A mixture model for estimating the risk of prostate cancer progression and the fraction of indolent cancer in active surveillance. 

Active surveillance has become a widely accepted management strategy to reduce overtreatment for low-risk prostate cancer patients. Prostate cancer is monitored through biopsies at scheduled visits to detect cancer upgrade to high-risk, leading to interval-censored outcomes when estimating the time to progression using data collected from active surveillance. Besides interval-censoring, there is heterogeneity in patients that induces additional challenges. Individuals who already have high-grade cancer at baseline (i.e., prevalent cases) may still undergo active surveillance because diagnostic tests are imperfect; and, some low-risk cancers may remain indolent indefinitely. Furthermore, all individuals are subject to misclassification during follow-up due to imperfect biopsies. In this paper, we assume a mixture model for prevalent cases, progressive and indolent cancers where the proportional hazards model incorporates the effect of time-independent or time-varying covariates on cancer progression. We propose a semiparametric likelihood-based approach to handle interval-censored observations while accounting for the misclassification rates of biopsy. The performance of the proposed approach is examined through simulation under various settings. We apply the proposed approach to the Canary Prostate Active Surveillance Study to evaluate potential risk factors for cancer progression and to estimate the indolent fraction under a range of biopsy sensitivity rates.