Abstract
Identifying effective and valid surrogate markers to make inference about a treatment effect on long-term outcomes is an important step in improving the efficiency of
clinical trials. Replacing a long term outcome with short term and/or cheaper surrogate markers can potentially shorten study duration and reduce trial costs. There
is a sizable statistical literature on methods to quantify the effectiveness of a single surrogate marker. Both parametric and nonparametric approaches have been well
developed for different outcome types. However, when there are multiple markers available, methods for combining markers to construct a composite marker with improved
surrogacy remain limited. In this paper, building on top of the optimal transformation
framework of Wang et al. (2020), we propose a novel calibrated model fusion approach
to optimally combine multiple markers to improve surrogacy. Specifically, we obtain
two initial estimates of optimal composite scores of the markers based on two sets
of models with one set approximating the underlying data distribution and the other
directly approximating the optimal transformation function. We then estimate an optimal calibrated combination of the two estimated scores which ensures both validity
of the final combined score and optimality with respect to the proportion of treatment effect explained (PTE) by the final combined score. This approach is unique in
that it identifies an optimal combination of the multiple surrogates without strictly
relying on parametric assumptions while borrowing modeling strategies to avoid fully
non-parametric estimation which is subject to curse of dimensionality. Our identified
optimal transformation can also be used to directly quantify the surrogacy of this identified combined score. Theoretical properties of the proposed estimators are derived
and finite sample performance of the proposed method is evaluated through simulation studies. We further illustrate the proposed method using data from the Diabetes
Prevention Program (DPP) study