Modeling of Clinical Phenotypes Assessed at Discrete Study Visits

In studies of clinical phenotypes, such as dementia, disability, and frailty, participants are typically assessed at in-person clinic visits. Thus, the precise time of onset for the phenotype is unknown. The discreteness of the clinic visits yields grouped event time data. We investigate how to perform a risk factor analysis in the case of grouped data. Since visits can be months to years apart, numbers of ties can be large, causing the exact tie-handling method of the Cox model to be computationally infeasible. We propose two, new, computationally efficient approximations to the exact method: Laplace approximation and an analytic approximation. Through extensive simulation studies, we compare these new methods to the Prentice-Gloeckler model and the Cox model using Efron's and Breslow's tie-handling methods. In addition, we compare the methods in an application to a large cohort study (N = 3,605) on the development of clinical frailty in older adults. In our simulations, the Laplace approximation has low bias in all settings, and the analytic approximation has low bias in settings where the regression coefficient is not large in magnitude. Their corresponding confidence intervals also have approximately the nominal coverage probability. In the data application, the results from the approximations are nearly identical to that of the Prentice-Gloeckler model.