Using a surrogate with heterogeneous utility to test for a treatment effect

Abstract

The primary benefit of identifying a valid surrogate marker is the ability to use it in a future trial to test for a treatment effect with shorter follow-up time or less cost. However, previous work has demonstrated potential heterogeneity in the utility of a surrogate marker. When such heterogeneity exists, existing methods that use the surrogate to test for a treatment effect while ignoring this heterogeneity may lead to inaccurate conclusions about the treatment effect, particularly when the patient population in the new study has a different mix of characteristics than the study used to evaluate the utility of the surrogate marker. In this article, we develop a novel test for a treatment effect using surrogate marker information that accounts for heterogeneity in the utility of the surrogate. We compare our testing procedure to a test that uses primary outcome information (gold standard) and a test that uses surrogate marker information, but ignores heterogeneity. We demonstrate the validity of our approach and derive the asymptotic properties of our estimator and variance estimates. Simulation studies examine the finite sample properties of our testing procedure and demonstrate when our proposed approach can outperform the testing approach that ignores heterogeneity. We illustrate our methods using data from an AIDS clinical trial to test for a treatment effect using CD4 count as a surrogate marker for RNA.

Keywords: heterogeneity; hypothesis test; nonparametric methods; surrogate marker; treatment effect.

FIGURE 1

Discrete data example

FIGURE 1

Estimated proportion of the treatment effect on the primary outcome (change in RNA) explained by the treatment effect on the surrogate marker (change in CD4), denoted as R_S, as a function of baseline CD4

FIGURE 2

Distribution of baseline CD4 in current study vs. prior study