Estimating the hazard ratio of excess mortality using a microsimulation framework with golden section search calibration: a methodological primer

BACKGROUND: Excess mortality in a population with a disease can be defined as extra mortality observed compared to the matched-general population, and expressed as a hazard ratio (HR). While excess hazard models and cure models exist, these commonly need patient-level data. In this paper, we show a method for estimation of excess mortality with aggregated data. METHODS: We detail the estimation of excess mortality in a microsimulation framework using the golden section search algorithm. This iterative algorithm identifies a local minimum within a predefined search interval. The overall excess mortality and residual excess (remaining mortality after accounting for modelled events) is estimated by calibrating microsimulation-derived survival curves to observed patient-sample survival curves. R code is provided. We apply the method to a study of aortic valve repair in non-elderly adults. RESULTS: The method enabled efficient estimation of excess mortality, expressed as overall and time-dependent hazard ratios through a piecewise function. The estimated excess mortality HR in the case-study was 2.70 without accounting from modelled events and 2.43 while accounting for modelled events, and the HR increased over time (1.23; 2.32; 5.50 at 0-60 months, 61-120 months and 121-188 months, respectively). CONCLUSIONS: This microsimulation framework provides an accessible, efficient method for estimating time-varying excess mortality hazard ratios, allowing for estimation of residual excess mortality, which excludes mortality due to modelled events, using only aggregated input data.