Estimation of non-monotonic transition rates in a semi-Markov process with covariates adjustments and application to caregivers' stress data.

With the large ongoing number of aged people and Alzheimer's disease (AD) patients worldwide, unpaid caregivers have become the primary sources of their daily caregiving. Alzheimer's family caregivers often suffer from physical and mental morbidities owing to various reasons. The aims of this paper were to develop alternate methods to understand the transition properties, the dynamic change, and the long-run behavior of AD caregivers' stress levels, by assuming their transition to the next level only depends on the duration of the current stress level. In this paper, we modeled the transition rates in the semi-Markov Process with log-logistic hazard functions. We assumed the transition rates were non-monotonic over time and the scale of transition rates depended on covariates. We also extended the uniform accelerated expansion to calculate the long-run probability distribution of stress levels while adjusting for multiple covariates. The proposed methods were evaluated through an empirical study. The application results showed that all the transition rates of caregivers' stress levels were right skewed. Care recipients' baseline age was significantly associated with the transitions. The long-run probability of severe state was slightly higher, implying a prolonged recovery time for severe stress patients.