Speaker
Description
Regression models for the hazard function have been proposed on both a multiplicative and an additive scale. In medical research the former is often suitable, but in some instances, it is more biologically plausible to assume an additive effect on the mortality rate. The best-known example is in population-based cancer patient survival, where the presence of cancer is assumed to have an additive effect on mortality. This excess mortality rate is typically measured using relative survival, where the observed mortality rate in the cancer population is compared to that in a similar cancer-free population (the expected mortality rate). In such analyses, a publicly available population mortality file stratified on sex, year, and age, is matched to the cancer population, and included in the relative survival model as an offset, and hence assumed to be measured exactly (i.e., without uncertainty). However, situations exist where this standard approach is not optimal or even possible. For example, it might be necessary to stratify the expected mortality on additional factors, such as socio-economy or comorbidity. Alternatively, a suitable population mortality file might simply not exist for the population at hand.
Here, we propose a flexible parametric excess hazard model on the log hazard scale, incorporating a modelled expected rate from a control population (e.g., matched comparators). By modelling the expected rate, we appropriately allow for uncertainty. Covariate effects are assumed to be multiplicative within the expected and the excess hazard, while the presence of disease among the studied population (e.g., cancer patients) has an additive effect. Following estimation, results are quantified through prediction of the survival, hazard, and cumulative incidence functions, as well as transformations of these, and crucially with associated confidence intervals on all measures.
Bias and coverage of predictions are evaluated using simulated data mimicking a 1:5 matched cohort study, with cancer cases followed from cancer diagnosis and matched comparators followed from matching date (which corresponds to the diagnosis date for the corresponding cancer case). We further illustrate the method using a population-based dataset of rectal cancer patients diagnosed 2007-2016, with comparators matched 1:6 on: sex, age, country, and being cancer-free using the Colorectal Cancer DataBase Sweden (CRCBaSe).
The proposed method, offers an alternative in situations when standard relative survival methods do not suffice, and is implemented in the Stata package stexcess (github.com/RedDoorAnalytics/stexcess).
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