Optimizing and evaluating biomarker combinations as trial-level general surrogates

Abstract

We extend the method proposed in a recent work by the Authors for trial-level general surrogate evaluation to allow combinations of biomarkers and provide a procedure for finding the "best" combination of biomarkers based on the absolute prediction error summary of surrogate quality. We use a nonparametric Bayesian model that allows us to select an optimal subset of biomarkers without having to consider a large number of explicit model specifications for that subset. This dramatically reduces the number of model comparisons needed. Given the model's flexibility, complex nonlinear relationships can be fit when enough data are available. We evaluate the operating characteristics of our proposed method in simulations designed to be similar to our motivating example. We use our method to compare and evaluate combinations of biomarkers as trial-level general surrogates for the pentavalent rotavirus vaccine RotaTeq™ (RV5) (Merck & Co, Inc, Kenilworth, New Jersey, USA), finding that the same single biomarker identified in our previously published analysis is likely the optimal subset.

Keywords: causal inference; nonparametric Bayesian; prediction; rotavirus; surrogacy.

FIGURE 1

Scatterplots showing the estimated treatment effects on the clinical outcome (${\widehat{T}}_{c,j}$ in log risk ratio) versus the estimated treatment effects on the potential surrogates (${\widehat{T}}_{S,j,(a)}$ in log titer ratio) for each of the six candidate surrogates. The crossbars indicate 95% confidence intervals.

FIGURE 2

Stacked density plots of the ${\tilde{D}}_{J+1,\left(a\right)}$ distributions for the sets of biomarkers with the six smallest mean ${\tilde{D}}_{J+1,\left(a\right)}$, and the null model with no biomarkers. The model selected by our algorithm is the bottom one, with only the biomarker G1.

FIGURE 3

Scatterplot of the estimated treatment effects on the clinical outcome in log risk ratio (rotavirus gastroenteritis) versus the estimated treatment effects on the selected TLGS in log titer ratio (serum response to G1). The solid curve, which is roughly linear, is the mean of the posterior distribution T_c,j+1 |O_J, T_s,J+1,G1, for T_s,J+1,G1 on the x-axis. The unfilled point with vertical line shows the predicted treatment effect and prediction interval on the clinical outcome in the 13th trial, in Taiwan, in which the clinical outcome is not observed.