Random changepoint segmented regression with smooth transition.

We consider random changepoint segmented regression models to analyse data from a study conducted to verify whether treatment with stem cells may delay the onset of a symptom of amyotrophic lateral sclerosis in genetically modified mice. The proposed models capture the biological aspects of the data, accommodating a smooth transition between the periods with and without symptoms. An additional changepoint is considered to avoid negative predicted responses. Given the nonlinear nature of the model, we propose an algorithm to estimate the fixed parameters and to predict the random effects by fitting linear mixed models iteratively via standard software. We compare the variances obtained in the final step with bootstrapped and robust ones.

Bayesian joint modeling of longitudinal and spatial survival AIDS data.

Joint analysis of longitudinal and survival data has received increasing attention in the recent years, especially for analyzing cancer and AIDS data. As both repeated measurements (longitudinal) and time-to-event (survival) outcomes are observed in an individual, a joint modeling is more appropriate because it takes into account the dependence between the two types of responses, which are often analyzed separately. We propose a Bayesian hierarchical model for jointly modeling longitudinal and survival data considering functional time and spatial frailty effects, respectively. That is, the proposed model deals with non-linear longitudinal effects and spatial survival effects accounting for the unobserved heterogeneity among individuals living in the same region. This joint approach is applied to a cohort study of patients with HIV/AIDS in Brazil during the years 2002-2006. Our Bayesian joint model presents considerable improvements in the estimation of survival times of the Brazilian HIV/AIDS patients when compared with those obtained through a separate survival model and shows that the spatial risk of death is the same across the different Brazilian states. Copyright © 2016 John Wiley & Sons, Ltd.