Surrogacy marker paradox measures in meta-analytic settings.

Because of the time and expense required to obtain clinical outcomes of interest, such as functional limitations or death, clinical trials often focus the effects of treatment on earlier and more easily obtained surrogate markers. Preliminary work to define surrogates focused on the fraction of a treatment effect "explained" by a marker in a regression model, but as notions of causality have been formalized in the statistical setting, formal definitions of high-quality surrogate markers have been developed in the causal inference framework, using either the "causal effect" or "causal association" settings. In the causal effect setting, high-quality surrogate markers have a large fraction of the total treatment effect explained by the effect of the treatment on the marker net of the treatment on the outcome. In the causal association setting, high-quality surrogate markers have large treatment effects on the outcome when there are large treatment effects on the marker, and small effects on the outcome when there are small effects on the marker. A particularly important feature of a surrogate marker is that the direction of a treatment effect be the same for both the marker and the outcome. Settings in which the marker and outcome are positively associated but the marker and outcome have beneficial and harmful or harmful and beneficial treatment effects, respectively, have been referred to as "surrogate paradoxes". If this outcome always occurs, it is not problematic; however, as correlations among the outcome, marker, and their treatment effects weaken, it may occur for some trials and not for others, leading to potentially incorrect conclusions, and real-life examples that shortened thousands of lives are unfortunately available. We propose measures for assessing the risk of the surrogate paradox using the meta-analytic causal association framework, which allows us to focus on the probability that a given treatment will yield treatment effect in different directions between the marker and the outcome, and to determine the size of a beneficial effect of the treatment on the marker required to minimize the risk of a harmful effect of the treatment on the outcome. We provide simulations and consider two applications.