Finding the right hazard function for time‐to‐event modeling: A tutorial and Shiny application

Parametric time‐to‐event analysis is an important pharmacometric method to predict the probability of an event up until a certain time as a function of covariates and/or drug exposure. Modeling is performed at the level of the hazard function describing the instantaneous rate of an event occurring at that timepoint. We give an overview of the parametric time‐to‐event analysis starting with graphical exploration by Kaplan–Meier plotting for the event data including censoring and nonparametric hazard estimators such as the kernel‐based visual hazard comparison for the underlying hazard. The most common hazard functions including the exponential, Gompertz, Weibull, log‐normal, log‐logistic, and circadian functions are described in detail. A Shiny application was developed to graphically guide the modeler which of the most common hazard functions presents a similar shape compared to the data in order to guide which hazard functions to test in the parametric time‐to‐event analysis. For the chosen hazard function(s), the Shiny application can additionally be used to explore corresponding parameter values to inform on suitable initial estimates for parametric modeling as well as on possible covariate or treatment relationships to certain parameters. Moreover, it can be used for the dissemination of results as well as communication, training, and workshops on time‐to‐event analysis. By guiding the modeler on which functions and what parameter values to test and compare as well as to assist in dissemination, the Shiny application developed here greatly supports the modeler in complicated parametric time‐to‐event modeling.