Trend-constrained corrected score for proportional hazards model with covariate measurement error

In many medical research studies, survival time is typically the primary outcome of interest. The Cox proportional hazards model is the most popular method to investigate the relationship between covariates and possibly right-censored survival time. However, in many clinical trials, the true covariates may not always be accurately measured due to natural biological fluctuation or instrument error. It is well know that for regression analysis in general, naively using mismeasured covariates in conventional inference procedures may incur substantial estimation bias. In the presence of covariate measurement error, several functional modeling methods have been proposed under the situation where the distribution of the measurement error is known. Among them are parametric corrected score and conditional score. Although both methods are consistent, each suffers from severe problem of multiple roots or absence of appropriate root when the measurement error is substantial. The problem persists even when the sample size is practically large. We conduct a detailed investigation on the pathological behaviors of parametric corrected score and propose an approach of incorporating additional estimating functions to remedy these pathological behaviors. The estimation and inference are then accomplished by means of quadratic inference function. Extensive simulation studies are conducted to evaluate the performance of proposed method.