We propose BayesPIM, a Bayesian prevalence-incidence mixture model for estimating time- and covariate-dependent disease incidence from screening and surveillance data. The method is particularly suited to settings where some individuals may have the disease at baseline, baseline tests may be missing or incomplete, and the screening test has imperfect sensitivity. Building on the existing PIMixture framework, which assumes perfect sensitivity, BayesPIM accommodates uncertain test accuracy by incorporating informative priors. By including covariates, the model can quantify heterogeneity in disease risk, thereby informing personalized screening strategies. We motivate the model using data from high-risk familial colorectal cancer (CRC) surveillance through colonoscopy, where adenomas - precursors of CRC - may already be present at baseline and remain undetected due to imperfect test sensitivity. We show that conditioning incidence and prevalence estimates on covariates explains substantial heterogeneity in adenoma risk. Using a Metropolis-within-Gibbs sampler and data augmentation, BayesPIM robustly recovers incidence times while handling latent prevalence. Informative priors on the test sensitivity stabilize estimation and mitigate non-convergence issues. Model fit can be assessed using information criteria and validated against a non-parametric estimator. In this way, BayesPIM enhances estimation accuracy and supports the development of more effective, patient-centered screening policies.

翻译：我们提出BayesPIM，一种贝叶斯流行-发病混合模型，用于从筛查和监测数据中估计时间和协变量依赖的疾病发病率。该方法特别适用于以下场景：部分个体在基线时可能已患病，基线检测可能缺失或不完整，且筛查测试的灵敏度不完美。在现有假设完美灵敏度的PIMixture框架基础上，BayesPIM通过引入信息先验来适应测试准确性的不确定性。通过纳入协变量，该模型能够量化疾病风险的异质性，从而为个性化筛查策略提供依据。我们以高风险家族性结直肠癌（CRC）结肠镜监测数据为例说明该模型的应用，其中CRC前体——腺瘤——可能在基线时已存在，并因测试灵敏度不完美而未被检出。研究表明，基于协变量对发病率和流行率进行条件估计，能够解释腺瘤风险的大量异质性。通过使用Metropolis-within-Gibbs采样器和数据增强技术，BayesPIM在处理潜在流行率的同时，稳健地恢复了发病时间。对测试灵敏度的信息先验能够稳定估计并缓解不收敛问题。模型拟合度可通过信息准则进行评估，并可通过与非参数估计量对比进行验证。由此，BayesPIM提升了估计准确性，并支持制定更有效、以患者为中心的筛查政策。