Hypoglycemic events analysis via recurrent time-to-event (HEART) models

Diabetes affects an estimated 25.8 million people in the United States and is one of the leading causes of death. A major safety concern in treating diabetes is the occurrence of hypoglycemic events. Despite this concern, the current methods of analyzing hypoglycemic events, including the Wilcoxon rank sum test and negative binomial regression, are not satisfactory. The aim of this article is to propose a new model to analyze hypoglycemic events with the goal of making this model a standard method in industry. Our method is based on a gamma frailty recurrent event model. To make this method broadly accessible to practitioners, this article provides many details of how this method works and discusses practical issues with supporting theoretical proofs. In particular, we make efforts to translate conditions and theorems from abstract counting process and martingale theories to intuitive and clinical meaningful explanations. For example, we provide a simple proof and illustration of the coarsening at random condition so that the practitioner can easily verify this condition. Connections and differences with traditional methods are discussed, and we demonstrate that under certain scenarios the widely used Wilcoxon rank sum test and negative binomial regression cannot control type 1 error rates while our proposed method is robust in all these situations. The usefulness of our method is demonstrated through a diabetes dataset which provides new clinical insights on the hypoglycemic data.