Abstract
ABSTRACT
The cure model extends standard survival models to analyze survival data with a cure or nonsusceptible fraction. Numerous methods have been developed to infer such data using the mixture cure model, which separately models and interprets the cure rate and the failure time of uncured subjects. Most of these methods assume that all covariates are measured precisely. Cure models that account for mismeasured covariates are scarce in the literature, largely due to the challenges they pose for estimation, inference, and asymptotic theory. This article considers a logistic‐proportional odds mixture cure model for right‐censored survival data with mismeasured covariates and proposes a functional modeling approach to correct measurement errors. We develop a two‐stage estimation method with extensively corrected scores to sequentially infer the cure rate and failure time of uncured subjects. The computational algorithm is straightforward to implement, and its large sample properties are established. We conduct simulation studies to assess the approach's performance and apply it to a real dataset for illustration.