Evaluating surrogate markers of clinical outcome when measured with error

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 can produce biased estimates and lead to incorrect conclusions when evaluating a potential surrogate. We propose a two-stage approach to account for the measurement error and reduce the bias of the estimate. 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. We demonstrate through extensive simulations that this methodology reduces the bias of the regression estimate and correctly identifies good surrogate markers more often than the naive approach. An application evaluating CD4 count as a surrogate of disease progression in an AIDS clinical trial is presented.