Practical Considerations for Sandwich Variance Estimation in 2-Stage Regression Settings

In this paper, we present a practical approach for computing the sandwich variance estimator in 2-stage regression model settings. As a motivating example for 2-stage regression, we consider regression calibration, a popular approach for addressing covariate measurement error. The sandwich variance approach has rarely been applied in regression calibration, despite its requiring less computation time than popular resampling approaches for variance estimation, specifically the bootstrap. This is probably because it requires specialized statistical coding. Here we first outline the steps needed to compute the sandwich variance estimator. We then develop a convenient method of computation in R for sandwich variance estimation, which leverages standard regression model outputs and existing R functions and can be applied in the case of a simple random sample or complex survey design. We use a simulation study to compare the sandwich estimator to a resampling variance approach for both settings. Finally, we further compare these 2 variance estimation approaches in data examples from the Women's Health Initiative (1993-2005) and the Hispanic Community Health Study/Study of Latinos (2008-2011). In our simulations, the sandwich variance estimator typically had good numerical performance, but simple Wald bootstrap confidence intervals were unstable or overcovered in certain settings, particularly when there was high correlation between covariates or large measurement error.

Integrative Pathogenicity Assay and Operational Taxonomy-Based Detection of New Forma Specialis of Fusarium oxysporum Causing Datepalm Wilt

Pathogenicity-associated genes are highly host-specific and contribute to host-specific virulence. We tailored the traditional Koch's postulates with integrative omics by hypothesizing that the effector genes associated with host-pathogenicity are determinant markers for virulence, and developed Integrative Pathogenicity (IP) postulates for authenticated pathogenicity testing in plants. To set the criteria, we experimented on datepalm (Phoenix dactylifera) for the vascular wilt pathogen and confirmed the pathogen based on secreted in xylem genes (effectors genes) using genomic and transcriptomic approaches, and found it a reliable solution when pathogenicity is in question. The genic regions ITS, TEF1-α, and RPBII of Fusarium isolates were examined by phylogenetic analysis to unveil the validated operational taxonomy at the species level. The hierarchical tree generated through phylogenetic analysis declared the fungal pathogen as Fusarium oxysporum. Moreover, the Fusarium isolates were investigated at the subspecies level by probing the IGS, TEF1-α, and Pgx4 genic regions to detect the forma specialis of F. oxysporum that causes wilt in datepalm. The phylogram revealed a new forma specialis in F. oxysporum that causes vascular wilt in datepalm.

Synthesizing studies for comparing different treatment sequences in clinical trials

With advances in cancer treatments and improved patient survival, more patients may go through multiple lines of treatment. It is of clinical importance to choose a sequence of effective treatments (eg, lines of treatment) for individual patients with the goal of optimizing their long-term clinical outcome (eg, survival). Several important issues arise in cancer studies. First, cancer clinical trials are usually conducted by each line of treatment. For a treatment sequence, we may have first line and second line treatment data from two different studies. Second, there is typically a treatment initiation period varying from patient to patient between progression of disease and the start of the second line treatment due to administrative reasons. Additionally, the choice of the second line treatment for patients with progression of disease may depend on their characteristics. We address all these issues and develop semiparametric methods under the potential outcome framework for the estimation of the overall survival probability for a treatment sequence and for comparing different treatment sequences. We establish the large sample properties of the proposed inferential procedures. Simulation studies and an application to a colorectal clinical trial are provided.

Sample Size Requirements for Simple and Complex Mediation Models

Mediation models have been widely used in many disciplines to better understand the underlying processes between independent and dependent variables. Despite their popularity and importance, the appropriate sample sizes for estimating those models are not well known. Although several approaches (such as Monte Carlo methods) exist, applied researchers tend to use insufficient sample sizes to estimate their models of interest, which might result in unstable and inaccurate estimation of the model parameters including mediation effects. In the present study, sample size requirements were investigated for four frequently used mediation models: one simple mediation model and three complex mediation models. For each model, path and structural equation modeling approaches were examined, and partial and complete mediation conditions were considered. Both the percentile bootstrap method and the multivariate delta method were compared for testing mediation effects. A series of Monte Carlo simulations was conducted under various simulation conditions, including those concerning the level of effect sizes, the number of indicators, the magnitude of factor loadings, and the proportion of missing data. The results not only present practical and general guidelines for substantive researchers to determine minimum required sample sizes but also improve understanding of which factors are related to sample size requirements in mediation models.

Bootstrap-Based Between-Study Heterogeneity Tests in Meta-Analysis

Meta-analysis combines pertinent information from existing studies to provide an overall estimate of population parameters/effect sizes, as well as to quantify and explain the differences between studies. However, testing between-study heterogeneity is one of the most challenging tasks in meta-analysis research. Existing methods for testing heterogeneity, such as the Q test and likelihood ratio (LR) test, have been criticized for their failure to control Type I error rate and/or failure to attain enough statistical power. Although better reference distribution approximations have been proposed in the literature, their application is limited. Additionally, when the interest is to test whether the size of the heterogeneity is larger than a specific level, existing methods are far from mature. To address these issues, we propose new heterogeneity tests. Specifically, we combine bootstrap methods with existing heterogeneity tests (i.e., the maximum LR test, the restricted maximum LR test, and the Q test) to overcome the reference distribution issue and denote them as B-ML-LRT, B-REML-LRT, and B-Q, respectively. Simulation studies were conducted to examine and compare the performance of the proposed methods with the regular LR test, the regular Q test, and the Kulinskaya's improved Q test in both random- and mixed-effects meta-analyses. Based on the results of Type I error rates and statistical power, B-REML-LRT is recommended. Additionally, the improved Q test is also recommended when it is applicable. An R package boot.heterogeneity is provided to facilitate the implementation of the proposed tests.

Efficient Multiple Imputation for Sensitivity Analysis of Recurrent Events Data with Informative Censoring

Missing data are commonly encountered in clinical trials due to dropout or nonadherence to study procedures. In trials in which recurrent events are of interest, the observed count can be an undercount of the events if a patient drops out before the end of the study. In many applications, the data are not necessarily missing at random and it is often not possible to test the missing at random assumption. Consequently, it is critical to conduct sensitivity analysis. We develop a control-based multiple imputation method for recurrent events data, where patients who drop out of the study are assumed to have a similar response profile to those in the control group after dropping out. Specifically, we consider the copy reference approach and the jump to reference approach. We model the recurrent event data using a semiparametric proportional intensity frailty model with the baseline hazard function completely unspecified. We develop nonparametric maximum likelihood estimation and inference procedures. We then impute the missing data based on the large sample distribution of the resulting estimators. The variance estimation is corrected by a bootstrap procedure. Simulation studies demonstrate the proposed method performs well in practical settings. We provide applications to two clinical trials.

Analysis of the Cutting Abilities of the Multilayer Grinding Wheels-Case of Ti-6Al-4V Alloy Grinding

This paper presents an effectiveness analysis of the grinding process with the use of a new multi-layer abrasive tool. The designed abrasive tool consists of external layers with a conventional structure, whose task is to decrease the grinding wheel load and ensure high grinding volumetric efficiency. The inner layer of the grinding wheel contains a 30% addition of abrasive aggregates. The task of the inner layer is to provide lower roughness of the machined surface. The aim of the research presented in this paper was to evaluate the topography of the designed abrasive tool and to analyze the middle layer properties influencing the machined surface roughness. The differentiation of the active surface features of the abrasive tool was determined for the conventional layer and the layer with the addition of abrasive aggregates. The machining potential of the layers was also determined using the Shos parameter. The surface topography of Ti-6Al-4V alloys ground with the use of a multi-layer wheel and a conventional grinding wheel was analyzed. With the application of the bootstrap hypothesis, the set of roughness parameters differentiating the topography of ground surfaces was determined.

Classical and Bayesian Inference of an Exponentiated Half-Logistic Distribution under Adaptive Type II Progressive Censoring

The point and interval estimations for the unknown parameters of an exponentiated half-logistic distribution based on adaptive type II progressive censoring are obtained in this article. At the beginning, the maximum likelihood estimators are derived. Afterward, the observed and expected Fisher’s information matrix are obtained to construct the asymptotic confidence intervals. Meanwhile, the percentile bootstrap method and the bootstrap-t method are put forward for the establishment of confidence intervals. With respect to Bayesian estimation, the Lindley method is used under three different loss functions. The importance sampling method is also applied to calculate Bayesian estimates and construct corresponding highest posterior density (HPD) credible intervals. Finally, numerous simulation studies are conducted on the basis of Markov Chain Monte Carlo (MCMC) samples to contrast the performance of the estimations, and an authentic data set is analyzed for exemplifying intention.

Asymptotic Standard Errors of Generalized Partial Credit Model True Score Equating Using Characteristic Curve Methods

In this study, the delta method was applied to estimate the standard errors of the true score equating when using the characteristic curve methods with the generalized partial credit model in test equating under the context of the common-item nonequivalent groups equating design. Simulation studies were further conducted to compare the performance of the delta method with that of the bootstrap method and the multiple imputation method. The results indicated that the standard errors produced by the delta method were very close to the criterion empirical standard errors as well as those yielded by the bootstrap method and the multiple imputation method under all the manipulated conditions.

Exploring heterogeneities with geographically weighted quantile regression: An enhancement based on the bootstrap approach

Geographically weighted quantile regression (GWQR) has been proposed as a spatial analytical technique to simultaneously explore two heterogeneities, one of spatial heterogeneity with respect to data relationships over space and one of response heterogeneity across different locations of the outcome distribution. However, one limitation of GWQR framework is that the existing inference procedures are established based on asymptotic approximation, which may suffer computation difficulties or yield incorrect estimates with finite samples. In this paper, we suggest a bootstrap approach to address this limitation. Our bootstrap enhancement is first validated by a simulation experiment and then illustrated with an empirical US mortality data. The results show that the bootstrap provides a practical alternative for inference in GWQR and enhances the utilization of GWQR.

[What is clinical relevance?]

BACKGROUND

Statistical significance is not the same as clinical relevance. Clinical relevance exists only when the patient feels a clear improvement by a measure.

METHOD

In six doctors' offices, 40 patients were interviewed on the outcome of which they would find an improvement that they could call satisfying. It can be assumed that these directly expressed patient data are an average of improvement.

RESULTS

About 600 responses showed that the frequency of clinically relevant improvements was very different. The data varied depending on the severity of restriction, the level oft he initial values and the measure. On average 41% reported a clinically relevant improvement with a variation of 24% and 57% (95% confidence interval). The largest improvements according to the bootstrap method were e. g. hospitalization (59%) and sleep disturbances (56%), the slightest improvements were e.g. mobility (33%) and intellectual activity (24%).

CONCLUSION

Clinically relevant improvements, regardless of age, for most severely impaired patients, were associated with only minor changes, while those with mild limitations rated only normal options as satisfactory.

Metabolic covariance networks combining graph theory measuring aberrant topological patterns in mesial temporal lobe epilepsy

OBJECTIVE

We aimed to study the networks' mechanism of metabolic covariance networks in mesial temporal lobe epilepsy (mTLE), through examining the brain value of fluorine-18-fluorodeoxyglucose positron emission tomography (¹⁸ F-FDG-PET).

METHODS

¹⁸ F-FDG-PET images from 16 patients with mTLE were analyzed using local and global metabolic covariance network (MCN) approaches, including whole metabolic pattern analysis (WMPA), hippocampus-based (h-) MCN, whole brain (w-) MCN, and edge-based connectivity analysis (EBCA).

RESULTS

WMPA showed a typical ipsilateral hypometabolism and contralateral hypermetabolism pattern to epileptic zones in mTLE. h-MCN revealed decreased hippocampus-based synchronization in contralateral regions. w-MCN exhibited a disrupted metabolic network with globally increased small-world properties and regionally decreased nodal metrics in the ipsilateral hemisphere. Hippocampus (h)-EBCA and whole brain EBCA (w-EBCA) both detected a reduced-connectivity dominated metabolic covariant network. Moreover, the reduced interhemisphere connectivity seemingly played a major role in the aberrant epileptic topological pattern.

CONCLUSION

From a metabolic point of view, we demonstrated the damaging effects with reduced contralateral intranetwork metrics properties and the compensatory effects in contralateral intranetworks with increased network properties. However, the import role of significant reduced interhemisphere connection has rarely been reported in other mTLE studies. Taken together, ¹⁸ F-FDG-PET MCN analysis provides new evidence that the mTLE is a system neurological disorder with disrupted networks.

New expectation-maximization-type algorithms via stochastic representation for the analysis of truncated normal data with applications in biomedicine

To analyze univariate truncated normal data, in this paper, we stochastically represent the normal random variable as a mixture of a truncated normal random variable and its complementary random variable. This stochastic representation is a new idea and it is the first time to appear in literature. According to this stochastic representation, we derive important distributional properties for the truncated normal distribution and develop two new expectation-maximization algorithms to calculate the maximum likelihood estimates of parameters of interest for Type I data (without and with covariates) and Type II/III data. Bootstrap confidence intervals of parameters for small sample sizes are provided. To evaluate the performance of the proposed methods for the truncated normal distribution, in simulation studies, we first focus on the comparison of estimation results between including the unobserved data counts and excluding the unobserved data counts, and we next investigate the impact of the number of unobserved data on the estimation results. The plasma ferritin concentration data collected by Australian Institute of Sport and the blood fat content data are used to illustrate the proposed methods and to compare the truncated normal distribution with the half normal, the folded normal, and the folded normal slash distributions based on Akaike information criterion and Bayesian information criterion.

Efficient nonparametric confidence bands for receiver operating-characteristic curves

Receiver operating-characteristic curve is a popular graphical method frequently used in order to study the diagnostic capacity of continuous (bio)markers. In spite of the existence of a huge number of papers devoted to both theoretical and practical aspects of this topic, the construction of confidence bands has had little impact in the specialized literature. As far as the authors know, in the CRAN there are only three R packages providing receiver operating-characteristic curve confidence regions: plotROC, pROC and fbroc. This work tries to fill this gap studying and proposing a new nonparametric method to build confidence bands for both the standard receiver operating-characteristic curve and its generalization for nonmonotone relationships. The behavior of the proposed procedure is studied via Monte Carlo simulations and the methodology is applied on two real-world biomedical problems. In addition, an R function to compute the proposed and some of the previously existing methodologies is provided as online supplementary material.

Genetic Network Inference Using Hierarchical Structure

Many methods for inferring genetic networks have been proposed, but the regulations they infer often include false-positives. Several researchers have attempted to reduce these erroneous regulations by proposing the use of a priori knowledge about the properties of genetic networks such as their sparseness, scale-free structure, and so on. This study focuses on another piece of a priori knowledge, namely, that biochemical networks exhibit hierarchical structures. Based on this idea, we propose an inference approach that uses the hierarchical structure in a target genetic network. To obtain a reasonable hierarchical structure, the first step of the proposed approach is to infer multiple genetic networks from the observed gene expression data. We take this step using an existing method that combines a genetic network inference method with a bootstrap method. The next step is to extract a hierarchical structure from the inferred networks that is consistent with most of the networks. Third, we use the hierarchical structure obtained to assign confidence values to all candidate regulations. Numerical experiments are also performed to demonstrate the effectiveness of using the hierarchical structure in the genetic network inference. The improvement accomplished by the use of the hierarchical structure is small. However, the hierarchical structure could be used to improve the performances of many existing inference methods.

How to select the most relevant 3D roughness parameters of a surface

In order to conduct a comprehensive roughness analysis, around sixty 3D roughness parameters are created to describe most of the surface morphology with regard to specific functions, properties or applications. In this paper, a multiscale surface topography decomposition method is proposed with application to stainless steel (AISI 304), which is processed by rolling at different fabrication stages and by electrical discharge tool machining. Fifty-six 3D-roughness parameters defined in ISO, EUR, and ASME standards are calculated for the measured surfaces. Then, expert software "MesRug" is employed to perform statistical analysis on acquired data in order to find the most relevant parameters characterizing the effect of both processes (rolling and machining), and to determine the most appropriate scale of analysis. For the rolling process: The parameter Vmc (the Core Material Volume--defined as volume of material comprising the texture between heights corresponding to the material ratio values of p = 10% and q = 80%) computed at the scale of 3 µm is the most relevant parameter to characterize the cold rolling process. For the EDM Process, the best roughness parameter is SPD that represents the number of peaks per unit area after segmentation of a surface into motifs computed at the scale of 8 µm.

The progressivity of health-care financing in Kenya

BACKGROUND

Health-care financing should be equitable. In many developing countries such as Kenya, changes to health-care financing systems are being implemented as a means of providing equitable access to health care with the aim of attaining universal coverage. Vertical equity means that people of dissimilar ability to pay make dissimilar levels of contribution to the health-care financing system. Vertical equity can be analysed by measuring progressivity.

OBJECTIVES

The aim of this study was to analyse progressivity by measuring deviations from proportionality in the relationship between sources of health-care financing and ability to pay using Kakwani indices applied to data from the Kenya Household Health Utilisation and Expenditure Survey 2007.

METHODS

Concentration indices and Kakwani indices were obtained for the sources of health-care financing: direct and indirect taxes, out of pocket (OOP) payments, private insurance contributions and contributions to the National Hospital Insurance Fund. The bootstrap method was used to analyse the sensitivity of the Kakwani index to changes in the equivalence scale or the use of an alternative measure of ability to pay.

RESULTS

The overall health-care financing system was regressive. Out of pocket payments were regressive with all other payments being proportional. Direct taxes, indirect taxes and private insurance premiums were sensitive to the use of income as an alternative measure of ability to pay. However, the overall finding of a regressive health-care system remained.

CONCLUSION

Reforms to the Kenyan health-care financing system are required to reduce dependence on out of pocket payments. The bootstrap method can be used in determining the sensitivity of the Kakwani index to various assumptions made in the analysis. Further analyses are required to determine the equity of health-care utilization and the effect of proposed reforms on overall equity of the Kenyan health-care system.

Joint confidence region estimation for area under ROC curve and Youden index

In the field of diagnostic studies, the area under the ROC curve (AUC) serves as an overall measure of a biomarker/diagnostic test's accuracy. Youden index, defined as the overall correct classification rate minus one at the optimal cut-off point, is another popular index. For continuous biomarkers of binary disease status, although researchers mainly evaluate the diagnostic accuracy using AUC, for the purpose of making diagnosis, Youden index provides an important and direct measure of the diagnostic accuracy at the optimal threshold and hence should be taken into consideration in addition to AUC. Furthermore, AUC and Youden index are generally correlated. In this paper, we initiate the idea of evaluating diagnostic accuracy based on AUC and Youden index simultaneously. As the first step toward this direction, this paper only focuses on the confidence region estimation of AUC and Youden index for a single marker. We present both parametric and non-parametric approaches for estimating joint confidence region of AUC and Youden index. We carry out extensive simulation study to evaluate the performance of the proposed methods. In the end, we apply the proposed methods to a real data set.

Intergenerational effects of shifts in women's educational distribution in South Korea: Transmission, differential fertility, and assortative mating

This study examines the intergenerational effects of changes in women's education in South Korea. We define intergenerational effects as changes in the distribution of educational attainment in an offspring generation associated with the changes in a parental generation. Departing from the previous approach in research on social mobility that has focused on intergenerational association, we examine the changes in the distribution of educational attainment across generations. Using a simulation method based on Mare and Maralani's recursive population renewal model, we examine how intergenerational transmission, assortative mating, and differential fertility influence intergenerational effects. The results point to the following conclusions. First, we find a positive intergenerational effect: improvement in women's education leads to improvement in daughter's education. Second, we find that the magnitude of intergenerational effects substantially depends on assortative marriage and differential fertility: assortative mating amplifies and differential fertility dampens the intergenerational effects. Third, intergenerational effects become bigger for the less educated and smaller for the better educated over time, which is a consequence of educational expansion. We compare our results with Mare and Maralani's original Indonesian study to illustrate how the model of intergenerational effects works in different socioeconomic circumstances.

Testing the generalizability of national reimbursement rates with respect to local setting: the costs of abdominal aortic aneurysm surgery in Denmark

Objective:

The purpose of this study is to investigate if the Danish national diagnosis-related group (DRG) tariffs for surgery for abdominal aortic aneurysm (AAA) were good estimates of the actual costs in two local hospitals in the Central Region of Denmark.

Methods:

We collected clinical data for 178 AAA patients operated at Skejby Hospital and Viborg Hospital in the period 2005–2006 from the Danish National Vascular Registry and economic data from the administrative systems in the hospitals. We used bootstrap methods to calculate 95% confidence intervals (CIs) for the mean costs of surgery for ruptured AAA, nonruptured AAA and AAA where the patient died within 30 days by applying a cost-trimming rule that the Danish National Board of Health uses in calculating national DRG tariffs.

Results:

The national DRG tariff lies within the calculated Danish Krone (DKK) CIs (CI ruptured AAA, 98,178–195,327 [€13,196–€26,254]; CI nonruptured AAA, 79,039–98,178 [€10,624–€13,196]; CI dead, 42,023–111,685 [€5,648–€15,011]), and thus national DRG tariffs could be a good estimate for the actual costs in the local hospitals.

Conclusion:

The bootstrap method is useful for testing the generalizability of national DRG tariffs as estimates of local surgical costs.