Evaluating surrogate markers of clinical outcome when measured with error

In most clinical trials, markers are measured periodically with error. In t he presence of measurement error, the naive method of using the observed ma rker values in the Cox model to evaluate the relationship between the marke r and clinical outcome can produce biased estimates and lead to incorrect c onclusions when evaluating a potential surrogate. We propose a two-stage ap proach to account for the measurement error and reduce the bias of the esti mate. In the first stage, an empirical Bayes estimate of the time-dependent covariate is computed at each event time. In the second stage, these estim ates are imputed in the Cox proportional hazards model to estimate the regr ession parameter of interest. We demonstrate through extensive simulations that this methodology reduces the bias of the regression estimate and corre ctly identifies good surrogate markers more often than the naive approach. An application evaluating CD4 count as a surrogate of disease progression i n an AIDS clinical trial is presented.