🤖 AI Summary
In insurance analytics, risk assessment for newly enrolled populations is hindered by two interrelated challenges: reporting delays (inducing right-censoring) and administrative constraints limiting follow-up duration—both rendering true event times unobservable. To address this, we propose a parametric proportional hazards model that jointly models event occurrence time and reporting delay time. We introduce latent variables representing the underlying event status and perform marginalization over these latent states to enable valid inference. A two-stage estimation framework based on the EM algorithm is developed, ensuring asymptotic consistency and numerical stability. Our method substantially improves both timeliness and accuracy of risk prediction for new cohorts. Extensive simulations and empirical analysis demonstrate rapid convergence, robust performance, and practical utility. The approach establishes a novel, interpretable, and implementable paradigm for survival analysis under reporting delay.
📝 Abstract
Survival analysis is a statistical technique used to estimate the time until an event occurs. Although it is applied across a wide range of fields, adjusting for reporting delays under practical constraints remains a significant challenge in the insurance industry. Such delays render event occurrences unobservable when their reports are subject to right censoring. This issue becomes particularly critical when estimating hazard rates for newly enrolled cohorts with limited follow-up due to administrative censoring. Our study addresses this challenge by jointly modeling the parametric hazard functions of event occurrences and report timings. The joint probability distribution is marginalized over the latent event occurrence status. We construct an estimator for the proposed survival model and establish its asymptotic consistency. Furthermore, we develop an expectation-maximization algorithm to compute its estimates. Using these findings, we propose a two-stage estimation procedure based on a parametric proportional hazards model to evaluate observations subject to administrative censoring. Experimental results demonstrate that our method effectively improves the timeliness of risk evaluation for newly enrolled cohorts.