A Bayesian Random‐Effects Markov Model for Tumor Progression in Women with a Family History of Breast Cancer

Abstract

It makes intuitive sense to model the natural history of breast cancer, tumor progression from preclinical screen-detectable phase (PCDP) to clinical disease, as a multistate process, but the multilevel structure of the available data, which generally comes from cluster (family)-based service screening programs, makes the required parameter estimation intractable because there is a correlation between screening rounds in the same individual, and between subjects within clusters (families). There is also residual heterogeneity after adjusting for covariates. We therefore proposed a Bayesian hierarchical multistate Markov model with fixed and random effects and applied it to data from a high-risk group (women with a family history of breast cancer) participating in a family-based screening program for breast cancer. A total of 4867 women attended (representing 4464 families) and by the end of 2002, a total of 130 breast cancer cases were identified. Parameter estimation was carried out using Markov chain Monte Carlo (MCMC) simulation and the Bayesian software package WinBUGS. Models with and without random effects were considered. Our preferred model included a random-effect term for the transition rate from preclinical to clinical disease (sigma(2)(2f)), which was estimated to be 0.50 (95% credible interval = 0.22-1.49). Failure to account for this random effect was shown to lead to bias. The incorporation of covariates into multistate models with random effect not only reduced residual heterogeneity but also improved the convergence of stationary distribution. Our proposed Bayesian hierarchical multistate model is a valuable tool for estimating the rate of transitions between disease states in the natural history of breast cancer (and possibly other conditions). Unlike existing models, it can cope with the correlation structure of multilevel screening data, covariates, and residual (unexplained) variation.