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Health measures and long-term care use in the European frail population

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This paper explores the association between health measures and long-term care (LTC) use in the 70+ old population. We examine how different measures of health—subjective versus objective—predict LTC use, provided either formally or informally. We consider an absolute measure of subjective health, the grade given by the individual to his/her health status, and additionally construct a relative measure capturing the difference between this grade and the average grade given to health by individuals sharing the same characteristics. Conceptually, this difference comes from the perception of the individual, corresponding to both the private health information and the reporting behavior affecting self-rated health. We use the baseline data from the SPRINTT study, an ongoing randomized control trial on 1519 subjects facing physical frailty and sarcopenia (PF&S) in 11 European countries. Our sample population is older than 70 (mean: 79 years) and comprises a majority (71%) of women. Results show that self-rated health indicators correlate to formal care even when objective health measures are included, while it is not the case for informal care. Formal care consumption thus appears to be more sensitive to the individual's perception of health than informal care.

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Data access is subject to approval from the SPRINTT consortium.

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  1. A 400-m walk test is also available in the data, but since walking speed is already considered in a subtest of the SPPB, we do not include it in our analysis of objective variables. The correlation coefficient between the SPPB score (either total or subtest) and the walking speed from the 400-m walk test is of about − 0.5.

  2. To define an individual as frail, we use the cut-off points defined by the FNIH to categorize individuals: males whose grip strength is lower than 26 kg, and females whose grip strength is lower than 16 kg, are categorized in the “low grip strength'' category [53]. Similarly, males with an aLM lower than 19.75 kg and females with an aLM lower than 15.02 kg are in the “low aLM local'' category [54]. Regarding the SPPB score, we considered a threshold of 6 to identify frailest participants [55, 56]).

  3. These domains are the following: heart, vascular, hematopoietic, respiratory, eyes/ears/nose/throat/larynx, upper and lower gastrointestinal (GI), liver, renal, genitourinary, musculoskeletal/intergument, neurological, endocrine/metabolic and breast, and psychatric.

  4. This last variable is divided into three categories: (1) superior, corresponding to managers, administrators, skilled crafts, and professional, technical, and related occupations; (2) service, corresponding to military members, clerical and sales occupations, laborers; (3) manual, corresponding to farmers, operators, and related occupations.

  5. The 106 individuals that are excluded because of missing values are more frequently women, living with someone (else than a spouse), having a lower number of children and education level, with and missing values for income and previous job.

  6. AIC is − 2(LL − M) and BIC is − 2LL + MlnN where LL is the model log likelihood, M is the number of parameters, and N is the number of observations. They measure the loss of information coming from the model: the lower the indicator, the better.

  7. A model including the number of medical diagnostics in categorical form rather than in linear form shows that the effect is driven by one category with several medical diagnostics and a low LTC use. Results are available upon request.


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The research leading to these results has received support from the Innovative Medicines Initiative Joint Undertaking under grant agreement no 115621, resources of which are composed of financial contribution from the European Union’ Seventh Framework Programme (FP7/2007–2013) and European Federation of Pharmaceutical Industries and Associations (EFPIA) companies’ in kind contribution. It has benefited from valuable feedbacks from the participations of the seminar of Laboratoire Interdisciplinaire de Recherche Appliquée en Economie de la Santé (LIRAES EA4470) and from the workshop “Atelier bien-être” at the Bureau d’Economie Théorique et Appliquée (BETA UMR7522).

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Apppendix A: Details on the construction of the relative self-rated health indicator

This Appendix presents the construction of the relative SRH indicator. The procedure is inspired from the methodology proposed by Layes et al. [35], designed in three steps.

The first step consists in regressing the grade given to his/her health status by the individual on the objective health variables. The distribution of the subjective grade is described by Fig. 3. The mean grade given to health in our sample is 63.7, with a median value at 65 and a standard deviation of 18.6. In the objective variables, we include several clinical outcomes (SPPB, aLM, grip strength, number of medical diagnostics, MMSE, and CESD). These variables are interacted together to improve the predictive power of our model. We additionally include demographic dimensions (sex and age) and recent health events (hospital use in the last 6 months, fall in the last year), while controlling for the individual's country to compare people in similar context. We have tested several sets of variables in this first step and have finally chosen the combination that maximizes the explanatory power of our model (R2). The main characteristics of the different estimations which we have considered are summarized in Table 5. The comparisons of the different estimations show that the explanatory power of the model is considerably increased when including successively country fixed effects, presence of depressive symptoms, and recent health events. A flexible specification allowing interactions between the variables additionally contributes to improve the explanatory power of the model. M5 is the final model we have chosen to construct the relative indicator.

Fig. 3
figure 3

Distribution of self-rated health in the sample. Sample: 1413 individuals included in the SPRINTT experiment

Table 5 Self-rated health regressed on objective variables

This step is described by the following equation:

$$S{H}_{i}= {\gamma }_{0}+{\gamma }_{1}{H}_{i}+{\gamma }_{2}{X}_{i}+{\gamma }_{3} {H}_{i}\#{H}_{i}+{\epsilon }_{i},$$

where \({H}_{i}\) is a set of objective health variables (SPPB, aLM, grip strength, number of medical diagnostics, cognitive troubles, depressive symptoms, hospitalization, and recent fall in Model 5), \({X}_{i}\) is a set of socio-demographic controls (age, sex, country fixed effects), and \({H}_{i}\#{H}_{i}\) is a set of interactions terms of each health variable.

In the second step, the estimation of this model is used to predict the health grade that can be expected from each individual, given his/her objective characteristics. The deviation of the expected grade of individual i (\(\widehat{S{H}_{i}}\)) from the observed grade \((S{H}_{i}\)) is denoted \(\text{dev}_{i}\) and is defined as:


This deviation measures the difference between the observed grade and the average grade given to health by individuals sharing the same objective characteristics.

We use this deviation to construct our relative SRH indicator. This indicator is regarded as positive when the observed grade is much higher than the expected grade (difference higher than one standard deviation). Conversely, the negative reporting corresponds to the situation when the observed grade is lower than the expected grade. Consistent reporting is the case when the observed grade is close to the expected grade (difference lower than one standard deviation).

Appendix B: Countries represented in the sample


Number of observations (% of the sample)


51 (3.61)

Czech Republic

113 (8.00)


137 (9.70)


154 (10.9)


123 (8.70)


23 (1.63)


421 (29.79)

The Netherlands

54 (3.82)


93 (6.58)


179 (12.67)

United Kingdom

65 (4.60)

  1. Sample: 1413 individuals included in the SPRINTT experiment

Appendix C: Alternative estimations

Appendix C.1: Functional forms

We test the sensitivity of our results to the functional form used in our baseline estimations. Instead of a biprobit model, we fit a system of seemingly unrelated regression equations (SURE). The two equations correspond to linear probability models and the model allows the unobserved determinants of the two types of care to be correlated. Our results are overall robust to this change in the functional form, even though it is associated with a loss a precision. In particular, the coefficient of the grade given to health overtakes conventional significant threshold (p value = 0.119) (Table 6).

Table 6 Test of the sensitivity of results to the functional form

Appendix C.2: Dealing with omitted variable bias

It is possible that an omitted variable affects both LTC use and perception. To test this hypothesis, we have implemented the procedure proposed by Oster [57] to evaluate robustness to omitted variable bias. Assuming the correlation between the unobserved variables and the variable of interest is proportional to the correlation between the observable controls and the variable of interest, this test makes it possible to compute a biased-adjusted coefficient for the main effect of interest. This coefficient depends on coefficient and R-squared movements when taking unobservables into account. The test can only be performed after linear regression models: we thus estimate independent linear probability models. A key input in the test is the hypothetical R-squared from a regression where both observed and unobserved controls are included. Following Oster [57], we assume that this value equals 1.3 times the observed R-squared of the regression. Since two variables cannot be tested simultaneously, we only include for the relative indicator the positive category, and the reference is then consistent and negative (both categories are not significantly different in our baseline estimations). Table 7 presents the identified set of regression coefficients concerning the correlation of subjective health measures with each LTC outcome. Since these sets exclude zero, the results from the baseline regressions can be considered robust to omitted variable bias.

Table 7 Oster tests

Appendix C.3: Intensive margin

In the main results, our interest variables are binary: we consider the utilization of formal care or informal care. Among individuals using care, however, volumes consumed might be highly heterogenous. In the experiment, individuals additionally provide information of the frequency of care provision and the average duration of each intervention. Though the volume declared is likely to be subject to measurement errors, it gives an insight of the total volume of care received by users. Seven subjects were lost, because they did not indicate the volume of IC/FC use.

We have estimated an alternative model considering the intensive margin of formal and informal care use. Explanatory variables are the log-number of hours declared by the individual. To deal with zero values of non-consumers, we add 1 to the value of these variables. According to Table 8, the sign of the association is unchanged, while absolute measure of SRH looses significance and the results on relative SRH are robust.

Table 8 Correlation of subject if health measures with formal care and informal care hours

Appendix C.4: Availability of informal caregivers


















Est (SE)

Est (SE)

Est (SE)

Est (SE)

Est (SE)

Est (SE)

Est (SE)

Est (SE)

Subjective health

 Grade (/100)

− 0.715*** (0.249)

− 0.631*** (0.228)


− 0.409 (0.261)

− 0.301 (0.246)


 Relative indicator



− 0.110 (0.131)

− 0.178 (0.125)



0.197 (0.126)

0.067 (0.125)

  Ref: consistent

Objective health


 Number of frailty indicators


0.131** (0.052)

0.167*** (0.049)

0.131** (0.052)

0.165*** (0.049)

0.135*** (0.052)

0.168*** (0.049)

 Medical diagnostics


0.091*** (0.028)

0.049* (0.029)

0.087*** (0.028)

0.046 (0.029)

0.094*** (0.029)

0.047 (0.029)

 Has been hospitalizeda


0.154 (0.111)

0.034 (0.109)

0.146 (0.111)

0.031 (0.109)

0.151 (0.112)

0.034 (0.109)

 Fell in the last year


0.290*** (0.106)

0.104 (0.107)

0.279*** (0.106)

0.095 (0.107)

0.295*** (0.106)

0.111 (0.107)

 Depressive symptoms (high CESD)


0.031 (0.093)

0.115 (0.087)

0.026 (0.094)

0.111 (0.087)

0.038 (0.094)

0.120 (0.087)

 Cognitive troubles (low MMSE)


0.267*** (0.097)

0.390*** (0.091)

0.235** (0.100)

0.369*** (0.094)

0.262*** (0.097)

0.389*** (0.092)






  1. 1253 individuals included in the SPRINTT experiment and having spouse and/or children
  2. Robust standard errors in parentheses
  3. ***p < 0.01, **p < 0.05, *p < 0.1. Coefficients from biprobit estimations. Country fixed effects are included
  4. aEmergency or hospital use during the last 6 months

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Roquebert, Q., Sicsic, J., Rapp, T. et al. Health measures and long-term care use in the European frail population. Eur J Health Econ 22, 405–423 (2021).

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