Variable selection and estimation for recurrent event model with covariates subject to measurement error

This article focuses on variable selection in the Andersen-Gill model for recurrent event analysis, particularly when covariates are subject to measurement errors. We propose a comprehensive three-stage procedure that incorporates simulation-extrapolation with various penalty functions. This approach allows for the simultaneous selection of significant covariates, estimation of regression parameters, and adjustment for measurement errors. Through extensive simulation studies, we demonstrate that our method outperforms approaches that fail to account for measurement errors or the need for variable selection. Specifically, our procedure excels in removing unimportant error-prone covariates and accurately estimating the coefficients of important variables. The results also reveal that the magnitude of measurement error has a substantial negative impact on variable selection outcomes. Additionally, we apply our method to a real-world dataset, further illustrating its practical effectiveness and robustness.