A stochastic estimation procedure for intermittently-observed semi-Markov multistate models with back transitions

A semi-Markov multistate cure model for estimating intervention effects in stepped wedge design trials

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.

A new framework for semi-Markovian parametric multi-state models with interval censoring

There are few computational and methodological tools available for the analysis of general multi-state models with interval censoring. Here, we propose a general framework for parametric inference with interval censored multi-state data. Our framework can accommodate any parametric model for the transition times, and covariates may be included in various ways. We present a general method for constructing the likelihood, which we have implemented in a ready-to-use R package, smms, available on GitHub. The R package also computes the required high-dimensional integrals in an efficient manner. Further, we explore connections between our modelling framework and existing approaches: our models fall under the class of semi-Markovian multi-state models, but with a different, and sparser parameterisation than what is often seen. We illustrate our framework through a dataset monitoring heart transplant patients. Finally, we investigate the effect of some forms of misspecification of the model assumptions through simulations.

Multistate models for the natural history of cancer progression

BACKGROUND

Multistate models can be effectively used to characterise the natural history of cancer. Inference from such models has previously been useful for setting screening policies.

METHODS

We introduce the basic elements of multistate models and the challenges of applying these models to cancer data. Through simulation studies, we examine (1) the impact of assuming time-homogeneous Markov transition intensities when the intensities depend on the time since entry to the current state (i.e., the process is time-inhomogenous semi-Markov) and (2) the effect on precancer risk estimation when observation times depend on an unmodelled intermediate disease state.

RESULTS

In the settings we examined, we found that misspecifying a time-inhomogenous semi-Markov process as a time-homogeneous Markov process resulted in biased estimates of the mean sojourn times. When screen-detection of the intermediate disease leads to more frequent future screening assessments, there was minimal bias induced compared to when screen-detection of the intermediate disease leads to less frequent screening.

CONCLUSIONS

Multistate models are useful for estimating parameters governing the process dynamics in cancer such as transition rates, sojourn time distributions, and absolute and relative risks. As with most statistical models, to avoid incorrect inference, care should be given to use the appropriate specifications and assumptions.