Multi-State Modelling Incorporating a Combined Additive and Relative Hazards Model

OBJECTIVES: Research on late effects of treatment among cancer survivors continuous to be increasingly important as more patients are cured from their disease. Multi-state models have proven to be a useful tool to study patient pathways over long follow-up, and treatment-related disease (or mortality) can under certain assumptions be estimated with excess hazards. This typically involves application of relative survival methods, which requires an appropriate population incidence (mortality) file which is often not available. We propose to utilize an appropriately matched control population to enable combined estimation of the expected and excess hazards, and further incorporate this novel model in a multi-state setting.

METHODS: Applicable to one or more of the transitions in a multi-state model, we have developed a flexible parametric survival model which combines one component for the excess hazard and another for the expected rate (based on the control population). In other words, covariate effects are assumed to be multiplicative within both the expected hazard and the excess hazard, while the presence of disease among the cancer patients has an additive effect, hence the excess hazard. By modelling the expected rate, we can appropriately allow for uncertainty. The model is extended to include time-dependent effects and multiple timescales. Following estimation, we quantify results through the prediction of the survival, hazard, and cumulative incidence functions, as well as transformations of these, and crucially with associated confidence intervals on all measures.

RESULTS: The method is illustrated on a study of excess incidence and mortality from diseases of the circulatory system among 1,929 Swedish patients treated for Hodgkin lymphoma.

CONCLUSIONS: The proposed method extends multi-state models by incorporating estimation of expected and excess hazards, the sharing of transition models, and multiple time scales. This enables prediction of survivor trajectories in a real-world setting. We provide user-friendly Stata software.