Causal assessment of surrogacy in a meta-analysis of colorectal cancer trials

Abstract

When the true end points (T) are difficult or costly to measure, surrogate markers (S) are often collected in clinical trials to help predict the effect of the treatment (Z). There is great interest in understanding the relationship among S, T, and Z. A principal stratification (PS) framework has been proposed by Frangakis and Rubin (2002) to study their causal associations. In this paper, we extend the framework to a multiple trial setting and propose a Bayesian hierarchical PS model to assess surrogacy. We apply the method to data from a large collection of colon cancer trials in which S and T are binary. We obtain the trial-specific causal measures among S, T, and Z, as well as their overall population-level counterparts that are invariant across trials. The method allows for information sharing across trials and reduces the nonidentifiability problem. We examine the frequentist properties of our model estimates and the impact of the monotonicity assumption using simulations. We also illustrate the challenges in evaluating surrogacy in the counterfactual framework that result from nonidentifiability.

Fig. 1.

Population-level (solid lines) and trial-specific (dashed lines) surrogacy measures: NDE and NAE for ACCENT data. Left panel: with monotonicity; and Right panel: without monotonicity.

Fig. 2.

Population-level (solid lines) and trial-specific (dashed lines) surrogacy measures: AP and SAP for ACCENT data. Left panel: with monotonicity; and Right panel: without monotonicity.

Fig. 3.

Prior and posterior distributions on population-level counterfactual probabilities. Dashed lines for the prior distributions and solid lines for the posterior distributions.