Flexible evaluation of surrogacy in platform studies

Surrogate Marker Evaluation: A Tutorial Using R

The practice of using a surrogate marker to replace a primary outcome in clinical studies has become widespread. Typically, the primary outcome requires long-term patient follow-up, is expensive, or is invasive or burdensome for patients to measure, while the surrogate marker is not (or less so). Of course, a surrogate marker must be validated before it should be used to make a decision about the effectiveness of a treatment. There has been a tremendous amount of statistical and clinical research focused on evaluating and validating surrogate markers over the past 35 years. Although there is ongoing debate over the optimal evaluation method, the development of new approaches and insights has greatly enriched the field. In this tutorial, we describe available statistical frameworks for evaluating a surrogate marker and specifically focus on the practical implementation of the proportion of treatment effect explained framework. We consider both uncensored and censored outcomes, parametric and non-parametric estimation, evaluating multiple surrogates, heterogeneity in the utility of the surrogate marker, surrogate evaluation from a prediction perspective, and the surrogate paradox. We include R code to implement these procedures with a follow-along R markdown. We close with a discussion on open problems in this research area, particularly in terms of using the surrogate marker to test for treatment in a future study, which is the ultimate goal of surrogate marker evaluation.

Assessing heterogeneity in surrogacy using censored data

Determining whether a surrogate marker can be used to replace a primary outcome in a clinical study is complex. While many statistical methods have been developed to formally evaluate a surrogate marker, they generally do not provide a way to examine heterogeneity in the utility of a surrogate marker. Similar to treatment effect heterogeneity, where the effect of a treatment varies based on a patient characteristic, heterogeneity in surrogacy means that the strength or utility of the surrogate marker varies based on a patient characteristic. The few methods that have been recently developed to examine such heterogeneity cannot accommodate censored data. Studies with a censored outcome are typically the studies that could most benefit from a surrogate because the follow-up time is often long. In this paper, we develop a robust nonparametric approach to assess heterogeneity in the utility of a surrogate marker with respect to a baseline variable in a censored time-to-event outcome setting. In addition, we propose and evaluate a testing procedure to formally test for heterogeneity at a single time point or across multiple time points simultaneously. Finite sample performance of our estimation and testing procedure are examined in a simulation study. We use our proposed method to investigate the complex relationship between change in fasting plasma glucose, diabetes, and sex hormones using data from the diabetes prevention program study.

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.