An evaluation of a measure of the proportion of the treatment effect explained by a surrogate marker.

Time-dependent markers, such as CD4 and viral load, are potential surrogate markers in AIDS clinical trials. A critical issue with surrogate markers is whether changes in these markers explain the beneficial effect of treatment on the real end point of the clinical trial. A statistic to measure the proportion of the treatment effect explained by the surrogate is p(FGS) = 1 - gamma/alpha, where alpha is the treatment effect coefficient in a Cox model and gamma is the treatment effect coefficient from a time-dependent Cox model adjusted for the marker. In this article we evaluate the statistical properties of p(FGS). Using a Monte Carlo study we show that the statistic is not well calibrated, because it can fall outside the range zero to one, even in very large samples. In the simulation study we consider situations where the time-dependent marker is measured with error at a fixed number of times. We show that a method of fitting a time-dependent Cox model involving smoothing the marker reduces the bias in the estimate of p(FGS) compared with the standard method of using the current or last observed marker value. We also show that the estimate of p(FGS) has considerable variability and can have wide confidence intervals. We conclude that p(FGS) is only likely to be useful in large trials with a strong treatment effect. The methods are illustrated using CD4 counts from an AIDS clinical trial of zidovidine versus placebo.