A unified procedure for meta-analytic evaluation of surrogate end points in randomized clinical trials

Abstract

The meta-analytic approach to evaluating surrogate end points assesses the predictiveness of treatment effect on the surrogate toward treatment effect on the clinical end point based on multiple clinical trials. Definition and estimation of the correlation of treatment effects were developed in linear mixed models and later extended to binary or failure time outcomes on a case-by-case basis. In a general regression setting that covers nonnormal outcomes, we discuss in this paper several metrics that are useful in the meta-analytic evaluation of surrogacy. We propose a unified 3-step procedure to assess these metrics in settings with binary end points, time-to-event outcomes, or repeated measures. First, the joint distribution of estimated treatment effects is ascertained by an estimating equation approach; second, the restricted maximum likelihood method is used to estimate the means and the variance components of the random treatment effects; finally, confidence intervals are constructed by a parametric bootstrap procedure. The proposed method is evaluated by simulations and applications to 2 clinical trials.

Fig. 1.

The EXPLORE study: the x-axis is the treatment effect (log odds ratio) on SDURA intercourse; the y-axis is the treatment effect (log hazard ratio) on time to HIV acquisition. Eight subgroups were formed based on alcohol consumption, depression, and noninjection-drug use. The sizes of circles are proportional to sample sizes in subgroups.

Fig. 2.

The ovarian cancer trials: the x-axis is the treatment effect (log hazard ratio) on time to progression or death; the y-axis is the treatment effect (log hazard ratio) on time to death. Twelve groups were formed by collapsing small clinical sites to have minimal within-group sample size 50. The sizes of circles are proportional to sample sizes in the groups.