Meta-regression model choice and the interpretation of trial-level surrogacy

Abstract

The use of surrogate endpoints can improve feasibility of clinical trials. The results of trial-level analyses are a key factor affecting regulatory policy regarding the uptake of a surrogate endpoint. Trial-level analyses aim to quantify the strength of association between treatment effects on an established clinical endpoint and treatment effects on the surrogate. Unfortunately, there is a well-documented lack of standardization in the meta-regression models used for these analyses. Common models differ in how they account for estimation errors, leading to variation in surrogacy estimands across approaches. This has caused confusion regarding surrogate quality. Moreover, the most used modeling approaches can lead to pessimistic inferences of surrogate quality. We overview common meta-regression models and their corresponding estimands for evaluating trial-level surrogacy, focusing on how each modeling approach accounts for sampling errors. Two broad classes of models can be differentiated. The models in the first class quantify the association between observed, estimated treatment effects, based on unweighted (least squares) or weighted linear regression (weighted least squares with weights proportional to trial sample size). The second class consists of hierarchical meta-regression models, which quantify the association between latent, true treatment effects. We target the trial-level coefficient of determination (R 2 ) in our inferences. We use patient-level meta-analysis of 66 previously conducted chronic kidney disease clinical trials and a small statistical simulation to characterize differences in results between modeling approaches. Across our analyses, use of simple and weighted linear regression produced R 2 estimates which were lower than those produced by the hierarchical models. In simulation analyses, use of simple and weighted linear regression resulted in downward bias in R 2 when the estimand is defined as the R 2 representing the trial-level association of true treatment effects on the clinical and surrogate endpoints. Commonly used methods for evaluating surrogate endpoints can produce unduly pessimistic conclusions of surrogate quality depending on the target of inference. This is because these methods partially or completely ignore estimation error in the analysis. Hierarchical models can be used to overcome such limitations.