• The Korean Journal of Applied Statistics
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• v.33 no.4
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• pp.379-393
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• 2020

A terminal event such as death may censor an intermediate event such as relapse, but not vice versa in semi-competing risks data, which is often seen in medicine, public health, and epidemiology. We propose a Weibull regression model with a normal frailty to analyze semi-competing risks data when all three transition times of the illness-death model are possibly interval-censored. We construct the conditional likelihood separately depending on the types of subjects: still alive with or without the intermediate event, dead with or without the intermediate event, and dead with the intermediate event missing. Optimal parameter estimates are obtained from the iterative quasi-Newton algorithm after the marginalization of the full likelihood using the adaptive importance sampling. We illustrate the proposed method with extensive simulation studies and PAQUID (Personnes Agées Quid) data.