Covariate measurement error adjustment for matched case-control studies

We propose a conditional scores procedure for obtaining bias-corrected estimates of log odds ratios from matched case-control data in which one or more covariates are subject to measurement error. The approach involves conditioning on sufficient statistics for the unobservable true covariates that are treated as fixed unknown parameters. For the case of Gaussian nondifferential measurement error, we derive a set of unbiased score equations that can then be solved to estimate the log odds ratio parameters of interest. The procedure successfully removes the bias in naive estimates, and standard error estimates are obtained by resampling methods. We present an example of the procedure applied to data from a matched case-control study of prostate cancer and serum hormone levels, and we compare its performance to that of regression calibration procedures.     

Bayesian inference for prevalence in longitudinal two-phase studies

We consider Bayesian inference and model selection for prevalence estimation using a longitudinal two-phase design in which subjects initially receive a low-cost screening test followed by an expensive diagnostic test conducted on several occasions. The change in the subject's diagnostic probability over time is described using four mixed-effects probit models in which the subject-specific effects are captured by latent variables. The computations are performed using Markov chain Monte Carlo methods. These models are then compared using the deviance information criterion. The methodology is illustrated with an analysis of alcohol and drug use in adolescents using data from the Great Smoky Mountains Study.     

Fully semiparametric Bayesian approach for modeling survival data with cure fraction

In this paper, we consider a piecewise exponential model (PEM) with random time grid to develop a full semiparametric Bayesian cure rate model. An elegant mechanism enjoying several attractive features for modeling the randomness of the time grid of the PEM is assumed. To model the prior behavior of the failure rates of the PEM we assume a hierarchical modeling approach that allows us to control the degree of parametricity in the right tail of the survival curve. Properties of the proposed model are discussed in detail. In particular, we investigate the impact of assuming a random time grid for the PEM on the estimation of the cure fraction. We further develop an efficient collapsed Gibbs sampler algorithm for carrying out posterior computation. A Bayesian diagnostic method for assessing goodness of fit and performing model comparisons is briefly discussed. Finally, we illustrate the usefulness of the new methodology with the analysis of a melanoma clinical trial that has been discussed in the literature.     

Bayesian monitoring of clinical trials with failure-time endpoints

This article presents an aid for monitoring clinical trials with failure-time endpoints based on the Bayesian nonparametric analyses of the data. The posterior distribution is a mixture of Dirichlet processes in the presence of censoring if one assumes a Dirichlet process prior for the survival distribution. Using Gibbs sampling, one can generate random samples from the posterior distribution. With samples from the posterior distributions of treatment-specific survival curves, one can evaluate the current evidence in favor of stopping or continuing the trial based on summary statistics of these survival curves. Because the method is nonparametric, it can easily be used, for example, in situations where hazards cross or are suspected to cross and where relevant clinical decisions might be based on estimating when the integral between the curves might be expected to become positive and in favor of the new but toxic therapy. An example based on an actual trial illustrates the method.     

Statistical analysis for haplotype-based matched case-control studies

Using unphased genotype data, we studied statistical inference for association between a disease and a haplotype in matched case-control studies. Statistical inference for haplotype data is complicated due to ambiguity of genotype phases. An estimating equation-based method is developed for estimating odds ratios and testing disease-haplotype association. The method potentially can also be applied to testing haplotype-environment interaction. Simulation studies show that the proposed method has good performance. The performance of the method in the presence of departures from Hardy-Weinberg equilibrium is also studied.     

Semiparametric Bayesian analysis of case-control data under conditional gene-environment independence

In case-control studies of gene-environment association with disease, when genetic and environmental exposures can be assumed to be independent in the underlying population, one may exploit the independence in order to derive more efficient estimation techniques than the traditional logistic regression analysis (Chatterjee and Carroll, 2005, Biometrika92, 399-418). However, covariates that stratify the population, such as age, ethnicity and alike, could potentially lead to nonindependence. In this article, we provide a novel semiparametric Bayesian approach to model stratification effects under the assumption of gene-environment independence in the control population. We illustrate the methods by applying them to data from a population-based case-control study on ovarian cancer conducted in Israel. A simulation study is conducted to compare our method with other popular choices. The results reflect that the semiparametric Bayesian model allows incorporation of key scientific evidence in the form of a prior and offers a flexible, robust alternative when standard parametric model assumptions do not hold.     

Bayesian semiparametric intensity estimation for inhomogeneous spatial point processes

In this work we propose a fully Bayesian semiparametric method to estimate the intensity of an inhomogeneous spatial point process. The basic idea is to first convert intensity estimation into a Poisson regression setting via binning data points on a regular grid, and then model the log intensity semiparametrically using an adaptive version of Gaussian Markov random fields to smooth the corresponding counts. The inference is carried by an efficient Markov chain Monte Carlo simulation algorithm. Compared to existing methods for intensity estimation, for example, parametric modeling and kernel smoothing, the proposed estimator not only provides inference regarding the dependence of the intensity function on possible covariates, but also uses information from the data to adaptively determine the amount of smoothing at the local level. The effectiveness of using our method is demonstrated through simulation studies and an application to a rainforest dataset.     

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 modeling of multiple episode occurrence and severity with a terminating event

An individual's health condition can affect the frequency and intensity of episodes that can occur repeatedly and that may be related to an event time of interest. For example, bleeding episodes during pregnancy may indicate problems predictive of preterm delivery. Motivated by this application, we propose a joint model for a multiple episode process and an event time. The frequency of occurrence and severity of the episodes are characterized by a latent variable model, which allows an individual's episode intensity to change dynamically over time. This latent episode intensity is then incorporated as a predictor in a discrete time model for the terminating event. Time-varying coefficients are used to distinguish among effects earlier versus later in gestation. Formulating the model within a Bayesian framework, prior distributions are chosen so that conditional posterior distributions are conjugate after data augmentation. Posterior computation proceeds via an efficient Gibbs sampling algorithm. The methods are illustrated using bleeding episode and gestational length data from a pregnancy study.     

Bayesian analysis of case control polygenic etiology studies with missing data

Many genetic studies are based on analysing multiple DNA regions of cases and controls. Usually each is tested separately for association with disease. However, some diseases may require interacting polymorphisms at several regions, and most disease susceptibility is polygenic. In this paper, we develop new methods for determining combinations of polymorphisms that affect the risk of disease. For example, two different genes might produce normal proteins, but these proteins improperly function when they occur together. We consider a Bayesian approach to analyse studies where DNA data from cases and controls have been analysed for polymorphisms at multiple regions and a polygenic etiology is suspected. The method of Gibbs sampling is used to incorporate data from individuals who have not had every region analysed at the DNA sequence or amino acid level. The Gibbs sampling algorithm alternatively generates a sample from the posterior distribution of the sequence of combinations of polymorphisms in cases and controls and then uses this sample to impute the data that are missing. After convergence the algorithm is used to generate a sample from the posterior distribution for the probability of each combination in order to identify groups of polymorphisms that best discriminate cases from controls. We apply the methods to a genetic study of type I diabetes. The protein encoded by the TAP2 gene is important in T cell function, and thus may affect the development of autoimmune diseases such as insulin dependent diabetes mellitus (IDDM). We determine pairs of polymorphisms of genetic fragments in the coding regions of linked HLA genes that may impact the risk of IDDM.     

Bayesian modeling of time-varying and waning exposure effects

In epidemiologic studies, there is often interest in assessing the association between exposure history and disease incidence. For many diseases, incidence may depend not only on cumulative exposure, but also on the ages at which exposure occurred. This article proposes a flexible Bayesian approach for modeling age-varying and waning exposure effects. The Cox model is generalized to allow the hazard of disease to depend on an integral, across the exposed ages, of a piecewise polynomial function of age, multiplied by an exponential decay term. Linearity properties of the model facilitate posterior computation via a Gibbs sampler, which generalizes previous algorithms for Cox regression with time-dependent covariates. The approach is illustrated by an application to the study of protective effects of breastfeeding on incidence of childhood asthma.