Dhiman Bhadra

A Bayesian Semiparametric Approach for Incorporating Longitudinal Information on Exposure History for Inference in Case–Control Studies

In a typical case-control study, exposure information is collected at a single time point for the cases and controls. However, case-control studies are often embedded in existing cohort studies containing a wealth of longitudinal exposure history about the participants. Recent medical studies have indicated that incorporating past exposure history, or a constructed summary measure of cumulative exposure derived from the past exposure history, when available, may lead to more precise and clinically meaningful estimates of the disease risk. In this article, we propose a flexible Bayesian semiparametric approach to model the longitudinal exposure profiles of the cases and controls and then use measures of cumulative exposure based on a weighted integral of this trajectory in the final disease risk model. The estimation is done via a joint likelihood. In the construction of the cumulative exposure summary, we introduce an influence function, a smooth function of time to characterize the association pattern of the exposure profile on the disease status with different time windows potentially having differential influence/weights. This enables us to analyze how the present disease status of a subject is influenced by his/her past exposure history conditional on the current ones. The joint likelihood formulation allows us to properly account for uncertainties associated with both stages of the estimation process in an integrated manner. Analysis is carried out in a hierarchical Bayesian framework using reversible jump Markov chain Monte Carlo algorithms. The proposed methodology is motivated by, and applied to a case-control study of prostate cancer where longitudinal biomarker information is available for the cases and controls.

A likelihood ratio test of quasi-independence for sparse two-way contingency tables

We consider a likelihood ratio test of independence for large two-way contingency tables having both structural (non-random) and sampling (random) zeros in many cells. The solution of this problem is not available using standard likelihood ratio tests. One way to bypass this problem is to remove the structural zeroes from the table and implement a test on the remaining cells which incorporate the randomness in the sampling zeros; the resulting test is a test of quasi-independence of the two categorical variables. This test is based only on the positive counts in the contingency table and is valid when there is at least one sampling (random) zero. The proposed (likelihood ratio) test is an alternative to the commonly used ad hoc procedures of converting the zero cells to positive ones by adding a small constant. One practical advantage of our procedure is that there is no need to know if a zero cell is structural zero or a sampling zero. We model the positive counts using a truncated multinomial distribution. In fact, we have two truncated multinomial distributions; one for the null hypothesis of independence and the other for the unrestricted parameter space. We use Monte Carlo methods to obtain the maximum likelihood estimators of the parameters and also the p-value of our proposed test. To obtain the sampling distribution of the likelihood ratio test statistic, we use bootstrap methods. We discuss many examples, and also empirically compare the power function of the likelihood ratio test relative to those of some well-known test statistics.

Estimation of Median Household Income for Small Areas : A Bayesian Semiparametric Approach

Abtsrcat Estimation of median income of small areas is one of the prin- cipal targets of inference of the U.S Bureau of Census. These estimates play an important role in the formulation of various governmental decisions and policies. Since these estimates are collected over time, they often possess an inherent longitudinal pattern. Taking proper account of this time varying pattern may result in better estimates for the current or future median house-hold incomes for a particular state or county. In this study, we put forward a semiparametric modeling procedure for estimating the median household income for all the U.S states. Our models include a nonparametric functional part for accommodating any unspecified time varying income pattern and also a state specific random effect to account for the within-state correlation of the income observations. Model fitting and parameter estimation is carried out in a hierarchical Bayesian framework using Markov chain Monte Carlo (MCMC) methodology. It is seen that the semiparametric model esti- mates can be superior to both the direct estimates and the Census Bureau estimates. Overall, our study indicates that proper modeling of the underly- ing longitudinal income profiles can improve the performance of model based estimates of household median income of small areas.

A Bayesian Analysis of Racial Differences in Treatment among Breast-cancer Patients

It is a well known fact that race and ethnicity specificc variations exist in the treatment and survival of cancer patients. Studies based on breast cancer patients admitted to community hospitals in U.S depicted that there is significant difference in patterns of care between black and white breast cancer patients with blacks receiving lower quality and quantity of care. In this study, we look at this problem from a different perspective, treating the hospitals as small areas, and employing Bayesian techniques for parameter estimation. Two separate models are constructed to estimate the odds ratio of receiving liver scan (a pattern of care) for blacks and whites. The first model uses hospital-specific information while the second one uses pooled hospital data by borrowing strength from neighbouring hospitals. We have used the non-central hyper-geometric distribution as the basis for constructing the likelihood while estimation has been carried out using the griddy Metropolis-Hastings sampler. We apply our methodology on a National Cancer Institute (NCI) database. Although our results corroborate some of the observations from previous studies, it proposes a computationally attractive alternative to the established procedures in formulating and analyzing this problem.