Evaluating multiple surrogate markers with censored data

Flexible evaluation of surrogate markers with Bayesian model averaging

When long-term follow up is required for a primary endpoint in a randomized clinical trial, a valid surrogate marker can help to estimate the treatment effect and accelerate the decision process. Several model-based methods have been developed to evaluate the proportion of the treatment effect that is explained by the treatment effect on the surrogate marker. More recently, a nonparametric approach has been proposed allowing for more flexibility by avoiding the restrictive parametric model assumptions required in the model-based methods. While the model-based approaches suffer from potential mis-specification of the models, the nonparametric method fails to give desirable estimates when the sample size is small, or when the range of the data does not follow certain conditions. In this paper, we propose a Bayesian model averaging approach to estimate the proportion of treatment effect explained by the surrogate marker. Our procedure offers a compromise between the model-based approach and the nonparametric approach by introducing model flexibility via averaging over several candidate models and maintains the strength of parametric models with respect to inference. We compare our approach with previous model-based methods and the nonparametric method. Simulation studies demonstrate the advantage of our method when surrogate supports are inconsistent and sample sizes are small. We illustrate our method using data from the Diabetes Prevention Program study to examine hemoglobin A1c as a surrogate marker for fasting glucose.

Robust approach to combining multiple markers to improve surrogacy

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 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 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 nonparametric estimation which is subject to the 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 the 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 study.

Estimation of the proportion of treatment effect explained by a high-dimensional surrogate

Clinical studies examining the effectiveness of a treatment with respect to some primary outcome often require long-term follow-up of patients and/or costly or burdensome measurements of the primary outcome of interest. Identifying a surrogate marker for the primary outcome of interest may allow one to evaluate a treatment effect with less follow-up time, less cost, or less burden. While much clinical and statistical work has focused on identifying and validating surrogate markers, available approaches tend to focus on settings in which only a single surrogate marker is of interest. Limited work has been done to accommodate the high-dimensional surrogate marker setting where the number of potential surrogates is greater than the sample size. In this article, we develop methods to estimate the proportion of treatment effect explained by high-dimensional surrogates. We study the asymptotic properties of our proposed estimator, propose inference procedures, and examine finite sample performance via a simulation study. We illustrate our proposed methods using data from a randomized study comparing a novel whey-based oral nutrition supplement with a standard supplement with respect to change in body fat percentage over 12 weeks, where the surrogate markers of interest are gene expression probesets.