A Method for Evaluating Surrogate Markers When Measured with Error Using the Cox Model

Abstract

The identification of a surrogate marker for a clinical endpoint is very important from an ethical as well as a cost containment point of view. In most clinical trials markers are measured periodically with error. In the presence of measurement error, the naive method of using the observed marker values in the Cox model to evaluate the relationship between the marker and clinical outcome produces biased estimates and can lead to incorrect conclusions when evaluating a potential surrogate. A two-stage approach for estimating the association of clinical outcome to the time-varying covariates and treatment is proposed. In the first stage, an empirical Bayes estimate of the time dependent covariate is computed at each event time. In the second stage, these estimates are imputed in the Cox proportional hazards model to estimate the regression parameter of interest. It is clearly demonstrated through extensive simulations that this methodology greatly reduces the bias of the regression estimate and correctly identifies good surrogate markers much more often than the naive approach.