A longitudinal study of the effects of age and time to death on hospital costs
Introduction
Although ageing populations are frequently associated with rising health care costs, only one of the many cross-national studies that have examined the determinants of health care expenditures in developed countries (Hitiris and Posnett, 1992) has found the age structure of the population (usually measured by the percentage of population over age 65) to be a consistently significant regressor, when accounting for the effects of income, lifestyle factors, and environmental factors (Gerdtham et al., 1992a, Gerdtham et al., 1992b; Gerdtham et al., 1998, Getzen, 1992, Hitiris and Posnett, 1992, Leu, 1986, O’Connell, 1996, OECD, 1987). Instead, several studies have found that health care costs tend to be associated with the end of life: the 6% of Medicare recipients who die in a given year account for 28% of Medicare expenditures, a finding that has remained stable from the late 1970s to the mid 1990s (Hogan et al., 2001, Lubitz and Prihoda, 1984, Lubitz and Riley, 1993, Riley et al., 1987). Similar findings have been reported for long term care (Stooker et al., 2001). Thus, the association between age and health expenditure may well be an artefact of a stronger relationship between proximity to death and health expenditure.
Using health care expenditure data from two sickness funds in Switzerland that followed costs of deceased individuals from 1983 to 1994, Zweifel et al. (1999) employed a Heckman sample selection model to examine the relationship between real quarterly health care costs and age, sex, type of insurance, quarter before death, and year of incurred costs. For patients who died at age 65 and over, age was irrelevant in determining health care expenditure in the last 2 years of life, while the quarter before death was highly significant, with costs rising closer to death. The model was repeated for health care costs in the last 5 years of life, to find similar age-neutrality of health care costs, once proximity to death was taken into account (Zweifel et al., 1999).
Rigorous modelling of such relationships between age, proximity to death, and costs will prove critical for projections of the effect of demographic change on health care costs. However, several issues must first be addressed. The short time period of analysis used thus far prevents the determination of whether the age-neutrality of expenditures holds when further from death, where age-related chronic diseases may play more of a role. The author himself noted, “A conclusive test of the two competing hypotheses [whether health care expenditures in older age increases as a function of closeness to the time of death or as a function of age] must rest on longitudinal data, which have not been available to this day.” (Zweifel, 2000) Moreover, analysis on a quarterly basis, while providing interesting findings, has limited application in designing expenditure models, since health care projections are estimated in years and not quarters. The study also did not provide any calculation of marginal effects of the variables, which would provide a more interpretable illustration of the effect of various demand drivers of health care than regression coefficients. If information of the effect of proximity to death on health care costs is to be used to inform policy-makers on the impact of ageing on health expenditures, a yearly analysis is needed, with clear estimates of all marginal cost effects.
Econometrically, the previous analyses approached the data as a cross-section of independent cost observations, without taking into account the clustering of longitudinal observations from the same individual. A panel-data approach could provide more robust findings and warrants a comparison to the cross-sectional approach. Additionally, incorporation of interaction effects between age and proximity to death into the regression model—i.e., whether the effects of proximity to death on cost vary depending on patient age—is needed. Finally, an examination of the temporal stability of the effects of age and proximity to death on cost could enhance projection models that are designed to generate predictions for several decades.
This paper addresses all of these issues with a more robust model applied to a large longitudinal dataset, in order to better inform how age and time to death affect health care costs. Section 2 presents the data. Section 3 presents a two-part model that examines the independent effects of age and proximity to death on average yearly hospital costs. Additional patient and hospital characteristics are included to improve the goodness-of-fit of the model, and methods for the estimation of marginal cost effects are described. Section 4 presents the empirical results. Section 5 then addresses the presence of any interaction effect between age and proximity to death, and the stability of the age-cost and time to death-cost relationships over time. Section 6 discusses the results, and Section 7 concludes.
Section snippets
Data
The Oxford Record Linkage Study (ORLS) began in 1963, collecting statistical abstracts longitudinally by patient for all hospital inpatient and day case care, with linkage to birth certificates and death certificates in a defined geographical area of Oxfordshire, England (Gill et al., 1993). The dataset contains information on patient date of birth, date of death, sex, social class, marital status, and cause of death, as well as information on each hospital episode, including dates of admission
Model specification
Because of the high proportion of non-users in any year, we specified a two-part model using STATA 7.0, with a probit regression examining the likelihood of being in hospital in a given year, and an OLS regression examining the cost levels among patients who were in hospital. A two-part model with independent probit and OLS parts was preferred to a Heckman sample selection model for two reasons: first, all zero cost observations were observed rather than unobserved in the ORLS data, and could
Results
The probability of being in hospital demonstrated an exponential increase from year 16 approaching death, with the probability of being hospitalised more than quadrupling from the penultimate to last year of life (Fig. 1). Costs once hospitalised also showed an increasing trend with approaching death from 11 years out, though the relationship was more linear than that for the probability of being in hospital. Average costs (multiplying the probability of being in hospital by costs once in
The interaction between proximity to death and age
After formulating the initial model, the two-part panel data model was re-specified to include an interaction term for age and proximity to death, to see if the effect of approaching death varied by patient age. Unfortunately, including the interaction terms for all 24 years prior to death created a matrix that was too large for STATA 7.0 to use, so the model was limited to 10 years prior to death.
A better understanding of the demographic factors that affect hospital costs
The analyses presented here clearly demonstrate that the effect of proximity to death on hospital costs far overshadow the effect of age. Average hospital costs increased seven-fold in the last three years of life, compared to a 30% cost increase from age 65–80. Using a panel-data analysis instead of a cross-sectional analysis further emphasised the effect of proximity to death, since the more robust panel data framework takes into account the prior hospitalisation history of each individual.
Conclusion
Building considerably upon previous longitudinal work examining the independent effects of age and time to death on health care costs, we found that proximity to death is strongly associated with hospital costs as far back as 15 years before death, and that this effect has remained consistent over the past three decades. Age, while significantly affecting costs in the last year of life, plays a much smaller role, and one which has changed over the past 30 years. The widespread belief that
References (36)
- et al.
Modeling risk using generalized linear models
Journal of Health Economics
(1999) - et al.
An econometric analysis of health care expenditure: A cross-section study of the OECD countries
Journal of Health Economics
(1992) - et al.
The determinants and effects of health expenditure in developed countries
Journal of Health Economics
(1992) - et al.
Estimating log models: to transform or not to transform?
Journal of Health Economics
(2001) - Baltagi, B.H., 1995. Econometric Analysis of Panel Data. Wiley, Chichester,...
- et al.
Use of acute hospital beds does not increase as the population ages: results from a seven year cohort study in Germany
Journal of Epidemiology and Community Health
(2002) - Chamberlain, G., 1984. Panel data. In: Griliches, Z., Intriligator, M. (Eds.), Handbook of Econometrics, vol. 2....
- Dow, W.H., Norton, E.C., 2002. The red herring that eats cake: Heckit versus two-part model redux. Triangle Health...
- Garber, A.M., MaCurdy, T., McClellan, M., 1998. Diagnosis and Medicare expenditures at the end of life. In: Wise, D.A....
- Gerdtham, U.-G., Sogaard, J., Jonsson, B., Andersson, F., 1992b. A pooled cross-section analysis of the health care...
Population aging and the growth of health expenditures
Journal of Gerontology
Computerised linking of medical records: Methodological guidelines
Journal of Epidemiology and Community Health
Medicare beneficiaries’ costs of care in the last year of life
Health Affairs
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2022, Journal of Economic Behavior and OrganizationCitation Excerpt :In the final two years of life, age was irrelevant in determining health care expenditures. The hypothesis that age is a red herring that acts as a proxy for TTD (known as the red herring hypothesis) is supported by a number of studies (Seshamani and Gray, 2004b; Zweifel et al., 2004; Seshamani and Gray, 2004a; Felder et al., 2010; Geue et al., 2014; Wong et al., 2011; Hazra et al., 2018). The rationale behind the red herring hypothesis is that the positive relationship between age and health care expenditure is observed because as individuals age they get closer to death and during the terminal years they receive more aggressive and expensive treatments.