Modeling multivariate survival data by a semiparametric random effects proportional odds model

Investigating Perceptions of Land Issues in a Threatened Landscape in Northern Cambodia

Land governance highly affects rural communities’ well-being in landscapes where land and its access are contested. This includes sites with high land pressures from development, but also from conservation interventions. In fact, local people’s motivations for sustainably managing their resources is highly tied to their perceptions of security, trust and participation in land management regimes. Understanding these perceptions is essential to ensure the internal legitimacy and sustainability of conservation interventions, especially in areas where development changes are fast paced. This paper presents an analysis of household perceptions of land issues in 20 villages across different conservation and development contexts in Northern Cambodia. We assess whether conservation and development interventions, as economic land concessions, influence perceptions of land issues in control and treatment sites by modelling five key perception indicators. We find that household characteristics rather than village contexts are the main factors influencing the perceptions of land issues. Interventions also affect perceptions, especially with regards to the negative effect of development pressures and population growth. While large-scale protected areas do not calm insecurity about land issues, some village-based payment for environmental services projects do. Ultimately, evidence from perception studies can help address current concerns and shape future conservation activities sustainably.

An item response theory based integrated model of headache, nausea, photophobia, and phonophobia in migraine patients

This study developed an integrated model of severity scores of migraine headache and the incidence of nausea, photophobia, and phonophobia to predict the natural time course of migraine symptoms, which are likely to occur by a common disease progression mechanism. Data were acquired from two phase 3 clinical trials conducted during the development of eletriptan. Only the placebo arm was used for analysis. A conventional proportional odds model was compared with an item response theory (IRT) based approach. Results suggested that the IRT based approach led to a better model fit, successfully revealing the difference in relief rates among different symptoms, which was the fastest in phonophobia and the slowest in headache. Simulation with the developed model suggested that using headache scores at 4 h post-dose attained greatest statistical power, yielding sample size of 100 per arm given drug effect of 40%, as compared to that of 200 per arm when 2 h post-dose scores were used as in the original eletriptan protocol. This work demonstrated the usefulness of an IRT based model as applied to analyzing multidimensional migraine symptoms and designing clinical trials. Our model can be similarly applied to analyzing other multiple endpoints sharing a common underlying mechanism.

Semiparametric odds rate model for modeling short-term and long-term effects with application to a breast cancer genetic study

The proportional odds model is commonly used in the analysis of failure time data. The assumption of constant odds ratios over time in the proportional odds model, however, can be violated in some applications. Motivated by a genetic study with breast cancer patients, we propose a novel semiparametric odds rate model for the analysis of right-censored survival data. The proposed model incorporates the short-term and long-term covariate effects on the failure time data and includes the proportional odds model as a nested model. We develop efficient likelihood-based inference procedures and establish the large sample properties of the proposed nonparametric maximum likelihood estimators. Simulation studies demonstrate that the proposed methods perform well in practical settings. An application to the motivating example is provided.

Nonparametric Covariate-Adjusted Association Tests Based on the Generalized Kendall's Tau()

Identifying the risk factors for comorbidity is important in psychiatric research. Empirically, studies have shown that testing multiple, correlated traits simultaneously is more powerful than testing a single trait at a time in association analysis. Furthermore, for complex diseases, especially mental illnesses and behavioral disorders, the traits are often recorded in different scales such as dichotomous, ordinal and quantitative. In the absence of covariates, nonparametric association tests have been developed for multiple complex traits to study comorbidity. However, genetic studies generally contain measurements of some covariates that may affect the relationship between the risk factors of major interest (such as genes) and the outcomes. While it is relatively easy to adjust these covariates in a parametric model for quantitative traits, it is challenging for multiple complex traits with possibly different scales. In this article, we propose a nonparametric test for multiple complex traits that can adjust for covariate effects. The test aims to achieve an optimal scheme of adjustment by using a maximum statistic calculated from multiple adjusted test statistics. We derive the asymptotic null distribution of the maximum test statistic, and also propose a resampling approach, both of which can be used to assess the significance of our test. Simulations are conducted to compare the type I error and power of the nonparametric adjusted test to the unadjusted test and other existing adjusted tests. The empirical results suggest that our proposed test increases the power through adjustment for covariates when there exist environmental effects, and is more robust to model misspecifications than some existing parametric adjusted tests. We further demonstrate the advantage of our test by analyzing a data set on genetics of alcoholism.

A Gaussian Copula Model for Multivariate Survival Data

We consider a Gaussian copula model for multivariate survival times. Estimation of the copula association parameter is easily implemented with existing software using a two-stage estimation procedure. Using the Gaussian copula, we are able to test whether the association parameter is equal to zero. When the association term is positive, the model can be extended to incorporate cluster-level frailty terms. Asymptotic properties are derived under the two-stage estimation scheme. Simulation studies verify finite sample utility. We apply the method to a Children's Oncology Group multi-center study of acute lymphoblastic leukemia. The analysis estimates marginal treatment effects and examines potential clustering within treatment institution.

Analysis of multilevel grouped survival data with time-varying regression coefficients

Correlated or multilevel grouped survival data are common in medical and dental research. Two common approaches to analyze such data are the marginal and the random-effects approaches. Models and methods in the literature generally assume that the treatment effect is constant over time. A researcher may be interested in studying whether the treatment effects in a clinical trial vary over time, say fade out gradually. This is of particular clinical value when studying the long-term effect of a treatment. This paper proposed to extend the random effects grouped proportional hazards models by incorporating the possibly time-varying covariate effects into the model in terms of a state-space formulation. The proposed model is very flexible and the estimation can be performed using the MCMC approach with non-informative priors in the Bayesian framework. The method is applied to a data set from a prospective clinical trial investigating the effectiveness of silver diamine fluoride (SDF) and sodium fluoride (NaF) varnish in arresting active dentin caries in the Chinese preschool children. It is shown that the treatment groups with caries removal prior to the topical fluoride applications are most effective in shortening the arrest times in the first 6-month interval, but their effects fade out rapidly since then. The effects of treatment groups without caries removal prior to topical fluoride application drop at a very slow rate and can be considered as more or less constant over time. The applications of SDF solution is found to be more effective than the applications of NaF vanish.

NONPARAMETRIC INFERENCE PROCEDURE FOR PERCENTILES OF THE RANDOM EFFECTS DISTRIBUTION IN META-ANALYSIS

To investigate whether treating cancer patients with erythropoiesis-stimulating agents (ESAs) would increase the mortality risk, Bennett et al. [Journal of the American Medical Association299 (2008) 914-924] conducted a meta-analysis with the data from 52 phase III trials comparing ESAs with placebo or standard of care. With a standard parametric random effects modeling approach, the study concluded that ESA administration was significantly associated with increased average mortality risk. In this article we present a simple nonparametric inference procedure for the distribution of the random effects. We re-analyzed the ESA mortality data with the new method. Our results about the center of the random effects distribution were markedly different from those reported by Bennett et al. Moreover, our procedure, which estimates the distribution of the random effects, as opposed to just a simple population average, suggests that the ESA may be beneficial to mortality for approximately a quarter of the study populations. This new meta-analysis technique can be implemented with study-level summary statistics. In contrast to existing methods for parametric random effects models, the validity of our proposal does not require the number of studies involved to be large. From the results of an extensive numerical study, we find that the new procedure performs well even with moderate individual study sample sizes.

Bayesian semiparametric dynamic frailty models for multiple event time data

Many biomedical studies collect data on times of occurrence for a health event that can occur repeatedly, such as infection, hospitalization, recurrence of disease, or tumor onset. To analyze such data, it is necessary to account for within-subject dependency in the multiple event times. Motivated by data from studies of palpable tumors, this article proposes a dynamic frailty model and Bayesian semiparametric approach to inference. The widely used shared frailty proportional hazards model is generalized to allow subject-specific frailties to change dynamically with age while also accommodating nonproportional hazards. Parametric assumptions on the frailty distribution are avoided by using Dirichlet process priors for a shared frailty and for multiplicative innovations on this frailty. By centering the semiparametric model on a conditionally conjugate dynamic gamma model, we facilitate posterior computation and lack-of-fit assessments of the parametric model. Our proposed method is demonstrated using data from a cancer chemoprevention study.

Bayesian Semiparametric Proportional Odds Models

Methodology for implementing the proportional odds regression model for survival data assuming a mixture of finite Polya trees (MPT) prior on baseline survival is presented. Extensions to frailties and generalized odds rates are discussed. Although all manner of censoring and truncation can be accommodated, we discuss model implementation, regression diagnostics, and model comparison for right-censored data. An advantage of the MPT model is the relative ease with which predictive densities, survival, and hazard curves are generated. Much discussion is devoted to practical implementation of the proposed models, and a novel MCMC algorithm based on an approximating parametric normal model is developed. A modest simulation study comparing the small sample behavior of the MPT model to a rank-based estimator and a real data example is presented.

Multilevel modelling of clustered grouped survival data using Cox regression model: an application to ART dental restorations

In some controlled clinical trials in dental research, multiple failure time data from the same patient are frequently observed that result in clustered multiple failure time. Moreover, the treatments are often delivered by more than one operator and thus the multiple failure times are clustered according to a multilevel structure when the operator effects are assumed to be random. In practice, it is often too expensive or even impossible to monitor the study subjects continuously, but they are examined periodically at some regular pre-scheduled visits. Hence, discrete or grouped clustered failure time data are collected. The aim of this paper is to illustrate the use of the Monte Carlo Markov chain (MCMC) approach and non-informative prior in a Bayesian framework to mimic the maximum likelihood (ML) estimation in a frequentist approach in multilevel modelling of clustered grouped survival data. A three-level model with additive variance components model for the random effects is considered in this paper. Both the grouped proportional hazards model and the dynamic logistic regression model are used. The approximate intra-cluster correlation of the log failure times can be estimated when the grouped proportional hazards model is used. The statistical package WinBUGS is adopted to estimate the parameter of interest based on the MCMC method. The models and method are applied to a data set obtained from a prospective clinical study on a cohort of Chinese school children that atraumatic restorative treatment (ART) restorations were placed on permanent teeth with carious lesions. Altogether 284 ART restorations were placed by five dentists and clinical status of the ART restorations was evaluated annually for 6 years after placement, thus clustered grouped failure times of the restorations were recorded. Results based on the grouped proportional hazards model revealed that clustering effect among the log failure times of the different restorations from the same child was fairly strong (corr(child)=0.55) but the effects attributed to the dentists could be regarded as negligible (corr(dentist)=0.03). Gender and the location of the restoration were found to have no effects on the failure times and no difference in failure times was found between small restorations placed on molars and non-molars. Large restorations placed on molars were found to have shorter failure times compared to small restorations. The estimates of the baseline parameters were increasing indicating increasing hazard rates from interval 1 to 6. Results based on the logistic regression models were similar. In conclusion, the use of the MCMC approach and non-informative prior in a Bayesian framework to mimic the ML estimation in a frequentist approach in multilevel modelling of clustered grouped survival data can be easily applied with the use of the software WinBUGS.

Semiparametric proportional odds models for spatially correlated survival data

The last decade has witnessed major developments in Geographical Information Systems (GIS) technology resulting in the need for statisticians to develop models that account for spatial clustering and variation. In public health settings, epidemiologists and health-care professionals are interested in discerning spatial patterns in survival data that might exist among the counties. This paper develops a Bayesian hierarchical model for capturing spatial heterogeneity within the framework of proportional odds. This is deemed more appropriate when a substantial percentage of subjects enjoy prolonged survival. We discuss the implementation issues of our models, perform comparisons among competing models and illustrate with data from the SEER (Surveillance Epidemiology and End Results) database of the National Cancer Institute, paying particular attention to the underlying spatial story.

Tests of trait—haplotype association when linkage phase is ambiguous, appropriate for matched case-control and cohort studies with competing risks

The impact of competing risks on tests of association between disease and haplotypes has been largely ignored. We consider situations in which linkage phase is ambiguous and show that tests for disease-haplotype association can lead to rejection of the null hypothesis, even when true, with more than the nominal 5 per cent frequency. This problem tends to occur if a haplotype is associated with overall mortality, even if the haplotype is not associated with disease risk. A small simulation study illustrates the magnitude of bias (high type I error rate) in the context of a cohort study in which a modest number of disease cases (about 350) occur over time. The bias remains even if the score test is based on a logistic model that includes age as a covariate. For cohort studies, we propose a new test based on a modification of the proportional hazards model and for case-control studies, a test based on a conditional likelihood that have the correct size under the null even in the presence of competing risks, and that can be used when haplotype is ambiguous.

REML and ML estimation for clustered grouped survival data

Clustered grouped survival data arise naturally in clinical medicine and biological research. For example, in a randomized clinical trial, the variable of interest is the time to occurrence of a certain event with or without a new treatment and the data are collected from possibly correlated subjects from independent clusters. However it is sometimes impossible or too expensive to monitor the experimental subjects continuously. The subjects are examined regularly and the continuous survival data are thus grouped into a discrete time scale. With such a design, researchers are mainly interested in the effectiveness of the new treatment as well as the correlation among subjects from the same cluster, namely the intracluster correlation. This paper suggests a random effects approach to the estimation of the regression parameter with various choices of regression model and also the dependence parameter which characterizes the intracluster correlation. Time dependent covariates can be accommodated in the proposed model, and the estimation procedure will not be further complicated with large cluster sizes. The proposed method is applied to the data from the Diabetic Retinopathy Study, the objective of which is to evaluate the effectiveness of laser photocoagulation in delaying or preventing the onset of blindness in the left and right eyes of individuals with diabetes-associated retinopathy. The intracluster correlation using a grouped proportional hazards regression model can be estimated and the relationship between the regression parameter estimates based on the random effects approach and the marginal approach using a dynamic logistic regression model are discussed. Results from a simulation study of the proposed method are also presented.