Comparing crossing hazard rate functions by joint modeling survival and longitudinal data

Abstract

Comparison of two hazard rate functions is important for evaluating treatment effect in studies concerning times to some important events. In practice, it is quite common that the two hazard rate functions cross each other at one or more unknown time points, representing temporal changes of the treatment effect. In certain applications, besides survival data, we also have related longitudinal data available regarding some time-dependent covariates. In such cases, a joint model that accommodates both types of data can allow us to infer the association between the survival and longitudinal data and to better assess the treatment effect. In our research, we propose a modeling approach for comparing two crossing hazard rate functions by joint modeling survival and longitudinal data. Maximum likelihood estimation is used in estimating the parameters of the proposed joint model using the EM algorithm. Asymptotic properties of the maximum likelihood estimators are studied. To illustrate the virtues of the proposed method, we compare the performance of the proposed method with several existing methods in a simulation study. Our proposed method is also demonstrated using a real dataset obtained from a HIV clinical trial. Furthermore, when jointly modeling the survival and longitudinal data in such cases, model selection and model diagnostics are especially important to provide reliable statistical analysis of the data. Therefore, we discuss several criteria for assessing model fit that have been used for model selection, and apply them to a joint modeling approach for comparing two crossing hazard rate functions when both survival and longitudinal data are available. Also, we propose both formal and informal methods for model assessment of the joint modeling approach. Our proposed methods are validated by a simulation study, and they are demonstrated by a real-data example concerning early breast cancer treatments.