A proportional hazards model for incidence and induced remission of disease

To assess the protective effects of a time-varying covariate, we develop a stochastic model based on tumor biology. The model assumes that individuals have a Poisson-distributed pool of initiated clones, which progress through predetectable, detectable mortal and detectable immortal stages. Time-independent covariates are incorporated through a log-linear model for the expected number of clones, resulting in a proportional hazards model for disease onset. By allowing time-dependent covariates to induce clone death, with rate dependent on a clone's state, the model is flexible enough to accommodate delayed disease onset and remission or cure of preexisting disease. Inference uses Bayesian methods via Markov chain Monte Carlo. Theoretical properties are derived, and the approach is illustrated through analysis of the effects of childbirth on uterine leiomyoma (fibroids).