Background: Dementia is a chronic disease characterised by neurodegenerative processes and vascular brain injury. In prospective population-based cohorts, the diagnosis of dementia is usually interval censored as it is made by a neuropsychologist at follow-up visits so that the exact time of dementia is not exactly known (1). In addition, dementia and then death may occur in between visits before a diagnosis of dementia can be made. The illness-death model for interval-censored data accounts for the uncertainty on the time of dementia and the probability of having dementia until the last visit or death (2). In this work, we proposed a new regularised estimation procedure for a high dimensional illness-death model with interval censored data, that performs variable selection. Variable selection will allow us to increase predictive abilities and possibly identify new risk factors of dementia.

Methods: We considered a proximal gradient algorithm maximising the regularised likelihood with lasso penalty on the transitions to dementia and those to death with and without dementia. Our algorithm simultaneously estimates all three transitions' regression parameters while having different penalty parameters on each transition. The optimal penalty parameter is chosen via the Bayesian Information Criteria. The performances of our algorithm were evaluated in simulations and compared to alternative strategies considering the oracle model, and standard competing risk approach that neglects interval censoring.

Results: The illness-death model accounting for interval-censored data provided a Mean Square Error on Prediction to dementia (MSEP) distribution close to the one of the oracle model and good performances for variable selection. In comparison, the standard competing risk model showed worse predictive abilities and tended to select irrelevant variables for some transitions when associated with another transition. 

Conclusion: Neglecting interval censoring of dementia can deteriorate prediction of future cases of dementia and lead to a misleading selection of risk factors. Variable selection in illness-death model handling interval censoring data allows to accurately predict future cases of dementia while identifying risk factors of dementia among a large number of predictors.

1. Leffondré K, Touraine C, Helmer C, Joly P. Interval-censored time-to-event and competing risk with death: is the illness-death model more accurate than the Cox model? Int J Epidemiol. août 2013;42(4):1177‑86.

2. Joly P. A penalized likelihood approach for an illness-death model with interval-censored data: application to age-specific incidence of dementia. Biostatistics. 1 sept 2002;3(3):433‑43.