Comparison of imputation methods for interval censored time-to-event data in joint modelling of tree growth and mortality

The authors link time-to-event models with longitudinal models through shared latent variables when the time of the event of interest is known only to lie within an interval. The context of tree growth and mortality studies presents a natural application of shared parameter joint modelling where a latent feature of each tree impacts both mortality and growth. The authors' developments are motivated by such an application, with the additional caveat that event-times are not known exactly, since the trees are subject to intermittent observation, with the time between measurements extending into decades or longer. Such interval censoring is a common occurrence in similar long-term experiments in resource management, ecology and health research. The additional numerical complexity resulting from interval censored time-to-event data often makes inference for joint models prohibitive. The authors examine properties of three event-time imputation methods that enable application of now standard joint modelling techniques to interval censored time-to-event data. The imputation techniques include the midpoint method, a kernel smoothing method, and a backsolve method which incorporates information from the longitudinal trajectory. Joint analysis of a designed, long-term, forestry experiment is presented, accompanied by a simulation study investigating the properties of the three event-time imputation techniques. The Canadian Journal of Statistics 39: 438-457; 2011 (C) 2011 Statistical Society of Canada