Measuring Surrogacy in Clinical Research: With an application to studying surrogate markers for HIV Treatment-as-Prevention

Abstract

In clinical research, validated surrogate markers are highly desirable in study design, monitoring, and analysis, as they do not only reduce the required sample size and follow-up duration, but also facilitate scientific discoveries. However, challenges exist to identify a reliable marker. One particular statistical challenge arises on how to measure and rank the surrogacy of potential markers quantitatively. We review the main statistical methods for evaluating surrogate markers. In addition, we suggest a new measure, the so-called "population surrogacy fraction of treatment effect," or simply the p-measure, in the setting of clinical trials. The p-measure carries an appealing population impact interpretation and supplements the existing statistical measures of surrogacy by providing "absolute" information. We apply the new measure along with other prominent measures to the HIV Prevention Trial Network 052 Study, a landmark trial for HIV/AIDS treatment-as-prevention.

Keywords: Population attributable fraction; Proportion of treatment effect explained; Randomized trial; Surrogate marker.

Fig. 1

The numerical behaviors of the π-measure, F-measure and p-measure for perfect surrogate markers, (a) α₁ < 0, ß_s = 0; (b) α₁ > 0, ß_s = 0.

Fig. 2

The numerical behaviors of the π-measure, F-measure and p-measure for useless surrogate markers, (a) α₁ = 0, ß_s < 0; (b) α₁ = 0, ß_s > 0; (c) ϕ_z = 0, ß_s < 0; (d) ϕ_z = 0,β_s > 0.

Fig. 3

The numerical behaviors of the π-measure, F-measure and p-measure for partial surrogate markers with typical configurations, (a) a₁ > 0, ß_s < 0; (b) a₁ > 0, ß₃ > 0; (c) a₁ < 0, ß_s < 0; (d) α₁ < 0, ß_s > 0.