A Frailty Model in Crossover Studies with Time-to-Event Response Variable

Abstract

In this article, we develop a model to study treatment, period, carryover, and other applicable effects in a crossover design with a time-to-event response variable. Because time-to-event outcomes on different treatment regimens within the crossover design are correlated for an individual, we adopt a proportional hazards frailty model. If the frailty is assumed to have a gamma distribution, and the hazard rates are piecewise constant, then the likelihood function can be determined via closed-form expressions. We illustrate the methodology via an application to a data set from an asthma clinical trial and run simulations that investigate sensitivity of the model to data generated from different distributions.

Keywords:

• Crossover design
• Frailty
• Maximum likelihood
• Proportional hazards

2000 Mathematics Subject Classification:

• Primary 62Nxx
• Secondary 62P10