The effect of classification errors in survival data analysis

Survival data analysis aims at collecting data on durations spent in a state by a sample of units, in order to analyse the process of transition to a different state. Survival analysis applied to social and economic phenomena typically relies upon data on transitions collected, for a sample of units, in one or more follow-up surveys. We explore the effect of misclassification of the transition indicator on parameter estimates in an appropriate statistical model for the duration spent in an origin state. Some empirical investigations about the bias induced when ignoring misclassification are reported, extending the model to include the possibility that the rate of misclassification can vary across units according to the value of some covariates. Finally it is shown how a Bayesian approach can lead to parameter estimates.     

Analysis of Failure Time Data with Mixed-Effects Accelerated Failure Time Model

In randomized clinical trials or observational studies, subjects are recruited at multiple treating sites. Factors that vary across sites may have some influence on outcomes; therefore, they need to be taken into account to get better results. We apply the accelerated failure time (AFT) model with linear mixed effects to analyze failure time data, accounting for correlations between outcomes. Specifically, we use Bayesian approach to fit the data, computing the regression parameters by Gibbs sampler combined with Buckley-James method. This approach is compared with the marginal independence approach and other methods through simulations and an application to a real example.     

Evaluation of Bayesian multiple stage estimation under spatial CAR model variants

In this study, an evaluation of Bayesian hierarchical models is made based on simulation scenarios to compare single-stage and multi-stage Bayesian estimations. Simulated datasets of lung cancer disease counts for men aged 65 and older across 44 wards in the London Health Authority were analysed using a range of spatially structured random effect components. The goals of this study are to determine which of these single-stage models perform best given a certain simulating model, how estimation methods (single- vs. multi-stage) compare in yielding posterior estimates of fixed effects in the presence of spatially structured random effects, and finally which of two spatial prior models – the Leroux or ICAR model, perform best in a multi-stage context under different assumptions concerning spatial correlation. Among the fitted single-stage models without covariates, we found that when there is low amount of variability in the distribution of disease counts, the BYM model is relatively robust to misspecification in terms of DIC, while the Leroux model is the least robust to misspecification. When these models were fit to data generated from models with covariates, we found that when there was one set of covariates – either spatially correlated or non-spatially correlated, changing the values of the fixed coefficients affected the ability of either the Leroux or ICAR model to fit the data well in terms of DIC. When there were multiple sets of spatially correlated covariates in the simulating model, however, we could not distinguish the goodness of fit to the data between these single-stage models. We found that the multi-stage modelling process via the Leroux and ICAR models generally reduced the variance of the posterior estimated fixed effects for data generated from models with covariates and a UH term compared to analogous single-stage models. Finally, we found the multi-stage Leroux model compares favourably to the multi-stage ICAR model in terms of DIC. We conclude that the mutli-stage Leroux model should be seriously considered in applications of Bayesian disease mapping when an investigator desires to fit a model with both fixed effects and spatially structured random effects to Poisson count data.     

Is regression adjustment supported by the Neyman model for causal inference?

This paper examines both theoretically and empirically whether the common practice of using OLS multivariate regression models to estimate average treatment effects (ATEs) under experimental designs is justified by the Neyman model for causal inference. Using data from eight large U.S. social policy experiments, the paper finds that estimated standard errors and significance levels for ATE estimators are similar under the OLS and Neyman models when baseline covariates are included in the models, even though theory suggests that this may not have been the case. This occurs primarily because treatment effects do not appear to vary substantially across study subjects.     

A Case Study for Modelling Cancer Incidence Using Bayesian Spatio‐Temporal Models

Researchers familiar with spatial models are aware of the challenge of choosing the level of spatial aggregation. Few studies have been published on the investigation of temporal aggregation and its impact on inferences regarding disease outcome in space–time analyses. We perform a case study for modelling individual disease outcomes using several Bayesian hierarchical spatio‐temporal models, while taking into account the possible impact of spatial and temporal aggregation. Using longitudinal breast cancer data from South East Queensland, Australia, we consider both parametric and non‐parametric formulations for temporal effects at various levels of aggregation. Two temporal smoothness priors are considered separately; each is modelled with fixed effects for the covariates and an intrinsic conditional autoregressive prior for the spatial random effects. Our case study reveals that different model formulations produce considerably different model performances. For this particular dataset, a classical parametric formulation that assumes a linear time trend produces the best fit among the five models considered. Different aggregation levels of temporal random effects were found to have little impact on model goodness‐of‐fit and estimation of fixed effects.     

A Bayesian approach for analysing longitudinal nominal outcomes using random coefficients transitional generalized logit model: an application to the labour force survey data

A random-effects transition model is proposed to model the economic activity status of household members. This model is introduced to take into account two kinds of correlations; one due to the longitudinal nature of the study, which will be considered using a transition parameter, and the other due to the existing correlation between responses of members of the same household which is taken into account by introducing random coefficients into the model. The results are presented based on the homogeneous (all parameters are not changed by time) and non-homogeneous Markov models with random coefficients. A Bayesian approach via the Gibbs sampling is used to perform parameter estimation. Results of using random-effects transition model are compared, using deviance information criterion, with those of three other models which exclude random effects and/or transition effects. It is shown that the full model gains more precision due to the consideration of all aspects of the process which generated the data. To illustrate the utility of the proposed model, a longitudinal data set which is extracted from the Iranian Labour Force Survey is analysed to explore the simultaneous effect of some covariates on the current economic activity as a nominal response. Also, some sensitivity analyses are performed to assess the robustness of the posterior estimation of the transition parameters to the perturbations of the prior parameters.     

The FGM Long-Term Bivariate Survival Copula Model: Modeling,Bayesian Estimation,and Case Influence Diagnostics

In this article, we propose a bivariate long-term distribution based on the Farlie-Gumbel-Morgenstern copula model. The proposed model allows for the presence of censored data and covariates. For inferential purposes, a Bayesian approach via Markov Chain Monte Carlo (MCMC) were considered. Further, some discussions on the model selection criteria are given. In order to examine outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated on artificial and real data.     

Bayesian spatial quantile regression for areal count data,with application on substitute care placements in Texas

Quantile regression (QR) allows one to model the effect of covariates across the entire response distribution, rather than only at the mean, but QR methods have been almost exclusively applied to continuous response variables and without considering spatial effects. Of the few studies that have performed QR on count data, none have included random spatial effects, which is an integral facet of the Bayesian spatial QR model for areal counts that we propose. Additionally, we introduce a simplifying alternative to the response variable transformation currently employed in the QR for counts literature. The efficacy of the proposed model is demonstrated via simulation study and on a real data application from the Texas Department of Family and Protective Services (TDFPS). Our model outperforms a comparable non-spatial model in both instances, as evidenced by the deviance information criterion (DIC) and coverage probabilities. With the TDFPS data, we identify one of four covariates, along with the intercept, as having a nonconstant effect across the response distribution.     

Time use of married couples: Bayesian approach

ABSTRACT

The living hours data of individuals' time spent on daily activities are compositional and include many zeros because individuals do not pursue all activities every day. Thus, we should exercise caution in using such data for empirical analyses. The Bayesian method offers several advantages in analyzing compositional data. In this study, we analyze the time allocation of Japanese married couples using the Bayesian model. Based on the Bayes factors, we compare models that consider and do not consider the correlations between married couples' time use data. The model that considers the correlation shows superior performance. We show that the Bayesian method can adequately take into account the correlations of wives' and husbands' living hours, facilitating the calculation of partial effects that their activities' variables have on living hours. The partial effects of the model that considers the correlations between the couples' time use are easily calculated from the posterior results.     

Small area estimation strategies for large population surveys: a comparison of design and model-based methods

Small area estimation (SAE) concerns with how to reliably estimate population quantities of interest when some areas or domains have very limited samples. This is an important issue in large population surveys, because the geographical areas or groups with only small samples or even no samples are often of interest to researchers and policy-makers. For example, large population health surveys, such as Behavioural Risk Factor Surveillance System and Ohio Mecaid Assessment Survey (OMAS), are regularly conducted for monitoring insurance coverage and healthcare utilization. Classic approaches usually provide accurate estimators at the state level or large geographical region level, but they fail to provide reliable estimators for many rural counties where the samples are sparse. Moreover, a systematic evaluation of the performances of the SAE methods in real-world setting is lacking in the literature. In this paper, we propose a Bayesian hierarchical model with constraints on the parameter space and show that it provides superior estimators for county-level adult uninsured rates in Ohio based on the 2012 OMAS data. Furthermore, we perform extensive simulation studies to compare our methods with a collection of common SAE strategies, including direct estimators, synthetic estimators, composite estimators, and Datta GS, Ghosh M, Steorts R, Maples J.'s [Bayesian benchmarking with applications to small area estimation. Test 2011;20(3):574–588] Bayesian hierarchical model-based estimators. To set a fair basis for comparison, we generate our simulation data with characteristics mimicking the real OMAS data, so that neither model-based nor design-based strategies use the true model specification. The estimators based on our proposed model are shown to outperform other estimators for small areas in both simulation study and real data analysis.     

Hierarchical Generalized Linear Models and Frailty Models with Bayesian Nonparametric Mixing

This paper proposes Bayesian nonparametric mixing for some well-known and popular models. The distribution of the observations is assumed to contain an unknown mixed effects term which includes a fixed effects term, a function of the observed covariates, and an additive or multiplicative random effects term. Typically these random effects are assumed to be independent of the observed covariates and independent and identically distributed from a distribution from some known parametric family. This assumption may be suspect if either there is interaction between observed covariates and unobserved covariates or the fixed effects predictor of observed covariates is misspecified. Another cause for concern might be simply that the covariates affect more than just the location of the mixed effects distribution. As a consequence the distribution of the random effects could be highly irregular in modality and skewness leaving parametric families unable to model the distribution adequately. This paper therefore proposes a Bayesian nonparametric prior for the random effects to capture possible deviances in modality and skewness and to explore the observed covariates' effect on the distribution of the mixed effects.     

A Bayesian random effects model for analyzing mixed negative binomial and continuous longitudinal responses

ABSTRACT

A general Bayesian random effects model for analyzing longitudinal mixed correlated continuous and negative binomial responses with and without missing data is presented. This Bayesian model, given some random effects, uses a normal distribution for the continuous response and a negative binomial distribution for the count response. A Markov Chain Monte Carlo sampling algorithm is described for estimating the posterior distribution of the parameters. This Bayesian model is illustrated by a simulation study. For sensitivity analysis to investigate the change of parameter estimates with respect to the perturbation from missing at random to not missing at random assumption, the use of posterior curvature is proposed. The model is applied to a medical data, obtained from an observational study on women, where the correlated responses are the negative binomial response of joint damage and continuous response of body mass index. The simultaneous effects of some covariates on both responses are also investigated.     

Longitudinal Poisson modeling: an application for CD4 counting in HIV-infected patients

In this paper, we present different “frailty” models to analyze longitudinal data in the presence of covariates. These models incorporate the extra-Poisson variability and the possible correlation among the repeated counting data for each individual. Assuming a CD4 counting data set in HIV-infected patients, we develop a hierarchical Bayesian analysis considering the different proposed models and using Markov Chain Monte Carlo methods. We also discuss some Bayesian discrimination aspects for the choice of the best model.     

Adaptive Lasso Variable Selection for the Accelerated Failure Models

This article considers the adaptive lasso procedure for the accelerated failure time model with multiple covariates based on weighted least squares method, which uses Kaplan-Meier weights to account for censoring. The adaptive lasso method can complete the variable selection and model estimation simultaneously. Under some mild conditions, the estimator is shown to have sparse and oracle properties. We use Bayesian Information Criterion (BIC) for tuning parameter selection, and a bootstrap variance approach for standard error. Simulation studies and two real data examples are carried out to investigate the performance of the proposed method.     

Extended Bayesian model averaging for heritability in twin studies

Family studies are often conducted to examine the existence of familial aggregation. Particularly, twin studies can model separately the genetic and environmental contribution. Here we estimate the heritability of quantitative traits via variance components of random-effects in linear mixed models (LMMs). The motivating example was a myopia twin study containing complex nesting data structures: twins and siblings in the same family and observations on both eyes for each individual. Three models are considered for this nesting structure. Our proposal takes into account the model uncertainty in both covariates and model structures via an extended Bayesian model averaging (EBMA) procedure. We estimate the heritability using EBMA under three suggested model structures. When compared with the results under the model with the highest posterior model probability, the EBMA estimate has smaller variation and is slightly conservative. Simulation studies are conducted to evaluate the performance of variance-components estimates, as well as the selections of risk factors, under the correct or incorrect structure. The results indicate that EBMA, with consideration of uncertainties in both covariates and model structures, is robust in model misspecification than the usual Bayesian model averaging (BMA) that considers only uncertainty in covariates selection.     

A Bayesian approach of joint models for clustered zero-inflated count data with skewness and measurement errors

Count data with excess zeros are widely encountered in the fields of biomedical, medical, public health and social survey, etc. Zero-inflated Poisson (ZIP) regression models with mixed effects are useful tools for analyzing such data, in which covariates are usually incorporated in the model to explain inter-subject variation and normal distribution is assumed for both random effects and random errors. However, in many practical applications, such assumptions may be violated as the data often exhibit skewness and some covariates may be measured with measurement errors. In this paper, we deal with these issues simultaneously by developing a Bayesian joint hierarchical modeling approach. Specifically, by treating intercepts and slopes in logistic and Poisson regression as random, a flexible two-level ZIP regression model is proposed, where a covariate process with measurement errors is established and a skew-t-distribution is considered for both random errors and random effects. Under the Bayesian framework, model selection is carried out using deviance information criterion (DIC) and a goodness-of-fit statistics is also developed for assessing the plausibility of the posited model. The main advantage of our method is that it allows for more robustness and correctness for investigating heterogeneity from different levels, while accommodating the skewness and measurement errors simultaneously. An application to Shanghai Youth Fitness Survey is used as an illustrate example. Through this real example, it is showed that our approach is of interest and usefulness for applications.     

Multivariate Parametric Spatiotemporal Models for County Level Breast Cancer Survival Data

In clustered survival settings where the clusters correspond to geographic regions, biostatisticians are increasingly turning to models with spatially distributed random effects. These models begin with spatially oriented frailty terms, but may also include further region-level terms in the parametrization of the baseline hazards or various covariate effects (as in a spatially-varying coefficients model). In this paper, we propose a multivariate conditionally autoregressive (MCAR) model as a mixing distribution for these random effects, as a way of capturing correlation across both the regions and the elements of the random effect vector for any particular region. We then extend this model to permit analysis of temporal cohort effects, where we use the term temporal cohort to mean a group of subjects all of whom were diagnosed with the disease of interest (and thus, entered the study) during the same time period (say, calendar year). We show how our spatiotemporal model may be efficiently fit in a hierarchical Bayesian framework implemented using Markov chain Monte Carlo (MCMC) computational techniques. We illustrate our approach in the context of county-level breast cancer data from 22 annual cohorts of women living in the state of Iowa, as recorded by the Surveillance, Epidemiology, and End Results (SEER) database. Hierarchical model comparison using the Deviance Information Criterion (DIC), as well as maps of the fitted county-level effects, reveal the benefit of our approach.     

Scalable spatio‐temporal Bayesian analysis of high‐dimensional electroencephalography data

We present a scalable Bayesian modelling approach for identifying brain regions that respond to a certain stimulus and use them to classify subjects. More specifically, we deal with multi‐subject electroencephalography (EEG) data with a binary response distinguishing between alcoholic and control groups. The covariates are matrix‐variate with measurements taken from each subject at different locations across multiple time points. EEG data have a complex structure with both spatial and temporal attributes. We use a divide‐and‐conquer strategy and build separate local models, that is, one model at each time point. We employ Bayesian variable selection approaches using a structured continuous spike‐and‐slab prior to identify the locations that respond to a certain stimulus. We incorporate the spatio‐temporal structure through a Kronecker product of the spatial and temporal correlation matrices. We develop a highly scalable estimation algorithm, using likelihood approximation, to deal with large number of parameters in the model. Variable selection is done via clustering of the locations based on their duration of activation. We use scoring rules to evaluate the prediction performance. Simulation studies demonstrate the efficiency of our scalable algorithm in terms of estimation and fast computation. We present results using our scalable approach on a case study of multi‐subject EEG data.     

On Estimation and Tests of Time-Varying Effects in the Proportional Hazards Model

Abstract.  Cox's proportional hazards model is routinely used in many applied fields, some times, however, with too little emphasis on the fit of the model. In this paper, we suggest some new tests for investigating whether or not covariate effects vary with time. These tests are a natural and integrated part of an extended version of the Cox model. An important new feature of the suggested test is that time constancy for a specific covariate is examined in a model, where some effects of other covariates are allowed to vary with time and some are constant; thus making successive testing of time-dependency possible. The proposed techniques are illustrated with the well-known Mayo liver disease data, and a small simulation study investigates the finite sample properties of the tests.