Keywords: dementia, EM algorithm, frailty, illness-death model, non-parametric; semi-competing risks
Semi-competing risks data are a variant of competing risks data. They occur when non-terminal events can be censored by well-defined terminal events, but not vice versa. The so-called illness-death model has been widely studied, which can be used to characterize semi-competing risks data. We utilize the shared gamma frailty Markov-model for non-parametric maximum likelihood estimation (NPMLE) of three hazards, namely healthy status to the non-terminal event, and healthy status to the terminal event with and without experiencing the non-terminal event. Particularly, we investigate when the maximum likelihood approach fails due to ill-behaved likelihood with simulation studies, and conclude that the conventional NPMLE for semi-competing risks data may not always be valid in practice. Practical guidelines based on plotting the profile likelihood are provided to determine whether semi-competing risks data can be analyzed with the NPMLE method under the shared gamma frailty Markov-Model. It is applied to the Indianapolis Ibadan Dementia Project data to illustrate how the incidence of dementia impacts mortality.