A time-varying coefficient rate model with intermittently observed covariates for recurrent event data

In the analysis of recurrent event data, some covariates have time-varying effect such as efficacy of certain treatments, while others are internally time-dependent, like blood pressure. Considering the variability of the covariate effects and covariate observation over time, a time-varying coefficient rate model with intermittently observed covariates was proposed. Generally, time-dependent covariates cannot be continuously observed. They are only recorded intermittently. The unobserved time-dependent covariates need to be imputed. Estimators were obtained using kernel likelihood for the time-varying coefficient and kernel smoothing for the time-dependent covariate. The proposed estimator was proved to be asymptotically unbiased and normally distributed. Some simulations were conducted to evaluate the estimation method, and the proposed method was applied to analyze a real data.