Modelling disease-specific mortality using an extended multi-state model

When examining the survival probability for a group of patients, various events that may occur through time can have an impact on their survival rate. Multi-state models have become a standard tool for considering such intermediate events in the analysis (e.g., relapse, disease progression, adverse event) and understanding their impact on the patients’ outcome. Nowadays, such models are widely used in the medical practice for further understanding the burden of the disease in question as well as the recovery process. In this work, the focus will be on analysing the mortality with respect to the cause of death, in the case when the cause of death information is not available in the data. Instead of considering all-cause mortality, the goal will be to distinguish between disease-specific and other-cause (population) mortality. The field of relative survival has dealt with such questions where distinguishing between the two causes is done with the help of external population mortality tables. The project will consider cause-specific mortality in a general multi-state model. The link between multi-state models and relative survival has been discussed in a previous article [1] where a merged approach has been proposed. However, this article concentrates solely on non-parametric estimation; in this project, the focus shifts to regression modelling. Until now, numerous regression approaches have been suggested for general multi-state models (mostly based on a Cox-type model), but this topic has been scantly covered for the cause-specific case. The main aim of the project will be to define a comprehensive regression framework that will deal with the primary difficulties that arise in this setting, like for example: considering intermediate events in the model and late entry of patients, defining estimators for the baseline hazard and regression coefficients, providing model predictions, and variance estimation. A crucial part of working on the suggested methodology will be to consider its theoretical properties and understand how it performs in practice. Thus, an all-around simulation study will be conducted which will give further insight into the characteristics of the statistical framework and check if any possible pitfalls exist. The motivation for defining the extended multi-state model has come from the medical practice and in the past year, the project leader has co-authored three articles that portray the clinical relevance of this methodology. The newest development will also be used on clinical data with the aim of obtaining further knowledge about the disease. It is our belief that such applications will showcase the relevance of this work in various clinical settings and present its practical benefits. Any new statistical methodology is commonly complemented with a user-friendly software implementation, and this will also be one of the project goals. The implemented code will rely upon the R packages relsurv (originally written by Maja Pohar Perme; currently maintained by the project leader) and mstate (written and maintained by the Dutch LUMC researchers Hein Putter and Liesbeth C. de Wreede). Both packages provide various functions for using relative survival and multi-state models and were also used in the previous work [1]. Thus, the developed methodology will finely fit within the already developed software. The research that has been performed so far [1] has been done with experts in both relative survival (Pohar Perme) and multi-state models (Putter, de Wreede). Collaborating with these researchers will also be of primary interest during the project so that all relevant details are well-discussed with leading researchers in these fields. [1] Manevski D, Putter H, Pohar Perme M, Bonneville EF, Schetelig J, de Wreede LC. Integrating relative survival in multi-state models—a non-parametric approach. SMMR. 2022 Jun;31(6):997-1012.