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 i s whether changes in these markers explain the beneficial effect of treatme nt 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 C ox model adjusted for the marker. In this article we evaluate the statistic al properties of p((FGS)). Using a Monte Carlo study we show that the stati stic 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 situat ions where the time-dependent marker is measured with error at a fixed numb er of times. We show that a method of fitting a time-dependent Cox model in volving smoothing the marker reduces the bias in the estimate of p((FGS)) c ompared with the standard method of using the current or last observed mark er value. We also show that the estimate of p((FGS)) has considerable varia bility 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. Th e methods are illustrated using CD4 counts from an AIDS clinical trial of z idovidine versus placebo. Controlled Clin Trials 1998;19:555-568 (C) Elsevi er Science Inc. 1998.