Affiliation:
1. Department of Statistics and Data Sciences The University of Texas at Austin Austin Texas
2. Department of Biomedical Data Science Stanford University Stanford California
3. Department of Biostatistics Harvard University Cambridge Massachusetts
Abstract
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.
Funder
National Institute of Diabetes and Digestive and Kidney Diseases
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