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Rodgers M, Epstein D, Bojke L, et al. Etanercept, Infliximab and Adalimumab for the Treatment of Psoriatic Arthritis: A Systematic Review and Economic Evaluation. Southampton (UK): NIHR Journals Library; 2011 Feb. (Health Technology Assessment, No. 15.10.)

# Appendix 19All-cause mortality

## Introduction

All-cause mortality rates for a given age are higher in people with PsA than the general population. Wong et al.29 found that men attending a PsA clinic have a 65% greater mortality rate than the general population in Canada and women 59% greater mortality. A UK population-based study using the General Practice Research Database found 50% greater mortality in patients with severe psoriasis than the general population and no change in this standardised mortality ratio after excluding patients with PsA, indicating that patients with PsA have similar mortality risk to those with severe psoriasis.239 However, there is no clear evidence that biologic therapies change these mortality risks.

Published life tables give mortality risks in the general population for a given age and gender. However, it has been shown that in developed countries, all-cause mortality hazards increase at an exponential rate after the age of 40 years, and a Gompertz function closely approximates these hazards.240 Using a parametric function instead of looking up the hazards directly from life tables requires fewer parameters in the decision model and arguably saves computation time. Furthermore, a parametric hazard function might allow more accurate interpolation of the hazards between years if the cycle length of the model is < 1 year.

This paper describes the estimation of the Gompertz function to predict all-cause mortality hazards.

## Methods

In the Gompertz function, mortality hazards h(x) at age x (where x ≥ 40) are:

h(x) = R exp (a x), where R and a are parameters.

Taking log:

log[h(x)] = log(R) + a x

This linear relationship is straightforward to estimate from life-table hazards using ordinary least-squares regression of log-hazards versus age. These hazards can be adjusted for the PsA population by multiplying by the standardised mortality ratio for the disease.

## Results

The results of the regression of log(life-table hazards) versus age in years are shown in Table 77 for the general population in men and women for the years 2006–8.

#### TABLE 77

Results of regression of log(life-table hazards) versus age in years in the general population aged ≥40 years.

## Conclusion

The Gompertz function can estimate general population life table all-cause hazards with a high degree of precision.

Included under terms of UK Non-commercial Government License.

Etanercept, Infliximab and Adalimumab for the Treatment of Psoriatic Arthritis: A Systematic Review and Economic Evaluation.
Health Technology Assessment, No. 15.10.
Rodgers M, Epstein D, Bojke L, et al.
Southampton (UK): NIHR Journals Library; 2011 Feb.