Should we adjust health expenditure for age structure on health systems efficiency? A worldwide analysis

INTRODUCTION: Healthcare expenditure, a common input used in health systems efficiency analyses is affected by population age structure. However, while age structure is usually considered to adjust health system outputs, health expenditure and other inputs are seldom adjusted. We propose methods for adjusting Health Expenditure per Capita (HEpC) for population age structure on health system efficiency analyses and assess the goodness-of-fit, correlation, reliability and disagreement of different approaches. METHODS: We performed a worldwide (188 countries) cross-sectional study of efficiency in 2015, using a stochastic frontier analysis. As single outputs, healthy life expectancy (HALE) at birth and at 65 years-old were considered in different models. We developed five models using as inputs: (1) HEpC (unadjusted); (2) age-adjusted HEpC; (3) HEpC and the proportion of 0–14, 15–64 and 65 + years-old; (4) HEpC and 5-year age-groups; and (5) HEpC ageing index. Akaike and Bayesian information criteria, Spearman’s rank correlation, intraclass correlation coefficient and information-based measure of disagreement were computed. RESULTS: Models 1 and 2 showed the highest correlation (0.981 and 0.986 for HALE at birth and HALE at 65 years-old, respectively) and reliability (0.986 and 0.988) and the lowest disagreement (0.011 and 0.014). Model 2, with age-adjusted HEpC, presented the lowest information criteria values. CONCLUSIONS: Despite different models showing good correlation and reliability and low disagreement, there was important variability when age structure is considered that cannot be disregarded. The age-adjusted HE model provided the best goodness-of-fit and was the closest option to the current standard. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s13561-023-00421-2.