Journal of Biometrics & Biostatistics

The purpose of this paper is to develop a statistical probability model and to obtain posterior inference for the parameters given the survival times of the White Hispanic female cancer patients. Stratified random sample of White Hispanic female patients’ survival data was used to derive a best fit statistical probability model. The study sample was extracted from the Surveillance Epidemiology and End Results (SEER) cancer registry database. Three model building criterions were utilized; Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and Deviance Information Criteria (DIC) to measure the goodness of fit. We found that the Exponentiated Weibull model fits the survival times better as compared to other widely known statistical probability models. The Bayesian approach is employed to derive the posterior inference for the parameters.

We compare two sample size calculation approaches for analysis of covariance with one covariate. Exact simulation studies are conducted to compare the sample size calculation based on an approach by Borm et al. (2007) (referred to as the B approach) and an exact approach (referred to as the F approach). Although the B approach and the F approach have similar performance when the correlation coefficient is small, the F approach generally has a more accurate sample size calculation as compared to the B approach. Therefore, the F approach for sample size calculation is generally recommended for use in practice.

When the sampling scheme is in clusters and when the pools (of size k) within a cluster are assumed not to be independent, the Dorfman model for estimating the proportion under the binomial model is incorrect. The purpose of this paper is to propose a method for analyzing correlated binary data under the group testing framework. First, assuming that the probability of an individual varies according to a beta distribution, we derived an analytic expression for the probability of a positive pool and the correlation between two pools in each cluster. Second, we derived the exact probability mass function of the number of positive pools in each cluster that should be used to obtain the maximum likelihood estimate (MLE) of the proportion of individuals with a positive outcome. However, this MLE is not efficient in terms of computational resources. For this reason, we proposed another estimator based on the beta-binomial model for obtaining the approximate MLE of the proportion of interest. Based on a simulation study, the approximate estimator produced results that are very close to the exact MLE of the proportion of interest, with the advantage that this approach is computationally more efficient.

Estimation of measures of familial aggregation is considered the first step in establishing whether a specified disease has a genetic component. Population based family study designs areusually used to estimate correlations among siblings. When the trait of interest is quantitative (e.g. blood pressure, body mass index, blood glucose level) testing the effect of gender differences on sib-sib correlations is achieved using the likelihood method of estimation under the assumption of multivariate normality. When the trait of interest is measured on the binary scale testing the equality of a brother-brother and sister-sister correlation is more complex. In this paper we develop likelihood-based inference procedures for this purpose which may beapplied to nuclear family data.