Multistate models are useful for studying exposures that affect transitions among a set of health states. However, they can be challenging to apply when exposures are time-varying. We develop a multistate model and a method of likelihood construction that allows application of the model to data in which interventions or other exposures can be time-varying and an individual may to be exposed to multiple intervention conditions while progressing through states. The model includes cure proportions, reflecting the possibility that some individuals will never leave certain states. We apply the approach to analyze patient vaccination data from a stepped wedge design trial evaluating two interventions to increase uptake of human papillomavirus vaccination. The states are defined as the number of vaccine doses the patient has received. We model state transitions as a semi-Markov process and include cure proportions to account for individuals who will never leave a given state (e.g. never receive their next dose). Multistate models typically quantify intervention effects as hazard ratios contrasting the intensities of transitions between states in intervention versus control conditions. For multistate processes, another clinically meaningful outcome is the change in the percentage of the study population that has achieved a specific state (e.g. completion of all required doses) by a specific point in time due to an intervention. We present a method for quantifying intervention effects in this manner. We apply the model to both simulated and real-world data and also explore some conditions under which such models may give biased results.

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