Penalised maximum likelihood estimation in multi-state models for interval-censored data

Abstract

Continuous-time multi-state Markov models can be used to describe transitions over time across health states. Given longitudinal interval-censored data on transitions between states, statistical inference on changing health is possible by specifying models for transition hazards. Parametric time-dependent hazards can be restrictive, and nonparametric hazard specifications using splines are presented as an alternative. The smoothing of the splines is controlled by using penalised maximum likelihood estimation. With multiple time-dependent hazards in a multi-state model, there are multiple penalty parameters and selecting the optimal amount of smoothing is a challenge. A grid search to estimate the penalty parameters is computational intensive especially when combined with methods to deal with interval-censored transition times. A new and efficient method is proposed to estimate multi-state models with splines where the estimation of the penalty parameters is automatic. A simulation study is undertaken to validate the method and to illustrate the effect of interval censoring. The feasibility of the method is illustrated with two applications.