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Background <p>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.</p> Methods <p>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.</p> Results <p>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).</p> Conclusions <p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月16日

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  • Reda Rhellab,
  • Maximiliaan L. Notenboom,
  • Jonathan R.G. Etnel,
  • Jolanda Kluin,
  • Ewout W. Steyerberg,
  • Johanna J.M. Takkenberg,
  • Kevin M. Veen

摘要

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.