Abstract
The objective of the present work is to explore the incremental costs of frailty associated with ambulatory health care expenditures (HCE) among the French population of community-dwellers aged 65 or more in 2012. We make use of a unique dataset that combines nationally representative health survey with respondents’ National Health Insurance data on ambulatory care expenditures. Several econometric specifications of generalized linear models are tested and an exponential model with gamma errors is eventually retained. Because frailty is a distinct health condition, its contribution to HCE was assessed in comparison with other health covariates (including chronic diseases and functional limitations, time-to-death, and a multidimensional composite health index). Results indicate that whatever health covariates are considered, frailty provides significant additional explanative power to the models. Frailty is an important omitted variable in HCE models. It depicts a progressive condition, which has an incremental effect on ambulatory health expenditures of roughly €750 additional euros for pre-frail individuals and €1500 for frail individuals.
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Notes
The health index combines several measures by means of a data reduction statistical technique (multiple correspondence analysis). The maths behind this synthetic index make it bear the same properties of variance decomposition in the regression model as the set of variables it is made of. In other words, this health index has the advantage of being mathematically equivalent to a set of health measures, without the disadvantage of a larger number of variables could have on multicollinearity. The health index thus does not modify the coefficient estimates in the regression when substituted to a large set of health measures, and provides more accurate standard errors. Because it is a data reduction process, there is no need for external validity of the health index.
GLM offer great flexibility in the choice of the functional form and the variance distribution. Basu and Rathouz [26] suggest the use of extended estimating equations (EEE) in order to estimate the appropriate link and variance functions. EEE rests on a flexible semi-parametric extension of the GLM model using power function (Box-Cox transformation) for the link function. As such, EEE are also referred to as Power-GLM or PGLM. Notice that the log-link function is a special case where the link parameter (i.e., the denominator of the power-function) is zero. Two alternative forms of variance distribution, power or quadratic, are also considered. EEE simultaneously estimates the link and variance parameters from the data along with the regression coefficients. Not only EEE can be used directly to estimate a model for health care costs they can also be used to select the appropriate link and variance functions for GLM. Comparison between PGLM and corresponding GLM based on standard goodness-of-fit tests provides interesting sensitivity analysis. Our results (not displayed here but available upon request) suggest that the value of link parameter λ = 0.205 is significantly equal to zero (p = 0.646) so the link function should be logarithmic, and estimates of variance parameters θ 1 and θ 2 are statistically equal to 1 (p = 0.602) and 2 (p = 0.369), respectively. This eventually suggests that the appropriate model should be close to our initial choice of GLM with Log-Gamma specification. Notice that a modified Park test on Model 4B strongly supports the choice of Gamma variance (p = 0.769).
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Acknowledgments
The authors would like to thank IRDES staff (Paris, France) for knowledge sharing on ESPS data. This work was supported by a grant from the National Solidarity Fund for Autonomy (CNSA, France)—COMPAS Research Project 2012–2015 (Research on Ageing, Functional disability, and Health Care Expenditures). The research leading to these results has received support from the Innovative Medicines Initiative Joint Undertaking under grant Agreement number 115,621, resources of which are composed of financial contribution from the European Union’s Seventh Framework Programme (FP7/2007–2013) and EFPIA companies’ in kind contribution”.
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Sirven, N., Rapp, T. The cost of frailty in France. Eur J Health Econ 18, 243–253 (2017). https://doi.org/10.1007/s10198-016-0772-7
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DOI: https://doi.org/10.1007/s10198-016-0772-7
Keywords
- Health care expenditures
- Functional disability
- Frailty
- Generalized linear models
- Ambulatory care
- Population aging