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This article is concerned with variable selection methods for the Cox proportional hazards regression model. Including excessive covariates causes extra variability and inflated confidence intervals for regression parameters; thus regimes for discarding the less informative ones are needed. Our framework has p covariates designated as "protected," while variables from a further set of q covariates are examined for possible inclusion or exclusion. We develop a focused information criterion (FIC) that for given interest parameter finds the best subset of covariates. Thus the FIC might find that the best model for predicting median survival time is different than the best model for estimating survival probabilities, and the best overall model for analyzing men's survival might not be the same as the best overall model for analyzing women's survival. Methodology is also developed for model averaging, wherein the final estimate of a quantity is a weighted average of estimates computed for a range of submodels. Our methods are illustrated in simulations and for a survival study of Danish skin cancer patients. [ABSTRACT FROM AUTHOR]

Pharmacokinetics is the study of the time course of a drug and its metabolites following its introduction into the body. Population pharmacokinetic studies are becoming increasingly important as an aid to drug development. The data from such studies typically consist of dose histories, drug concentrations with associated sampling times, and often covariate measurements such as the age and weight of each subject. These studies aim to provide an understanding of the pharmacokinetics of the drug in question and so lead to an informed choice of dosage regimen. Such an understanding includes determining those covariates that are important predictors of fundamental pharmacokinetic parameters, such as clearance, defined as the volume of plasma cleared of drug in a unit of time. Determining those subpopulations (e.g., the elderly) with altered kinetics has implications for the choice of an appropriate dosage regimens, because predictive concentration profiles arising from a particular regimen in different populations may be very different. In this article a general Bayesian hierarchical model is described. Pharmacokinetic models relating concentration to time are generally nonlinear, and the data are often sparse and/or noisy. The number of individuals on whom data have been collected is often large, and so the dimensionality of the parameter space is large. Consequently, estimation, from a Bayesian or a classical perspective, is not straightforward. In this article the Hastings-Metropolis algorithm is used for learning about the posterior distribution. An analysis of concentration data collected after the administration of the antiarrhythmic drug quinidine is presented. The data consist of 361 measurements on a total of 136 patients. Nine covariates are also available for each individual. These covariates are a mixture of discrete and continuous measurements. Some of the covariates are constant within an individual during the course of the study, whereas others change. A covariate model is constructed, and the sensitivity of the inferences to distributional assumptions is examined. The importance of assessing the appropriateness of modeling assumptions is emphasized and extensive model checking is carried out for the quinidine data using graphical diagnostics. [ABSTRACT FROM AUTHOR]