Regression analysis of longitudinal data with random change point.

A great deal of literature has been established for regression analysis of longitudinal data and in particular, many methods have been proposed for the situation where there exist some change points. However, most of these methods only apply to continuous response and focus on the situations where the change point only occurs on the response or the trend of the individual trajectory. In this article, we propose a new joint modeling approach that allows not only the change point to vary for different subjects or be subject-specific but also the effect heterogeneity of the covariates before and after the change point. The method combines a generalized linear mixed effect model with a random change point for the longitudinal response and a log-linear regression model for the random change point. For inference, a maximum likelihood estimation procedure is developed and the asymptotic properties of the resulting estimators, which differ from the standard asymptotic results, are established. A simulation study is conducted and suggests that the proposed method works well for practical situations. An application to a set of real data on COVID-19 is provided.

Efficient estimation of Cox model with random change point.

In clinical studies, the risk of a disease may dramatically change when some biological indexes of the human body exceed some thresholds. Furthermore, the differences in individual characteristics of patients such as physical and psychological experience may lead to subject-specific thresholds or change points. Although a large literature has been established for regression analysis of failure time data with change points, most of the existing methods assume the same, fixed change point for all study subjects. In this paper, we consider the situation where there exists a subject-specific change point and two Cox type models are presented. The proposed models also offer a framework for subgroup analysis. For inference, a sieve maximum likelihood estimation procedure is proposed and the asymptotic properties of the resulting estimators are established. An extensive simulation study is conducted to assess the empirical performance of the proposed method and indicates that it works well in practical situations. Finally the proposed approach is applied to a set of breast cancer data.

Stochastic Version of EM Algorithm for Nonlinear Random Change-Point Models.

Random effect change-point models are commonly used to infer individual-specific time of event that induces trend change of longitudinal data. Linear models are often employed before and after the change point. However, in applications such as HIV studies, a mechanistic nonlinear model can be derived for the process based on the underlying data-generation mechanisms and such nonlinear model may provide better ``predictions". In this article, we propose a random change-point model in which we model the longitudinal data by segmented nonlinear mixed effect models. Inference wise, we propose a maximum likelihood solution where we use the Stochastic Expectation-Maximization (StEM) algorithm coupled with independent multivariate rejection sampling through Gibbs's sampler. We evaluate the method with simulations to gain insights.

Bayesian piecewise mixture model for racial disparity in prostate cancer progression.

Racial differences in prostate cancer incidence and mortality have been reported. Several authors hypothesize that African Americans have a more rapid growth rate of prostate cancer compared to Caucasians, that manifests in higher recurrence and lower survival rates in the former group. In this paper we propose a Bayesian piecewise mixture model to characterize PSA progression over time in African Americans and Caucasians, using follow-up serial PSA measurements after surgery. Each individual's PSA trajectory is hypothesized to have a latent phase immediately following surgery followed by a rapid increase in PSA indicating regrowth of the tumor. The true time of transition from the latent phase to the rapid growth phase is unknown, and can vary across individuals, suggesting a random change point across individuals. Furthermore, some patients may not experience the latent phase due to the cancer having already spread outside the prostate before undergoing surgery. We propose a two-component mixture model to accommodate patients both with and without a latent phase. Within the framework of this mixture model, patients who do not have a latent phase are allowed to have different rates of PSA rise; patients who have a latent phase are allowed to have different PSA trajectories, represented by subject-specific change points and rates of PSA rise before and after the change point. The proposed Bayesian methodology is implemented using Markov Chain Monte Carlo techniques. Model selection is performed using deviance information criteria based on the observed and complete likelihoods. Finally, we illustrate the methods using a prostate cancer dataset.