Estimation of a recurrent event gap time distribution: an application to morbidity outcomes following lower extremity fracture in Veterans with spinal cord injury

Abstract

Recurrent event data is frequently encountered in biomedical research. Estimators describing the time to the next event occurrence could be useful information in healthcare settings to deliver targeted, preemptive, patient-specific care. Distribution estimation of recurrence times is varied based on both the underlying assumptions of the estimator (e.g., dependence vs. independence of recurrence times within individual) and estimator construct. In an example among Veterans with spinal cord injury, distributional changes in recurrence times of health complications subsequent lower extremity (LE) fracture are explored. Veterans with LE fracture (cases) were matched to Veterans without LE fracture (controls) on demographic (age, race), level of injury (paraplegia vs. tetraplegia), extent of injury, Veterans Affairs connected service status, and comorbidities using Mahalanobis metric matching. Stratified distributional estimates of recurrence times between successive morbidity outcomes are compared between Veterans with/without LE fracture using three estimators: independent identically distributed product limit estimator, Wang–Chang product limit estimator, and a gamma frailty maximum likelihood estimator. It can be seen that the estimator selection can provide a very different showcasing of a recurrence time distribution. There is a change in the time-to-recurrence of recurrent urinary tract infections and pressure ulcers for fracture cases directly following LE fracture, however testing if this difference is statistically significant remains unclear. Causal inference of gap time analyses in observational data with recurrent events is considered and a call for methods in this area is much warranted.