to a pre-specified time point τ , has been widely used to summarize the survival distribution due to its robustness and straightforward interpretation. In comparative studies with time-to-event data, the RMST-based test has been utilized as an alternative to the classic log-rank test because the power of the log-rank test deteriorates when the proportional hazards assumption is violated. To overcome the challenge of selecting an appropriate time point τ , we develop an RMST-based omnibus Wald test to detect the survival difference between two groups throughout the study follow-up period. Treating a vector of RMSTs at multiple quantile-based time points as a statistical functional, we construct a Wald χ 2 test statistic and derive its asymptotic distribution using the influence function. We further propose a new procedure based on the influence function to estimate the asymptotic covariance matrix in contrast to the usual bootstrap method. Simulations under different scenarios validate the size of our RMST-based omnibus test and demonstrate its advantage over the existing tests in power, especially when the true survival functions cross within the study follow-up period. For illustration, the proposed test is applied to two real datasets, which demonstrate its power and applicability in various situations.
Collapse
Affiliation(s)
- Jiaqi Gu
- Department of Neurology and Neurological Sciences, Stanford University, Palo Alto, CA, USA
| | - Yiwei Fan
- School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China
| | - Guosheng Yin
- Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong, China
| |
Collapse
|
5
|
Parvin R. A Statistical Investigation into the COVID-19 Outbreak Spread. Environ Health Insights 2023; 17:11786302221147455. [PMID: 36699646 PMCID: PMC9868487 DOI: 10.1177/11786302221147455] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/14/2022] [Accepted: 12/08/2022] [Indexed: 06/17/2023]
Abstract
OBJECTIVE Coronavirus-19 (COVID-19) outbreaks have been reported in a range of climates worldwide, including Bangladesh. There is less evidence of a link between the COVID-19 pandemic and climatic variables. This research article's purpose is to examine the relationship between COVID-19 outbreaks and climatic factors in Dhaka, Bangladesh. METHODS The daily time series COVID-19 data used in this study span from May 1, 2020, to April 14, 2021, for the study area, Dhaka, Bangladesh. The Climatic factors included in this study were average temperature, particulate matter ( P M 2 . 5 ), humidity, carbon emissions, and wind speed within the same timeframe and location. The strength and direction of the relationship between meteorological factors and COVID-19 positive cases are examined using the Spearman correlation. This study examines the asymmetric effect of climatic factors on the COVID-19 pandemic in Dhaka, Bangladesh, using the Nonlinear Autoregressive Distributed Lag (NARDL) model. RESULTS COVID-19 widespread has a substantial positive association with wind speed (r = .781), temperature (r = .599), and carbon emissions (r = .309), whereas P M 2 . 5 (r = -.178) has a negative relationship at the 1% level of significance. Furthermore, with a 1% change in temperature, the incidence of COVID-19 increased by 1.23% in the short run and 1.53% in the long run, with the remaining variables remaining constant. Similarly, in the short-term, humidity was not significantly related to the COVID-19 pandemic. However, in the long term, it increased 1.13% because of a 1% change in humidity. The changes in PM2.5 level and wind speed are significantly associated with COVID-19 new cases after adjusting population density and the human development index.
Collapse
Affiliation(s)
- Rehana Parvin
- Rehana Parvin, Department of Statistics, International University of Business Agriculture and Technology (IUBAT), 4 Embankment Drive Road, Sector 10, Uttara, Dhaka, Bangladesh.
| |
Collapse
|
6
|
Yusuf A, Mohd S. Nonlinear effects of public debt on economic growth in Nigeria. SN Bus Econ 2023; 3:88. [PMID: 36919014 PMCID: PMC9998008 DOI: 10.1007/s43546-023-00468-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2022] [Accepted: 02/26/2023] [Indexed: 03/11/2023]
Abstract
The COVID-19 pandemic induced governments all over the world to momentarily accumulate higher levels of public debt in order to invest in deficit spending and social protection programs to tackle the anticipated economic slump. The Nigerian government has borrowed heavily from domestic and foreign sources in order to resolve the growing budget deficits and return the economy to a sustainable growth trajectory. Previous studies frequently made the incorrect assumption that the relationship between public debt and growth is linear and symmetric, leading to empirical results that is frequently disputed and imprecise. This study's main objective is to examine the asymmetric impact of public debt on economic growth in Nigeria from 1980 to 2020 using the Nonlinear Autoregressive Distributed Lag method. Empirical evidence indicated that external debt have a significant positive and symmetric impact on economic growth in the long and short run, while debt service payment supporting the debt overhang hypothesis activated a symmetric effect that stifle growth. Domestic debt retarded growth asymmetrically in the short term and linearly over the long term. Foreign reserve holding, on the other hand, had an asymmetric long-run influence and a symmetric short-run impact on growth motivation. To mitigate the negative effects of unsustainable public debt, the study advocated for fiscal reforms that effectively reduce deficit financing to keep the level of government debt low and be able to respond robustly to an economic shock, improve domestic revenue generation and infrastructure spending, and strengthen governance practices and institutions.
Collapse
Affiliation(s)
- Abdulkarim Yusuf
- Department of Economics, Nigeria Police Academy, Kano Maiduguri Road, Wudil, Kano Nigeria
| | - Saidatulakmal Mohd
- Department of Economics, School of Social Sciences, Universiti Sains Malaysia (USM), Gelugor, Malaysia
| |
Collapse
|
7
|
Liu Y, Wu L, Tang G, Wahed AS. A series of two-sample non-parametric tests for quantile residual life time. Lifetime Data Anal 2023; 29:234-252. [PMID: 36593432 DOI: 10.1007/s10985-022-09580-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Accepted: 09/23/2022] [Indexed: 06/17/2023]
Abstract
Quantile residual lifetime (QRL) is of significant interest in many clinical studies as an easily interpretable quantity compared to other summary measures of survival distributions. In cancer or other chronic diseases, treatments are often compared based on the distributions or quantiles of the residual lifetime. Thus a common problem of interest is to test the equality of the QRL between two populations. In this paper, we propose two classes of tests to compare two QRLs; one class is based on the difference between two estimated QRLs, and the other is based on the estimating function of the QRL, where the estimated QRL from one sample is plugged into the QRL-estimating-function of the other sample. We outline the asymptotic properties of these test statistics. Simulation studies demonstrate that the proposed tests produced Type I errors closer to the nominal level and are superior to some existing tests based on both Type I error and power. Our proposed test statistics are also computationally less intensive and more straightforward compared to tests based on the confidence intervals. We applied the proposed methods to a randomized multicenter phase III trial for breast cancer patients.
Collapse
Affiliation(s)
- Yimeng Liu
- Department of Biostatistics, University of Pittsburgh, 130 Desoto street, Pittsburgh, PA, 15261, USA.
| | - Liwen Wu
- Department of Biostatistics, University of Pittsburgh, 130 Desoto street, Pittsburgh, PA, 15261, USA
| | - Gong Tang
- Department of Biostatistics, University of Pittsburgh, 130 Desoto street, Pittsburgh, PA, 15261, USA
| | - Abdus S Wahed
- Department of Biostatistics, University of Pittsburgh, 130 Desoto street, Pittsburgh, PA, 15261, USA
| |
Collapse
|
8
|
Phiri J, Malec K, Sakala A, Appiah-Kubi SNK, Činčera P, Maitah M, Gebeltová Z, Otekhile CA. Services as a Determinant of Botswana's Economic Sustainability. Int J Environ Res Public Health 2022; 19:15401. [PMID: 36430118 PMCID: PMC9690671 DOI: 10.3390/ijerph192215401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/21/2022] [Revised: 11/06/2022] [Accepted: 11/18/2022] [Indexed: 06/16/2023]
Abstract
In 2015, the services sector contributed about 58 percent to the gross domestic product (GDP) in Sub-Saharan Africa (SSA), which was a significant increase from the 47.6 percent observed in 2005, and a shift from the mining, agriculture, and manufacturing sector. This increase calls to support services as the catalyst for sustained economic development as indicated by the structural transformation and modernization theories. The main objective of this paper was to examine the relationship between and the impact of services on the economic development in Botswana and make recommendations on how Botswana can apply well-directed policies to improve its services sector and diversify its impact on other sectors and GDP, making it less reliant on mining which is vulnerable to price volatilities. The paper applied econometric modeling and results of the Autoregressive-Distributed Lag (ARDL) Bounds test for cointegration indicate that services and other industries services, agriculture, industry, mining, and investment impact GDP over the short and long run. These variables impacted GDP and converged to equilibrium at the speed of 46.89 percent, with a percent change in services in the short and long run impacting GDP by 0.328 and 0.241 percentages, respectively, and the outcome of the Wald test indicated causality from services to GDP growth. The services sectors have contributed over 40 percent to the country's GDP from 1995 to the present, though the sectors have not gone without challenges with limitations such as limited infrastructure development; poverty and inequality; unemployment of over 20 percent; disease, which has dampened productivity; and lack of proper governance and accountability, which has created a habitat for an increase in cases of corruption in state and private entities. The findings of the study with the lessons learned from other studies with similar findings recommend that the government of Botswana should formulate suitable policies and strategies for services diversification. This is by expanding the market for the sector in areas such as tourism that were impacted by the COVID-19 pandemic, escalating investments by instituting strategies to attract and grow domestic and foreign investments, and improve on management of institutions and resources.
Collapse
Affiliation(s)
- Joseph Phiri
- Department of Economics, Faculty of Economics and Management, Czech University of Life Sciences, 16500 Prague, Czech Republic
| | - Karel Malec
- Department of Economics, Faculty of Economics and Management, Czech University of Life Sciences, 16500 Prague, Czech Republic
| | - Aubrey Sakala
- Department of Economics, School of Humanities and Social Sciences, Copperbelt University, Jambo Drive, Riverside, Kitwe P.O. Box 21692, Zambia
| | - Seth Nana Kwame Appiah-Kubi
- Department of Economics, Faculty of Economics and Management, Czech University of Life Sciences, 16500 Prague, Czech Republic
| | - Pavel Činčera
- BEZK, z.s. Letohradská 669/17170 00 Praha 7, 17000 Prague, Czech Republic
| | - Mansoor Maitah
- Department of Economics, Faculty of Economics and Management, Czech University of Life Sciences, 16500 Prague, Czech Republic
| | - Zdeňka Gebeltová
- Department of Economics, Faculty of Economics and Management, Czech University of Life Sciences, 16500 Prague, Czech Republic
| | - Cathy-Austin Otekhile
- Department of Management and Marketing, Faculty of Economics and Management, Tomas Bata University, 76001 Zlin, Czech Republic
| |
Collapse
|
9
|
Ye P, Qiao X, Tang W, Wang C, He H. Testing latent class of subjects with structural zeros in negative binomial models with applications to gut microbiome data. Stat Methods Med Res 2022; 31:2237-2254. [PMID: 35899309 DOI: 10.1177/09622802221115881] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Human microbiome research has become a hot-spot in health and medical research in the past decade due to the rapid development of modern high-throughput. Typical data in a microbiome study consisting of the operational taxonomic unit counts may have over-dispersion and/or structural zero issues. In such cases, negative binomial models can be applied to address the over-dispersion issue, while zero-inflated negative binomial models can be applied to address both issues. In practice, it is essential to know if there is zero-inflation in the data before applying negative binomial or zero-inflated negative binomial models because zero-inflated negative binomial models may be unnecessarily complex and difficult to interpret, or may even suffer from convergence issues if there is no zero-inflation in the data. On the other hand, negative binomial models may yield invalid inferences if the data does exhibit excessive zeros. In this paper, we develop a new test for detecting zero-inflation resulting from a latent class of subjects with structural zeros in a negative binomial regression model by directly comparing the amount of observed zeros with what would be expected under the negative binomial regression model. A closed form of the test statistic as well as its asymptotic properties are derived based on estimating equations. Intensive simulation studies are conducted to investigate the performance of the new test and compare it with the classical Wald, likelihood ratio, and score tests. The tests are also applied to human gut microbiome data to test latent class in microbial genera.
Collapse
Affiliation(s)
- Peng Ye
- School of Statistics, 12630University of International Business and Economics, Beijing, China
- Department of Epidemiology, 25812School of Public Health and Tropical Medicine, Tulane University, New Orleans, LA, USA
| | - Xinhui Qiao
- School of Statistics, 12630University of International Business and Economics, Beijing, China
| | - Wan Tang
- Department of Biostatistics and Data Science, School of Public Health and Tropical Medicine, Tulane University, New Orleans, LA, USA
| | - Chunyi Wang
- Ruijin Hospital, School of Medicine, Shanghai Jiao Tong University, Shanghai, China
| | - Hua He
- Department of Epidemiology, 25812School of Public Health and Tropical Medicine, Tulane University, New Orleans, LA, USA
| |
Collapse
|
10
|
Gnona KM, Stewart WCL. Revisiting the Wald Test in Small Case-Control Studies With a Skewed Covariate. Am J Epidemiol 2022; 191:1508-1518. [PMID: 35355063 DOI: 10.1093/aje/kwac058] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2021] [Revised: 02/27/2022] [Accepted: 03/24/2022] [Indexed: 01/28/2023] Open
Abstract
The Wald test is routinely used in case-control studies to test for association between a covariate and disease. However, when the evidence for association is high, the Wald test tends to inflate small P values as a result of the Hauck-Donner effect (HDE). Here, we investigate the HDE in the context of genetic burden, both with and without additional covariates. First, we examine the burden-based P values in the absence of association using whole-exome sequence data from 1000 Genomes Project reference samples (n = 54) and selected preterm infants with neonatal complications (n = 74). Our careful analysis of the burden-based P values shows that the HDE is present and that the cause of the HDE in this setting is likely a natural extension of the well-known cause of the HDE in 2 × 2 contingency tables. Second, in a reanalysis of real data, we find that the permutation test provides increased power over the Wald, Firth, and likelihood ratio tests, which agrees with our intuition since the permutation test is valid for any sample size and since it does not suffer from the HDE. Therefore, we propose a powerful and computationally efficient permutation-based approach for the analysis and reanalysis of small case-control association studies.
Collapse
|
11
|
Li M, Wang K, Maity A, Staicu AM. Inference in Functional Linear Quantile Regression. J MULTIVARIATE ANAL 2022; 190:104985. [PMID: 35370319 PMCID: PMC8975129 DOI: 10.1016/j.jmva.2022.104985] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this paper, we study statistical inference in functional quantile regression for scalar response and a functional covariate. Specifically, we consider a functional linear quantile regression model where the effect of the covariate on the quantile of the response is modeled through the inner product between the functional covariate and an unknown smooth regression parameter function that varies with the level of quantile. The objective is to test that the regression parameter is constant across several quantile levels of interest. The parameter function is estimated by combining ideas from functional principal component analysis and quantile regression. An adjusted Wald testing procedure is proposed for this hypothesis of interest, and its chi-square asymptotic null distribution is derived. The testing procedure is investigated numerically in simulations involving sparse and noisy functional covariates and in a capital bike share data application. The proposed approach is easy to implement and the R code is published online at https://github.com/xylimeng/fQR-testing.
Collapse
Affiliation(s)
- Meng Li
- Department of Statistics, Rice University, Houston, TX
| | | | - Arnab Maity
- Department of Statistics, North Carolina State University, Raleigh, NC
| | - Ana-Maria Staicu
- Department of Statistics, North Carolina State University, Raleigh, NC
| |
Collapse
|
12
|
Xu K, Deng Y, Yu Z. Distributed Target Detection in Unknown Interference. Sensors (Basel) 2022; 22:2430. [PMID: 35408044 PMCID: PMC9002535 DOI: 10.3390/s22072430] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Revised: 03/11/2022] [Accepted: 03/17/2022] [Indexed: 06/14/2023]
Abstract
Interference can degrade the detection performance of a radar system. To overcome the difficulty of target detection in unknown interference, in this paper we model the interference belonging to a subspace orthogonal to the signal subspace. We design three effective detectors for distributed target detection in unknown interference by adopting the criteria of the generalized likelihood ratio test (GLRT), the Rao test, and the Wald test. At the stage of performance evaluation, we illustrate the detection performance of the proposed detectors in the presence of completely unknown interference (not constrained to lie in the above subspace). Numerical examples indicate that the proposed GLRT and Wald test can provide better detection performance than the existing detectors.
Collapse
Affiliation(s)
- Kaiming Xu
- The Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China; (Y.D.); (Z.Y.)
- The School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 101408, China
| | - Yunkai Deng
- The Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China; (Y.D.); (Z.Y.)
- The School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 101408, China
| | - Zhongjun Yu
- The Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China; (Y.D.); (Z.Y.)
- The School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 101408, China
| |
Collapse
|
13
|
Abstract
BACKGROUND Advancements in statistical methods and sequencing technology have led to numerous novel discoveries in human genetics in the past two decades. Among phenotypes of interest, most attention has been given to studying genetic associations with continuous or binary traits. Efficient statistical methods have been proposed and are available for both types of traits under different study designs. However, for multinomial categorical traits in related samples, there is a lack of efficient statistical methods and software. RESULTS We propose an efficient score test to analyze a multinomial trait in family samples, in the context of genome-wide association/sequencing studies. An alternative Wald statistic is also proposed. We also extend the methodology to be applicable to ordinal traits. We performed extensive simulation studies to evaluate the type-I error of the score test, Wald test compared to the multinomial logistic regression for unrelated samples, under different allele frequency and study designs. We also evaluate the power of these methods. Results show that both the score and Wald tests have a well-controlled type-I error rate, but the multinomial logistic regression has an inflated type-I error rate when applied to family samples. We illustrated the application of the score test with an application to the Framingham Heart Study to uncover genetic variants associated with diabesity, a multi-category phenotype. CONCLUSION Both proposed tests have correct type-I error rate and similar power. However, because the Wald statistics rely on computer-intensive estimation, it is less efficient than the score test in terms of applications to large-scale genetic association studies. We provide computer implementation for both multinomial and ordinal traits.
Collapse
Affiliation(s)
- Shuai Wang
- Pfizer Inc, Global Product Development, Groton, CT, 06340, USA.
| | - James B Meigs
- Division of General Internal Medicine, Massachusetts General Hospital, Boston, MA, 02114, USA.,Department of Medicine, Harvard Medical School, Boston, MA, 02115, USA.,Programs in Metabolism and Medical & Population Genetics, Broad Institute of MIT and Harvard, Cambridge, MA, 02142, USA
| | - Josée Dupuis
- Department of Biostatistics, Boston University School of Public Health, Boston, MA, 02118, USA
| |
Collapse
|
14
|
Nugent JR, Kleinman KP. Type I error control for cluster randomized trials under varying small sample structures. BMC Med Res Methodol 2021; 21:65. [PMID: 33812367 PMCID: PMC8019504 DOI: 10.1186/s12874-021-01236-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2019] [Accepted: 02/23/2021] [Indexed: 11/10/2022] Open
Abstract
Background Linear mixed models (LMM) are a common approach to analyzing data from cluster randomized trials (CRTs). Inference on parameters can be performed via Wald tests or likelihood ratio tests (LRT), but both approaches may give incorrect Type I error rates in common finite sample settings. The impact of different combinations of cluster size, number of clusters, intraclass correlation coefficient (ICC), and analysis approach on Type I error rates has not been well studied. Reviews of published CRTs find that small sample sizes are not uncommon, so the performance of different inferential approaches in these settings can guide data analysts to the best choices. Methods Using a random-intercept LMM stucture, we use simulations to study Type I error rates with the LRT and Wald test with different degrees of freedom (DF) choices across different combinations of cluster size, number of clusters, and ICC. Results Our simulations show that the LRT can be anti-conservative when the ICC is large and the number of clusters is small, with the effect most pronouced when the cluster size is relatively large. Wald tests with the between-within DF method or the Satterthwaite DF approximation maintain Type I error control at the stated level, though they are conservative when the number of clusters, the cluster size, and the ICC are small. Conclusions Depending on the structure of the CRT, analysts should choose a hypothesis testing approach that will maintain the appropriate Type I error rate for their data. Wald tests with the Satterthwaite DF approximation work well in many circumstances, but in other cases the LRT may have Type I error rates closer to the nominal level.
Collapse
Affiliation(s)
- Joshua R Nugent
- Department of Biostatistics and Epidemiology, School of Public Health and Health Sciences, University of Massachusetts Amherst, 715 North Pleasant Street, Amherst, 01003, Massachusetts, USA
| | - Ken P Kleinman
- Department of Biostatistics and Epidemiology, School of Public Health and Health Sciences, University of Massachusetts Amherst, 715 North Pleasant Street, Amherst, 01003, Massachusetts, USA.
| |
Collapse
|
15
|
Zhang C, Wang X, Chen M, Wang T. A comparison of hypothesis tests for homogeneity in meta-analysis with focus on rare binary events. Res Synth Methods 2021; 12:408-428. [PMID: 34231330 DOI: 10.1002/jrsm.1484] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2019] [Revised: 01/01/2021] [Accepted: 02/03/2021] [Indexed: 11/06/2022]
Abstract
Analysis of rare binary events is an important problem for biomedical researchers. Due to the sparsity of events in such problems, meta-analysis that integrates information across multiple studies can be applied to increase the efficiency of statistical inference. Although it is critical to examine whether the effect sizes are homogeneous across all studies, a comprehensive review of homogeneity tests has been lacking, and in particular, no attention has been paid to infrequent dichotomous outcomes. We systematically review statistical methods for homogeneity testing. By conducting an extensive simulation analysis and two case studies, we examine the performance of 30 tests in meta-analysis of rare binary outcomes. When using log-odds ratio as the association measure, our simulation results suggest that there is no uniform winner. However, we recommend the test proposed by Kulinskaya and Dollinger (BMC Med Res Methodol, 2015, 15), which uses a gamma distribution to approximate the null distribution, for its generally good performance; for very rare events coupled with small within-study sample sizes, in addition to the Kulinskaya-Dollinger test, we further recommend the conditional score test based on the random-effects hypergeometric model proposed by Liang and Self (Biometrika, 1985, 72:353-358). One should be cautious about the use of the Wald tests, the Lipsitz tests (Biometrics, 1998, 54:148-160), and tests proposed by Bhaumik et al (J Am Stat Assoc, 2012, 107:555-567).
Collapse
Affiliation(s)
- Chiyu Zhang
- Department of Statistical Science, Southern Methodist University, Dallas, Texas, USA
| | - Xinlei Wang
- Department of Statistical Science, Southern Methodist University, Dallas, Texas, USA
| | - Min Chen
- Department of Mathematical Sciences, University of Texas at Dallas, Richardson, Texas, USA.,Department of Population and Data Sciences, UT Southwestern Medical Center, Dallas, Texas, USA
| | - Tao Wang
- Department of Population and Data Sciences, UT Southwestern Medical Center, Dallas, Texas, USA
| |
Collapse
|
16
|
Abstract
This study proposes a multiple-group cognitive diagnosis model to account for the fact that students in different groups may use distinct attributes or use the same attributes but in different manners (e.g., conjunctive, disjunctive, and compensatory) to solve problems. Based on the proposed model, this study systematically investigates the performance of the likelihood ratio (LR) test and Wald test in detecting differential item functioning (DIF). A forward anchor item search procedure was also proposed to identify a set of anchor items with invariant item parameters across groups. Results showed that the LR and Wald tests with the forward anchor item search algorithm produced better calibrated Type I error rates than the ordinary LR and Wald tests, especially when items were of low quality. A set of real data were also analyzed to illustrate the use of these DIF detection procedures.
Collapse
Affiliation(s)
- Wenchao Ma
- The University of Alabama, Tuscaloosa,
USA
| | | | | |
Collapse
|
17
|
Zou Y, Peng Z, Cornell J, Ye P, He H. A new statistical test for latent class in censored data due to detection limit. Stat Med 2020; 40:779-798. [PMID: 33159355 DOI: 10.1002/sim.8802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2020] [Revised: 08/30/2020] [Accepted: 10/20/2020] [Indexed: 11/10/2022]
Abstract
Biomarkers of interest in urine, serum, or other biological matrices often have an assay limit of detection. When concentration levels of the biomarkers for some subjects fall below the limit, the measures for those subjects are censored. Censored data due to detection limits are very common in public health and medical research. If censored data from a single exposure group follow a normal distribution or follow a normal distribution after some transformations, Tobit regression models can be applied. Given a Tobit regression model and a detection limit, the proportion of censored data can be determined. However, in practice, it is common that the data can exhibit excessive censored observations beyond what would be expected under a Tobit regression model. One common cause is heterogeneity of the study population, that is, there exists a subpopulation who lack such biomarkers and their values are always under the detection limit, and hence are censored. In this article, we develop a new test for testing such latent class under a Tobit regression model by directly comparing the amount of observed censored data with what would be expected under the Tobit regression model. A closed form of the test statistic as well as its asymptotic properties are derived based on estimating equations. Simulation studies are conducted to investigate the performance of the new test and compare the new one with the existing ones including the Wald test, likelihood ratio test, and score test. Two real data examples are also included for illustrative purpose.
Collapse
Affiliation(s)
- Yuhan Zou
- School of Mathematics and Statistics, Southwest University, Chongqing, China
| | - Zuoxiang Peng
- School of Mathematics and Statistics, Southwest University, Chongqing, China
| | - Jerry Cornell
- Department of Biostatistics and Data Science, Tulane University School of Public Health and Tropical Medicine, New Orleans, Louisiana, USA
| | - Peng Ye
- School of Statistics, University of International Business and Economics, Beijing, China
| | - Hua He
- Department of Epidemiology, Tulane University School of Public Health and Tropical Medicine, New Orleans, Louisiana, USA
| |
Collapse
|
18
|
Pavlović DM, Guillaume BRL, Towlson EK, Kuek NMY, Afyouni S, Vértes PE, Yeo BTT, Bullmore ET, Nichols TE. Multi-subject Stochastic Blockmodels for adaptive analysis of individual differences in human brain network cluster structure. Neuroimage 2020; 220:116611. [PMID: 32058004 DOI: 10.1016/j.neuroimage.2020.116611] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2019] [Revised: 01/31/2020] [Accepted: 02/04/2020] [Indexed: 12/12/2022] Open
Abstract
There is considerable interest in elucidating the cluster structure of brain networks in terms of modules, blocks or clusters of similar nodes. However, it is currently challenging to handle data on multiple subjects since most of the existing methods are applicable only on a subject-by-subject basis or for analysis of an average group network. The main limitation of per-subject models is that there is no obvious way to combine the results for group comparisons, and of group-averaged models that they do not reflect the variability between subjects. Here, we propose two new extensions of the classical Stochastic Blockmodel (SBM) that use a mixture model to estimate blocks or clusters of connected nodes, combined with a regression model to capture the effects of subject-level covariates on individual differences in cluster structure. The proposed Multi-Subject Stochastic Blockmodels (MS-SBMs) can flexibly account for between-subject variability in terms of homogeneous or heterogeneous covariate effects on connectivity using subject demographics such as age or diagnostic status. Using synthetic data, representing a range of block sizes and cluster structures, we investigate the accuracy of the estimated MS-SBM parameters as well as the validity of inference procedures based on the Wald, likelihood ratio and permutation tests. We show that the proposed multi-subject SBMs recover the true cluster structure of synthetic networks more accurately and adaptively than standard methods for modular decomposition (i.e. the Fast Louvain and Newman Spectral algorithms). Permutation tests of MS-SBM parameters were more robustly valid for statistical inference and Type I error control than tests based on standard asymptotic assumptions. Applied to analysis of multi-subject resting-state fMRI networks (13 healthy volunteers; 12 people with schizophrenia; n=268 brain regions), we show that Heterogeneous Stochastic Blockmodel (Het-SBM) identifies a range of network topologies simultaneously, including modular and core structures.
Collapse
|
19
|
Abstract
Measures of substance concentration in urine, serum or other biological matrices often have an assay limit of detection. When concentration levels fall below the limit, the exact measures cannot be obtained. Instead, the measures are censored as only partial information that the levels are under the limit is known. Assuming the concentration levels are from a single population with a normal distribution or follow a normal distribution after some transformation, Tobit regression models, or censored normal regression models, are the standard approach for analyzing such data. However, in practice, it is often the case that the data can exhibit more censored observations than what would be expected under the Tobit regression models. One common cause is the heterogeneity of the study population, caused by the existence of a latent group of subjects who lack the substance measured. For such subjects, the measurements will always be under the limit. If a censored normal regression model is appropriate for modeling the subjects with the substance, the whole population follows a mixture of a censored normal regression model and a degenerate distribution of the latent class. While there are some studies on such mixture models, a fundamental question about testing whether such mixture modeling is necessary, i.e. whether such a latent class exists, has not been studied yet. In this paper, three tests including Wald test, likelihood ratio test and score test are developed for testing the existence of such latent class. Simulation studies are conducted to evaluate the performance of the tests, and two real data examples are employed to illustrate the tests.
Collapse
Affiliation(s)
- Hua He
- Department of Epidemiology, Tulane University School of Public Health and Tropical Medicine, New Orleans, LA, USA
| | - Wan Tang
- Department of Biostatistics and Data Science, Tulane University School of Public Health and Tropical Medicine, New Orleans, LA, USA
| | - Tanika Kelly
- Department of Epidemiology, Tulane University School of Public Health and Tropical Medicine, New Orleans, LA, USA
| | - Shengxu Li
- Children’s Minnesota Research Institute, Children’s Hospitals and Clinics of Minnesota Medicine, Minneapolis, MN, USA
| | - Jiang He
- Department of Epidemiology, Tulane University School of Public Health and Tropical Medicine, New Orleans, LA, USA
| |
Collapse
|
20
|
Lee CY, Chen X, Lam KF. Testing for change-point in the covariate effects based on the Cox regression model. Stat Med 2020; 39:1473-1488. [PMID: 32034921 DOI: 10.1002/sim.8491] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2019] [Revised: 01/13/2020] [Accepted: 01/14/2020] [Indexed: 11/11/2022]
Abstract
Models with change-point in covariates have wide applications in cancer research with the response being the time to a certain event. A Cox model with change-point in covariate is considered at which the pattern of the change-point effects can be flexibly specified. To test for the existence of the change-point effects, three statistical tests, namely, the maximal score, maximal normalized score, and maximal Wald tests are proposed. The asymptotic properties of the test statistics are established. Monte Carlo approaches to simulate the critical values are suggested. A large-scale simulation study is carried out to study the finite sample performance of the proposed test statistics under the null hypothesis of no change-points and various alternative hypothesis settings. Each of the proposed methods provides a natural estimate for the location of the change-point, but it is found that the performance of the maximal score test can be sensitive to the true location of the change-point in some cases, while the performance of the maximal Wald test is very satisfactory in general even in cases with moderate sample size. For illustration, the proposed methods are applied to two medical datasets concerning patients with primary biliary cirrhosis and breast cancer, respectively.
Collapse
Affiliation(s)
- Chun Yin Lee
- Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam, Hong Kong
| | - Xuerong Chen
- Centre of Statistical Research, Southwestern University of Finance and Economics, Chengdu, China
| | - Kwok Fai Lam
- Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam, Hong Kong.,Centre for Quantitative Medicine, Duke-NUS Medical School, Singapore
| |
Collapse
|
21
|
Ma W, de la Torre J. An empirical Q-matrix validation method for the sequential generalized DINA model. Br J Math Stat Psychol 2020; 73:142-163. [PMID: 30723890 DOI: 10.1111/bmsp.12156] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2017] [Revised: 11/26/2018] [Indexed: 06/09/2023]
Abstract
As a core component of most cognitive diagnosis models, the Q-matrix, or item and attribute association matrix, is typically developed by domain experts, and tends to be subjective. It is critical to validate the Q-matrix empirically because a misspecified Q-matrix could result in erroneous attribute estimation. Most existing Q-matrix validation procedures are developed for dichotomous responses. However, in this paper, we propose a method to empirically detect and correct the misspecifications in the Q-matrix for graded response data based on the sequential generalized deterministic inputs, noisy 'and' gate (G-DINA) model. The proposed Q-matrix validation procedure is implemented in a stepwise manner based on the Wald test and an effect size measure. The feasibility of the proposed method is examined using simulation studies. Also, a set of data from the Trends in International Mathematics and Science Study (TIMSS) 2011 mathematics assessment is analysed for illustration.
Collapse
Affiliation(s)
- Wenchao Ma
- Department of Educational Studies in Psychology, Research Methodology and Counseling, University of Alabama, Tuscaloosa, Alabama, USA
| | | |
Collapse
|
22
|
Xing X, Liu M, Ma P, Zhong W. Minimax Nonparametric Parallelism Test. J Mach Learn Res 2020; 21:94. [PMID: 38737400 PMCID: PMC11086968] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Figures] [Subscribe] [Scholar Register] [Indexed: 05/14/2024]
Abstract
Testing the hypothesis of parallelism is a fundamental statistical problem arising from many applied sciences. In this paper, we develop a nonparametric parallelism test for inferring whether the trends are parallel in treatment and control groups. In particular, the proposed nonparametric parallelism test is a Wald type test based on a smoothing spline ANOVA (SSANOVA) model which can characterize the complex patterns of the data. We derive that the asymptotic null distribution of the test statistic is a Chi-square distribution, unveiling a new version of Wilks phenomenon. Notably, we establish the minimax sharp lower bound of the distinguishable rate for the nonparametric parallelism test by using the information theory, and further prove that the proposed test is minimax optimal. Simulation studies are conducted to investigate the empirical performance of the proposed test. DNA methylation and neuroimaging studies are presented to illustrate potential applications of the test. The software is available at https://github.com/BioAlgs/Parallelism.
Collapse
Affiliation(s)
- Xin Xing
- Department of Statistics, Virginia Tech, Blacksburg, VA, 24061, USA
| | - Meimei Liu
- Department of Statistics, Virginia Tech, Blacksburg, VA, 24061, USA
| | - Ping Ma
- Department of Statistics, University of Georgia, Athens, GA 30601, USA
| | - Wenxuan Zhong
- Department of Statistics, University of Georgia, Athens, GA 30601, USA
| |
Collapse
|
23
|
Zhang YM. Genome-Wide Composite Interval Mapping (GCIM) of Expressional Quantitative Trait Loci in Backcross Population. Methods Mol Biol 2020; 2082:63-71. [PMID: 31849008 DOI: 10.1007/978-1-0716-0026-9_5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
One of the most remarkable findings in expressional quantitative trait locus (eQTL) mapping is that trans (distal) eQTL has small effect. The widely used approaches have a low power in the detection of small-effect eQTL. To overcome this issue, we integrate polygenic background control with multi-locus genetic model to develop genome-wide composite interval mapping (GCIM). This chapter covers the GCIM procedure in a backcross or doubled haploid populations. We describe the genetic model, parameter estimation, multi-locus genetic model, hypothesis tests, and software. Finally, some issues related to the GCIM method are discussed.
Collapse
|
24
|
Eckert M, Vach W. On the use of comparison regions in visualizing stochastic uncertainty in some two-parameter estimation problems. Biom J 2019; 62:598-609. [PMID: 31661558 DOI: 10.1002/bimj.201800232] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2018] [Revised: 07/17/2019] [Accepted: 07/29/2019] [Indexed: 11/08/2022]
Abstract
When considering simultaneous inference for two parameters, it is very common to visualize stochastic uncertainty by plotting two-dimensional confidence regions. This allows us to test post hoc null hypotheses about a single point in a simple manner. However, in some applications the interest is not in rejecting hypotheses on single points, but in demonstrating evidence for the two parameters to be in a convex subset of the parameter space. The specific convex subset to be considered may vary from one post hoc analysis to another. Then it is of interest to have a visualization allowing to perform corresponding analyses. We suggest comparison regions as a simple tool for this task.
Collapse
Affiliation(s)
- Maren Eckert
- Institute of Medical Biometry and Statistics, Section of Health Care Research and Rehabilitation Research, Faculty of Medicine and Medical Center, University of Freiburg, Freiburg, Germany
| | - Werner Vach
- Department of Orthopaedics and Traumatology, University Hospital Basel, Basel, Switzerland
| |
Collapse
|
25
|
Abstract
This paper is concerned with testing linear hypotheses in high-dimensional generalized linear models. To deal with linear hypotheses, we first propose constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are χ2 distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow non-central χ2 distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to ∞ at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures.
Collapse
Affiliation(s)
- Chengchun Shi
- Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, USA
| | - Rui Song
- Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, USA
| | - Zhao Chen
- Department of Statistics, and The Methodology Center, the Pennsylvania State University, University Park, PA 16802-2111, USA
| | - Runze Li
- Department of Statistics, and The Methodology Center, the Pennsylvania State University, University Park, PA 16802-2111, USA
| |
Collapse
|
26
|
Ren Y, Wang C, Shen M, Tsong Y. Non-inferiority tests for binary endpoints with variable margins. J Biopharm Stat 2019; 29:822-833. [PMID: 31486705 DOI: 10.1080/10543406.2019.1657136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Abstract
Non-inferiority comparison between binary response rates of test and reference treatments is often performed in clinical studies. The most common approach to assess non-inferiority is to compare the difference between the estimated response rates with some margin. Previous methods use a variety of margins, including fixed margin, step-wise constant margin, and piece-wise smooth margin, where the latter two are functions of the reference response rate. The fixed margin approach assumes that the margin can be determined from historical trials with the consistent difference between the reference treatment and placebo, which may not be available. The step-wise constant margin approach suffers discontinuity in the power function which can cause trouble in sample size determination. Furthermore, many methods ignore the variability in margins dependent on the estimated reference response rate, leading to poor type I error control and power function approximation. In this study, we propose a variable margin approach to overcome the difficulties in fixed and step-wise constant margin approaches. We discuss several test statistics and evaluate their performance through simulation studies.
Collapse
Affiliation(s)
- Yixin Ren
- Department of Mathematics, University of Maryland, College Park , Maryland , USA
| | - Chao Wang
- Office of Biostatistics, Center for Drug Evaluation and Research, Food and Drug Administration , Silver Spring , Maryland , USA
| | - Meiyu Shen
- Office of Biostatistics, Center for Drug Evaluation and Research, Food and Drug Administration , Silver Spring , Maryland , USA
| | - Yi Tsong
- Office of Biostatistics, Center for Drug Evaluation and Research, Food and Drug Administration , Silver Spring , Maryland , USA
| |
Collapse
|
27
|
Liu Y, Andersson B, Xin T, Zhang H, Wang L. Improved Wald Statistics for Item-Level Model Comparison in Diagnostic Classification Models. Appl Psychol Meas 2019; 43:402-414. [PMID: 31235985 PMCID: PMC6572908 DOI: 10.1177/0146621618798664] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Diagnostic classification models (DCMs) have been widely used in education, psychology, and many other disciplines. To select the most appropriate DCM for each item, the Wald test has been recommended. However, prior research has revealed that this test provides inflated Type I error rates. To address this problem, the authors propose to replace the asymptotic covariance matrix from the original version of the Wald statistic with a matrix obtained from improved computation methods. In this study, the Wald test based on the observed information matrix and the Wald test based on the sandwich-type matrix are proposed for item-level model comparisons and a simulation study is conducted to investigate their empirical behavior. Simulation results indicate that when the sample size is reasonably large ( N ≥ 1 , 000 ), the Type I error rates of the Wald test based on the sandwich-type matrix are accurate with adequate or excellent power under most of the simulation conditions.
Collapse
Affiliation(s)
| | | | - Tao Xin
- Beijing Normal University, China
| | | | | |
Collapse
|
28
|
Spiess M, Jordan P, Wendt M. Simplified Estimation and Testing in Unbalanced Repeated Measures Designs. Psychometrika 2019; 84:212-235. [PMID: 29736784 DOI: 10.1007/s11336-018-9620-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2017] [Revised: 04/20/2018] [Indexed: 06/08/2023]
Abstract
In this paper we propose a simple estimator for unbalanced repeated measures design models where each unit is observed at least once in each cell of the experimental design. The estimator does not require a model of the error covariance structure. Thus, circularity of the error covariance matrix and estimation of correlation parameters and variances are not necessary. Together with a weak assumption about the reason for the varying number of observations, the proposed estimator and its variance estimator are unbiased. As an alternative to confidence intervals based on the normality assumption, a bias-corrected and accelerated bootstrap technique is considered. We also propose the naive percentile bootstrap for Wald-type tests where the standard Wald test may break down when the number of observations is small relative to the number of parameters to be estimated. In a simulation study we illustrate the properties of the estimator and the bootstrap techniques to calculate confidence intervals and conduct hypothesis tests in small and large samples under normality and non-normality of the errors. The results imply that the simple estimator is only slightly less efficient than an estimator that correctly assumes a block structure of the error correlation matrix, a special case of which is an equi-correlation matrix. Application of the estimator and the bootstrap technique is illustrated using data from a task switch experiment based on an experimental within design with 32 cells and 33 participants.
Collapse
Affiliation(s)
- Martin Spiess
- Department of Psychology, University of Hamburg, Von-Melle-Park 5, 20146, Hamburg, Germany.
| | - Pascal Jordan
- Department of Psychology, University of Hamburg, Von-Melle-Park 5, 20146, Hamburg, Germany
| | - Mike Wendt
- Faculty of Human Sciences, Medical School Hamburg, Am Kaiserkai 1, 20457, Hamburg, Germany
| |
Collapse
|
29
|
Abstract
Excessive zeros are common in practice and may cause overdispersion and invalidate inferences when fitting Poisson regression models. Zero-inflated Poisson regression models may be applied if there are inflated zeros; however, it is desirable to test if there are inflated zeros before such zero-inflated Poisson models are applied. Assuming a constant probability of being a structural zero in a zero-inflated Poisson regression model, the existence of the inflated zeros may be tested by testing whether the constant probability is zero. In such situations, the Wald, score, and likelihood ratio tests can be applied. Without specifying a zero-inflated Poisson model, He et al. recently developed a test by comparing the amount of observed zeros with that expected under the Poisson model. In this paper, we develop a closed form for the test and compare it with the Wald, score, and likelihood ratio tests through simulation studies. The simulation studies show that the test of He et al. is the best in controlling type I errors, while the score test generally has the least power among the tests. The tests are illustrated with two real data examples.
Collapse
Affiliation(s)
- Yi Tang
- Department of Mathematics, Tulane University, New Orleans, LA, USA
| | - Wan Tang
- Department of Global Biostatistics and Data Science, School of Public Health and Tropical Medicine, Tulane University New, Orleans, LA, USA
| |
Collapse
|
30
|
Deng Y, Pan W. Improved Use of Small Reference Panels for Conditional and Joint Analysis with GWAS Summary Statistics. Genetics 2018; 209:401-408. [PMID: 29674520 PMCID: PMC5972416 DOI: 10.1534/genetics.118.300813] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2018] [Accepted: 04/04/2018] [Indexed: 02/08/2023] Open
Abstract
Due to issues of practicality and confidentiality of genomic data sharing on a large scale, typically only meta- or mega-analyzed genome-wide association study (GWAS) summary data, not individual-level data, are publicly available. Reanalyses of such GWAS summary data for a wide range of applications have become more and more common and useful, which often require the use of an external reference panel with individual-level genotypic data to infer linkage disequilibrium (LD) among genetic variants. However, with a small sample size in only hundreds, as for the most popular 1000 Genomes Project European sample, estimation errors for LD are not negligible, leading to often dramatically increased numbers of false positives in subsequent analyses of GWAS summary data. To alleviate the problem in the context of association testing for a group of SNPs, we propose an alternative estimator of the covariance matrix with an idea similar to multiple imputation. We use numerical examples based on both simulated and real data to demonstrate the severe problem with the use of the 1000 Genomes Project reference panels, and the improved performance of our new approach.
Collapse
Affiliation(s)
- Yangqing Deng
- Division of Biostatistics, University of Minnesota, Minneapolis, Minnesota 55455
| | - Wei Pan
- Division of Biostatistics, University of Minnesota, Minneapolis, Minnesota 55455
| |
Collapse
|
31
|
Abstract
There is growing interest in testing genetic pleiotropy, which is when a single genetic variant influences multiple traits. Several methods have been proposed; however, these methods have some limitations. First, all the proposed methods are based on the use of individual-level genotype and phenotype data; in contrast, for logistical, and other, reasons, summary statistics of univariate SNP-trait associations are typically only available based on meta- or mega-analyzed large genome-wide association study (GWAS) data. Second, existing tests are based on marginal pleiotropy, which cannot distinguish between direct and indirect associations of a single genetic variant with multiple traits due to correlations among the traits. Hence, it is useful to consider conditional analysis, in which a subset of traits is adjusted for another subset of traits. For example, in spite of substantial lowering of low-density lipoprotein cholesterol (LDL) with statin therapy, some patients still maintain high residual cardiovascular risk, and, for these patients, it might be helpful to reduce their triglyceride (TG) level. For this purpose, in order to identify new therapeutic targets, it would be useful to identify genetic variants with pleiotropic effects on LDL and TG after adjusting the latter for LDL; otherwise, a pleiotropic effect of a genetic variant detected by a marginal model could simply be due to its association with LDL only, given the well-known correlation between the two types of lipids. Here, we develop a new pleiotropy testing procedure based only on GWAS summary statistics that can be applied for both marginal analysis and conditional analysis. Although the main technical development is based on published union-intersection testing methods, care is needed in specifying conditional models to avoid invalid statistical estimation and inference. In addition to the previously used likelihood ratio test, we also propose using generalized estimating equations under the working independence model for robust inference. We provide numerical examples based on both simulated and real data, including two large lipid GWAS summary association datasets based on ∼100,000 and ∼189,000 samples, respectively, to demonstrate the difference between marginal and conditional analyses, as well as the effectiveness of our new approach.
Collapse
Affiliation(s)
- Yangqing Deng
- Division of Biostatistics, University of Minnesota, Minneapolis, Minnesota 55455
| | - Wei Pan
- Division of Biostatistics, University of Minnesota, Minneapolis, Minnesota 55455
| |
Collapse
|
32
|
Abstract
This paper discusses power and sample-size computation for likelihood ratio and Wald testing of the significance of covariate effects in latent class models. For both tests, asymptotic distributions can be used; that is, the test statistic can be assumed to follow a central Chi-square under the null hypothesis and a non-central Chi-square under the alternative hypothesis. Power or sample-size computation using these asymptotic distributions requires specification of the non-centrality parameter, which in practice is rarely known. We show how to calculate this non-centrality parameter using a large simulated data set from the model under the alternative hypothesis. A simulation study is conducted evaluating the adequacy of the proposed power analysis methods, determining the key study design factor affecting the power level, and comparing the performance of the likelihood ratio and Wald test. The proposed power analysis methods turn out to perform very well for a broad range of conditions. Moreover, apart from effect size and sample size, an important factor affecting the power is the class separation, implying that when class separation is low, rather large sample sizes are needed to achieve a reasonable power level.
Collapse
Affiliation(s)
- Dereje W Gudicha
- Department of Methodology and Statistics, Tilburg University, PO Box 90153, 5000LE, Tilburg, The Netherlands
| | - Verena D Schmittmann
- Department of Methodology and Statistics, Tilburg University, PO Box 90153, 5000LE, Tilburg, The Netherlands
| | - Jeroen K Vermunt
- Department of Methodology and Statistics, Tilburg University, PO Box 90153, 5000LE, Tilburg, The Netherlands.
| |
Collapse
|
33
|
Abstract
BACKGROUND Sample size calculation and power estimation are essential components of experimental designs in biomedical research. It is very challenging to estimate power for RNA-Seq differential expression under complex experimental designs. Moreover, the dependency among genes should be taken into account in order to obtain accurate results. RESULTS In this paper, we propose a simulation based procedure for power estimation using the negative binomial distribution and assuming a generalized linear model (at the gene level) that considers the dependence between gene expression level and its variance (dispersion) and also allows equal or unequal dispersion across conditions. We compared the performance of both Wald test and likelihood ratio test under different scenarios. The null distribution of the test statistics was simulated for the desired false positive control to avoid excess false positives with the usage of an asymptotic chi-square distribution. We applied this method to the TCGA breast cancer data set. CONCLUSIONS We provide a framework for power estimation of RNA-Seq data. The proposed procedure is able to properly control the false positive error rate at the nominal level.
Collapse
Affiliation(s)
- Lianbo Yu
- Center for Biostatistics, Department of Biomedical Informatics, The Ohio State University, 1800 Cannon Dr., Columbus, 43210, OH, USA.
| | - Soledad Fernandez
- Center for Biostatistics, Department of Biomedical Informatics, The Ohio State University, 1800 Cannon Dr., Columbus, 43210, OH, USA
| | - Guy Brock
- Center for Biostatistics, Department of Biomedical Informatics, The Ohio State University, 1800 Cannon Dr., Columbus, 43210, OH, USA
| |
Collapse
|
34
|
Tomizawa M, Shinozaki F, Hasegawa R, Shirai Y, Motoyoshi Y, Sugiyama T, Yamamoto S, Ishige N. Immunosuppressive agents are associated with peptic ulcer bleeding. Exp Ther Med 2017; 13:1927-1931. [PMID: 28565788 DOI: 10.3892/etm.2017.4214] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2016] [Accepted: 01/06/2017] [Indexed: 12/18/2022] Open
Abstract
Peptic ulcer bleeding can be fatal. Non-steroidal anti-inflammatory drugs (NSAIDs), corticosteroids and immunosuppressive agents are administered for long-term usage. The present study assessed the association between peptic ulcer bleeding and administration of NSAIDs, corticosteroids and immunosuppressive agents. Furthermore, the efficacy of lowering the risk of peptic ulcer bleeding with proton pump inhibitors (PPI) and histamine 2 receptor antagonists (H2RA) was evaluated. Medical records were retrospectively analyzed for patients subjected to an upper gastrointestinal (GI) endoscopy performed at the National Hospital Organization Shimoshizu Hospital (Yotsukaido, Japan) from October 2014 to September 2015. During this period, a total of 1,023 patients underwent an upper GI endoscopy. A total of 1,023 patients, including 431 males (age, 68.1±12.9 years) and 592 females (age, 66.4±12.3 years), who had been administered NSAIDs, corticosteroids, immunosuppressive agents, PPIs and H2RAs, were respectively enrolled. Endoscopic findings of the patients were reviewed and their data were statistically analyzed. Logistic regression analysis was used to determine the odds ratio of peptic ulcer bleeding for each medication; immunosuppressive agents had an odds ratio of 5.83, which was larger than that for NSAIDs (4.77). The Wald test was applied to confirm the correlation between immunosuppressive agents and peptic ulcer bleeding. Furthermore, χ2 tests were applied to the correlation between peptic ulcer bleeding and administration of PPIs or H2RAs. Immunosuppressive agents had the largest χ2, and the P-value was 0.03. Administration of PPIs was significantly correlated with non-peptic ulcer bleeding (P=0.02); furthermore, a tendency toward non-peptic ulcer bleeding with administration of H2RA was indicated, but it was not statistically significant (P=0.12). In conclusion, immunosuppressive agents were correlated with peptic ulcer bleeding and PPIs were effective at lowering the risk of peptic ulcer bleeding.
Collapse
Affiliation(s)
- Minoru Tomizawa
- Department of Gastroenterology, National Hospital Organization Shimoshizu Hospital, Yotsukaido, Chiba 284-0003, Japan
| | - Fuminobu Shinozaki
- Department of Radiology, National Hospital Organization Shimoshizu Hospital, Yotsukaido, Chiba 284-0003, Japan
| | - Rumiko Hasegawa
- Department of Surgery, National Hospital Organization Shimoshizu Hospital, Yotsukaido, Chiba 284-0003, Japan
| | - Yoshinori Shirai
- Department of Surgery, National Hospital Organization Shimoshizu Hospital, Yotsukaido, Chiba 284-0003, Japan
| | - Yasufumi Motoyoshi
- Department of Neurology, National Hospital Organization Shimoshizu Hospital, Yotsukaido, Chiba 284-0003, Japan
| | - Takao Sugiyama
- Department of Rheumatology, National Hospital Organization Shimoshizu Hospital, Yotsukaido, Chiba 284-0003, Japan
| | - Shigenori Yamamoto
- Department of Pediatrics, National Hospital Organization Shimoshizu Hospital, Yotsukaido, Chiba 284-0003, Japan
| | - Naoki Ishige
- Department of Neurosurgery, National Hospital Organization Shimoshizu Hospital, Yotsukaido, Chiba 284-0003, Japan
| |
Collapse
|
35
|
Abstract
The precision of estimates in many statistical models can be expressed by a confidence interval (CI). CIs based on standard errors (SE) are common in practice, but likelihood-based CIs are worth consideration. In comparison to SEs, likelihood-based CIs are typically more difficult to estimate, but are more robust to model (re)parameterization. In latent variable models, some parameters may take on values outside of their interpretable range. Therefore, it is desirable to place a bound to keep the parameter interpretable. For likelihood-based CI, a correction is needed when a parameter is bounded. The correction is known (Wu & Neale, 2012), but is difficult to implement in practice. A novel automatic implementation that is simple for an applied researcher to use is introduced. A simulation study demonstrates the accuracy of the correction using a latent growth curve model and the method is illustrated with a multilevel confirmatory factor analysis.
Collapse
Affiliation(s)
- Joshua N Pritikin
- Department of Psychiatry and Virginia Institute for Psychiatric and Behavior Genetics, Virginia Commonwealth University
| | - Lance M Rappaport
- Department of Psychiatry and Virginia Institute for Psychiatric and Behavior Genetics, Virginia Commonwealth University
| | - Michael C Neale
- Department of Psychiatry and Virginia Institute for Psychiatric and Behavior Genetics, Virginia Commonwealth University
| |
Collapse
|
36
|
Lin SX, Morrison L, Smith PWF, Hargood C, Weal M, Yardley L. Properties of bootstrap tests for N-of-1 studies. Br J Math Stat Psychol 2016; 69:276-290. [PMID: 27339626 PMCID: PMC5082548 DOI: 10.1111/bmsp.12071] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/14/2014] [Revised: 04/25/2016] [Indexed: 06/06/2023]
Abstract
N-of-1 study designs involve the collection and analysis of repeated measures data from an individual not using an intervention and using an intervention. This study explores the use of semi-parametric and parametric bootstrap tests in the analysis of N-of-1 studies under a single time series framework in the presence of autocorrelation. When the Type I error rates of bootstrap tests are compared to Wald tests, our results show that the bootstrap tests have more desirable properties. We compare the results for normally distributed errors with those for contaminated normally distributed errors and find that, except when there is relatively large autocorrelation, there is little difference between the power of the parametric and semi-parametric bootstrap tests. We also experiment with two intervention designs: ABAB and AB, and show the ABAB design has more power. The results provide guidelines for designing N-of-1 studies, in the sense of how many observations and how many intervention changes are needed to achieve a certain level of power and which test should be performed.
Collapse
Affiliation(s)
- Sharon X Lin
- Southampton Statistical Sciences Research Institute (S3RI), University of Southampton, UK.
- National Institute for Health Research (NIHR) Wessex Collaboration for Leadership and Research in Health Care (CLAHRC), University of Southampton, UK.
| | | | - Peter W F Smith
- Southampton Statistical Sciences Research Institute (S3RI), University of Southampton, UK
| | - Charlie Hargood
- Electronics and Computer Science, University of Southampton, UK
| | - Mark Weal
- Electronics and Computer Science, University of Southampton, UK
| | - Lucy Yardley
- Academic Unit of Psychology, University of Southampton, UK
| |
Collapse
|
37
|
Nathanson BH. Subgroup models cannot tell the whole story when assessing relative age in attention deficit hyperactivity disorder. J Pediatr 2016; 175:245. [PMID: 27245294 DOI: 10.1016/j.jpeds.2016.05.015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/18/2016] [Accepted: 05/05/2016] [Indexed: 11/18/2022]
|
38
|
Abstract
The main objective of this paper is to derive the valid sampling distribution of the observed counts in a case-control study with missing data under the assumption of missing at random by employing the conditional sampling method and the mechanism augmentation method. The proposed sampling distribution, called the case-control sampling distribution, can be used to calculate the standard errors of the maximum likelihood estimates of parameters via the Fisher information matrix and to generate independent samples for constructing small-sample bootstrap confidence intervals. Theoretical comparisons of the new case-control sampling distribution with two existing sampling distributions exhibit a large difference. Simulations are conducted to investigate the influence of the three different sampling distributions on statistical inferences. One finding is that the conclusion by the Wald test for testing independency under the two existing sampling distributions could be completely different (even contradictory) from the Wald test for testing the equality of the success probabilities in control/case groups under the proposed distribution. A real cervical cancer data set is used to illustrate the proposed statistical methods.
Collapse
Affiliation(s)
- Guo-Liang Tian
- 1 Department of Mathematics, South University of Science and Technology of China, Shenzhen City, Guangdong, P. R. China
| | - Chi Zhang
- 2 Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, P. R. China
| | - Xuejun Jiang
- 1 Department of Mathematics, South University of Science and Technology of China, Shenzhen City, Guangdong, P. R. China
| |
Collapse
|
39
|
Abstract
Selecting the most appropriate cognitive diagnosis model (CDM) for an item is a challenging process. Although general CDMs provide better model-data fit, specific CDMs have more straightforward interpretations, are more stable, and can provide more accurate classifications when used correctly. Recently, the Wald test has been proposed to determine at the item level whether a general CDM can be replaced by specific CDMs without a significant loss in model-data fit. The current study examines the practical consequence of the test by evaluating whether the attribute-vector classification based on CDMs selected by the Wald test is better than that based on general CDMs. Although the Wald test can detect the true underlying model for certain CDMs, it is yet unclear how effective it is at distinguishing among the wider range of CDMs found in the literature. This study investigates the relative similarity of the various CDMs through the use of the newly developed dissimiliarity index, and explores the implications for the Wald test. Simulations show that the Wald test cannot distinguish among additive models due to their inherent similarity, but this does not impede the ability of the test to provide higher correct classification rates than general CDMs, particularly when the sample size is small and items are of low quality. An empirical example is included to demonstrate the viability of the procedure.
Collapse
Affiliation(s)
- Wenchao Ma
- Rutgers, The State University of New Jersey, New Brunswick, USA
| | | | | |
Collapse
|
40
|
Abstract
In a multivariate setting, we consider the task of identifying features whose correlations with the other features differ across conditions. Such correlation shifts may occur independently of mean shifts, or differences in the means of the individual features across conditions. Previous approaches for detecting correlation shifts consider features simultaneously, by computing a correlation-based test statistic for each feature. However, since correlations involve two features, such approaches do not lend themselves to identifying which feature is the culprit. In this article, we instead consider a serial testing approach, by comparing columns of the sample correlation matrix across two conditions, and removing one feature at a time. Our method provides a novel perspective and favorable empirical results compared with competing approaches.
Collapse
Affiliation(s)
- Elisa Sheng
- Department of Biostatistics, University of Washington, Seattle, WA, USA
| | - Daniela Witten
- Department of Biostatistics, University of Washington, Seattle, Washington, USA and Department of Statistics, University of Washington, Seattle, Washington, USA
| | - Xiao-Hua Zhou
- Department of Biostatistics, University of Washington, Seattle, Washington, USA and Veterans Affairs Seattle Medical Center, Seattle, Washington, USA
| |
Collapse
|
41
|
Draxler C, Alexandrowicz RW. Sample Size Determination Within the Scope of Conditional Maximum Likelihood Estimation with Special Focus on Testing the Rasch Model. Psychometrika 2015; 80:897-919. [PMID: 26155756 DOI: 10.1007/s11336-015-9472-y] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2013] [Indexed: 06/04/2023]
Abstract
This paper refers to the exponential family of probability distributions and the conditional maximum likelihood (CML) theory. It is concerned with the determination of the sample size for three groups of tests of linear hypotheses, known as the fundamental trinity of Wald, score, and likelihood ratio tests. The main practical purpose refers to the special case of tests of the class of Rasch models. The theoretical background is discussed and the formal framework for sample size calculations is provided, given a predetermined deviation from the model to be tested and the probabilities of the errors of the first and second kinds.
Collapse
Affiliation(s)
- Clemens Draxler
- The Health and Life Sciences University, EWZ 1, 6060 , Hall, Austria.
- University of Klagenfurt, Psychology Institute, Universitaetsstrasse 65-67, 9020, Klagenfurt, Austria.
| | - Rainer W Alexandrowicz
- The Health and Life Sciences University, EWZ 1, 6060 , Hall, Austria
- University of Klagenfurt, Psychology Institute, Universitaetsstrasse 65-67, 9020, Klagenfurt, Austria
| |
Collapse
|
42
|
Luo J, D'Angela G, Gao F, Ding J, Xiong C. Bivariate correlation coefficients in family-type clustered studies. Biom J 2015; 57:1084-109. [PMID: 26360805 DOI: 10.1002/bimj.201400131] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2014] [Revised: 04/16/2015] [Accepted: 04/20/2015] [Indexed: 11/08/2022]
Abstract
We propose a unified approach based on a bivariate linear mixed effects model to estimate three types of bivariate correlation coefficients (BCCs), as well as the associated variances between two quantitative variables in cross-sectional data from a family-type clustered design. These BCCs are defined at different levels of experimental units including clusters (e.g., families) and subjects within clusters and assess different aspects on the relationships between two variables. We study likelihood-based inferences for these BCCs, and provide easy implementation using standard software SAS. Unlike several existing BCC estimators in the literature on clustered data, our approach can seamlessly handle two major analytic challenges arising from a family-type clustered design: (1) many families may consist of only one single subject; (2) one of the paired measurements may be missing for some subjects. Hence, our approach maximizes the use of data from all subjects (even those missing one of the two variables to be correlated) from all families, regardless of family size. We also conduct extensive simulations to show that our estimators are superior to existing estimators in handling missing data or/and imbalanced family sizes and the proposed Wald test maintains good size and power for hypothesis testing. Finally, we analyze a real-world Alzheimer's disease dataset from a family clustered study to investigate the BCCs across different modalities of disease markers including cognitive tests, cerebrospinal fluid biomarkers, and neuroimaging biomarkers.
Collapse
Affiliation(s)
- Jingqin Luo
- Division of Biostatistics, Washington University School of Medicine, 660 S. Euclid Avenue, Box 8067, St. Louis, MO, 63110, USA
| | - Gina D'Angela
- Division of Biostatistics, Washington University School of Medicine, 660 S. Euclid Avenue, Box 8067, St. Louis, MO, 63110, USA
| | - Feng Gao
- Division of Biostatistics, Washington University School of Medicine, 660 S. Euclid Avenue, Box 8067, St. Louis, MO, 63110, USA
| | - Jimin Ding
- Department of Mathematics and Statistics, Washington University, St. Louis, MO, 63110, USA
| | - Chengjie Xiong
- Division of Biostatistics, Washington University School of Medicine, 660 S. Euclid Avenue, Box 8067, St. Louis, MO, 63110, USA
| |
Collapse
|
43
|
Wu B, Guan W. Reader reaction on the generalized Kruskal-Wallis test for genetic association studies incorporating group uncertainty. Biometrics 2014; 71:556-7. [PMID: 25351417 DOI: 10.1111/biom.12260] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2014] [Revised: 09/01/2014] [Accepted: 10/01/2014] [Indexed: 11/29/2022]
Abstract
Acar and Sun (2013, Biometrics 69, 427-435) presented a generalized Kruskal-Wallis (GKW) test for genetic association studies that incorporated the genotype uncertainty and showed its robust and competitive performance compared to existing methods. We present another interesting way to derive the GKW test via a rank linear model.
Collapse
Affiliation(s)
- Baolin Wu
- Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A
| | - Weihua Guan
- Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A
| |
Collapse
|
44
|
Abstract
Motivated by recent work on studying massive imaging data in various neuroimaging studies, we propose a novel spatially varying coefficient model (SVCM) to capture the varying association between imaging measures in a three-dimensional (3D) volume (or 2D surface) with a set of covariates. Two stylized features of neuorimaging data are the presence of multiple piecewise smooth regions with unknown edges and jumps and substantial spatial correlations. To specifically account for these two features, SVCM includes a measurement model with multiple varying coefficient functions, a jumping surface model for each varying coefficient function, and a functional principal component model. We develop a three-stage estimation procedure to simultaneously estimate the varying coefficient functions and the spatial correlations. The estimation procedure includes a fast multiscale adaptive estimation and testing procedure to independently estimate each varying coefficient function, while preserving its edges among different piecewise-smooth regions. We systematically investigate the asymptotic properties (e.g., consistency and asymptotic normality) of the multiscale adaptive parameter estimates. We also establish the uniform convergence rate of the estimated spatial covariance function and its associated eigenvalues and eigenfunctions. Our Monte Carlo simulation and real data analysis have confirmed the excellent performance of SVCM.
Collapse
Affiliation(s)
- Hongtu Zhu
- Department of Biostatistics and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill, hapel Hill, NC 27599, USA
| | - Jianqing Fan
- Department of Oper Res and Fin. Eng, Princeton University, Princeton, NJ 08540
| | - Linglong Kong
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB Canada T6G 2G1
| |
Collapse
|
45
|
Neumann C, Taub MA, Younkin SG, Beaty TH, Ruczinski I, Schwender H. Analytic power and sample size calculation for the genotypic transmission/disequilibrium test in case-parent trio studies. Biom J 2014; 56:1076-92. [PMID: 25123830 DOI: 10.1002/bimj.201300148] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2013] [Revised: 05/29/2014] [Accepted: 06/21/2014] [Indexed: 11/05/2022]
Abstract
Case-parent trio studies considering genotype data from children affected by a disease and their parents are frequently used to detect single nucleotide polymorphisms (SNPs) associated with disease. The most popular statistical tests for this study design are transmission/disequilibrium tests (TDTs). Several types of these tests have been developed, for example, procedures based on alleles or genotypes. Therefore, it is of great interest to examine which of these tests have the highest statistical power to detect SNPs associated with disease. Comparisons of the allelic and the genotypic TDT for individual SNPs have so far been conducted based on simulation studies, since the test statistic of the genotypic TDT was determined numerically. Recently, however, it has been shown that this test statistic can be presented in closed form. In this article, we employ this analytic solution to derive equations for calculating the statistical power and the required sample size for different types of the genotypic TDT. The power of this test is then compared with the one of the corresponding score test assuming the same mode of inheritance as well as the allelic TDT based on a multiplicative mode of inheritance, which is equivalent to the score test assuming an additive mode of inheritance. This is, thus, the first time the power of these tests are compared based on equations, yielding instant results and omitting the need for time-consuming simulation studies. This comparison reveals that these tests have almost the same power, with the score test being slightly more powerful.
Collapse
Affiliation(s)
- Christoph Neumann
- Faculty of Statistics, TU Dortmund University, 44221, Dortmund, Germany
| | | | | | | | | | | |
Collapse
|
46
|
Krishnamoorthy K, Lee M, Zhang D. Closed-form fiducial confidence intervals for some functions of independent binomial parameters with comparisons. Stat Methods Med Res 2014; 26:43-63. [PMID: 24919827 DOI: 10.1177/0962280214537809] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Approximate closed-form confidence intervals (CIs) for estimating the difference, relative risk, odds ratio, and linear combination of proportions are proposed. These CIs are developed using the fiducial approach and the modified normal-based approximation to the percentiles of a linear combination of independent random variables. These confidence intervals are easy to calculate as the computation requires only the percentiles of beta distributions. The proposed confidence intervals are compared with the popular score confidence intervals with respect to coverage probabilities and expected widths. Comparison studies indicate that the proposed confidence intervals are comparable with the corresponding score confidence intervals, and better in some cases, for all the problems considered. The methods are illustrated using several examples.
Collapse
Affiliation(s)
| | - Meesook Lee
- 2 South Louisiana Community College, Lafayette, USA
| | - Dan Zhang
- 1 Dept of Mathematics, University of Louisiana, Lafayette, USA
| |
Collapse
|
47
|
Almendra-Arao F. A new noninferiority test for independent dichotomous variables based on a shrinkage proportion estimator. J Biopharm Stat 2014; 25:157-69. [PMID: 24836379 DOI: 10.1080/10543406.2014.919929] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Abstract
A new noninferiority test for the difference between two independent proportions is presented. The test is based on a Wald-type statistic in which maximum likelihood estimators and a type of shrinkage estimator are used to estimate proportions. This new test was compared with another Wald-type test that has been shown to behave well in terms of test size and power. For the comparison, the behavior of the new test, in terms of its size and power, was analyzed over several configurations. While the two tests exhibited similar behavior, the new test is easier to implement and thus constitutes a practical alternative.
Collapse
Affiliation(s)
- Félix Almendra-Arao
- a Departamento de Ciencias Básicas , UPIITA del Instituto Politécnico Nacional , México , D.F. , México
| |
Collapse
|
48
|
Hao C, Orlando D, Hou C. Rao and Wald tests for nonhomogeneous scenarios. Sensors (Basel) 2012; 12:4730-6. [PMID: 22666055 DOI: 10.3390/s120404730] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/12/2012] [Revised: 03/28/2012] [Accepted: 03/29/2012] [Indexed: 11/17/2022]
Abstract
In this paper, we focus on the design of adaptive receivers for nonhomogeneous scenarios. More precisely, at the design stage we assume a mismatch between the covariance matrix of the noise in the cell under test and that of secondary data. Under the above assumption, we show that the Wald test is the adaptive matched filter, while the Rao test coincides with the receiver obtained by using the Rao test design criterion in homogeneous environment, hence providing a theoretical explanation of the enhanced selectivity of this receiver.
Collapse
|
49
|
Pan J, Wang H, Tong H. Estimation and tests for power-transformed and threshold GARCH models. J Econom 2008; 142:352-378. [PMID: 32287880 PMCID: PMC7116990 DOI: 10.1016/j.jeconom.2007.06.004] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/11/2006] [Revised: 03/03/2007] [Accepted: 06/20/2007] [Indexed: 06/11/2023]
Abstract
Consider a class of power-transformed and threshold GARCH ( p , q ) (PTTGRACH ( p , q ) ) model, which is a natural generalization of power-transformed and threshold GARCH(1,1) model in Hwang and Basawa [2004. Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes. Statistics & Probability Letters 68, 209-220.] and includes the standard GARCH model and many other models as special cases. We first establish the asymptotic normality for quasi-maximum likelihood estimators (QMLE) of the parameters under the condition that the error distribution has finite fourth moment. For the case of heavy-tailed errors, we propose a least absolute deviations estimation (LADE) for PTTGARCH ( p , q ) model, and prove that the LADE is asymptotically normally distributed under very weak moment conditions. This paves the way for a statistical inference based on asymptotic normality for heavy-tailed PTTGARCH ( p , q ) models. As a consequence, we can construct the Wald test for GARCH structure and discuss the order selection problem in heavy-tailed cases. Numerical results show that LADE is more accurate than QMLE for heavy-tailed errors. Furthermore, the theory is applied to the daily returns of the Hong Kong Hang Seng Index, which suggests that asymmetry and nonlinearity could be present in the financial time series and the PTTGARCH model is capable of capturing these characteristics. As for the probabilistic structure of PTTGARCH ( p , q ) model, we give in the appendix a necessary and sufficient condition for the existence of a strictly stationary solution of the model, the existence of the moments and the tail behavior of the strictly stationary solution.
Collapse
Affiliation(s)
- Jiazhu Pan
- School of Mathematical Sciences, Peking University, Beijing 100871, China
- Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK
| | - Hui Wang
- School of Finance, Central University of Finance and Economics, China
| | - Howell Tong
- Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK
| |
Collapse
|