ArticleBMC medical research methodology2026
Estimating the hazard ratio of excess mortality using a microsimulation framework with golden section search calibration: a methodological primer.
Article in BMC medical research methodology, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
backgroundExcess 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.
methodsWe 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.
resultsThe 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).
conclusionsThis 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.
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