Bayesian analysis of capture-recapture model and diagnostic test in clinical trials

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Capture-recapture models have been widely used to estimate the size of a target wildlife population. There are three major sources of variations that can affect capture probabilities: time (i.e., capture probabilities vary with time or trapping occasion), behavioral response (i.e., capture probabilities vary due to a trap response of animals to the first capture), and heterogeneity (i.e., capture probabilities vary by individual animal). There are eight models regarding possible combinations of these factors, including M0, Mt, Mb, Mh, Mtb, Mth, Mbh, and Mtbh. A capture-recapture model (Mb model) was created to present the behavioral response effect. The objective Bayesian analysis for the population size was developed and compared with common maximum likelihood estimates (MLEs). Simulation results demonstrate the advantages of the objective Bayesian over MLEs. Two real examples about a deer mouse are presented and one R package (OBMbpkg) was built for application. Companion diagnostics (CDx) for personalized medicine is commonly applied to in vitro diagnostic (IVD) industry and clinical trials for specific disease or treatment with biomarkers (e.g. molecular targets). The Bayesian method with Gibbs sampler was used to estimate the potential bias caused by imperfect CDx under the targeted design, where only patients with a positive diagnosis were enrolled the clinical trials. A simulation study was conducted to evaluate the performance of the Bayesian method and to compare with the EM algorithm. The Bayesian model selection method with G-prior was used to test treatment effects of targeted drugs for patients with biomarkers under the targeted design. A simulation study was conducted to evaluate the performance of the Bayesian method and to compare it with the original method and EM method when sample size is small. Eventually a biomarker-stratified design was studied, while patients enrolled in clinical trials could be divided into two groups (i.e., those with a positive or negative diagnosis). Both the EM algorithm and Bayesian method were used to estimate the potential bias caused by imperfect CDx. Simulation results demonstrate the advantages of the Bayesian method over the original method and EM method.