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Differing types of medical prevention appeal to different individuals

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Abstract

We analyze participation in medical prevention with an expected utility model that is sufficiently rich to capture diverging features of different prevention procedures. The predictions of the model are not rejected with data from SHARE. A decrease in individual health decreases participation in breast cancer screening and dental prevention and increases participation in influenza vaccination, cholesterol screening, blood pressure screening, and blood sugar screening. Positive income effects are most pronounced for dental prevention. Increased mortality risk is an important predictor in the model for breast cancer screening, but not for the other procedures. Targeted screening and vaccination programs increase participation.

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Notes

  1. None of the general characteristics used in Jusot et al. [18] turn out to have a significant effect for the explanation of influenza vaccination and breast cancer screening.

  2. In our model a “period” is defined as the normal amount of time in which an individual has to choose whether or not to participate in prevention. For influenza, a period is a 1-year interval, since an individual will have to decide to participate in prevention every year before the influenza season starts. For breast cancer screening on the other hand, the normal screening interval is 2 years. Furthermore, we assume for simplicity and clarity that this amount of time corresponds to the period in which a disease can develop into a severe illness that requires curative care, or in case of a fatal disease might result in death. While this is true for many diseases such as e.g., influenza, it is not always the case. The assumption can however be relaxed and our model adapted so that the prevention period and the period of disease development do not necessarily coincide. In this section, we drop the subscript t for notational convenience.

  3. A natural interpretation of our model is that h refers to the “health flow” corresponding to a Grossman-type health capital stock, and that m refers to a specific health shock. Our model then assumes that the health (and hence utility) effects of a specific type of shock depend on its interaction with the general background health level.

  4. The terminology “early” and “late” stage is just used as a convenient shortcut to indicate different levels of severity. Since we will later restrict ourselves to a two-period model, the timing of the treatment will not be analyzed in detail.

  5. Income can be used for consumption goods that are complements to good health, e.g., travel, or substitutes for good health, e.g., assistance with self-care or a guide dog for the blind. The existing empirical results with respect to the sign and the magnitude of the cross-effect between health and income (or consumption) are inconclusive [14]. The results for the unrestricted utility function u(yhm) are available from the authors on request.

  6. After a positive test result, a more conclusive second test (e.g., breast tissue biopsy) can reveal that the disorder was falsely suggested in the first round while the individual does not have the disorder. This is defined in the literature as a false-positive test. The frequency of false-positive results is captured by the test specificity, which is the probability that the test yields a negative result for an individual without the disorder. In order to simplify our analysis we abstract from the possibility of a second screening round. The results from a more complete model are similar. They can be obtained from the authors on request.

  7. Of course, this just means that the two parameters play the same role in both models, not that their numerical values are identical when comparing different procedures.

  8. Results for a many-periods model can be obtained from the authors on request. If there are more periods, the issue of adherence to a prevention strategy can, in principle, become relevant (see, e.g., [10, 19]).

  9. If \(I(nf)=0\), the patient dies at the end of the first period.

  10. Another assumption that influences the comparative statics with respect to the future is that the frequency of prevention and the period of disease development coincide. If this is not the case, and e.g., prevention is recommended to be taken yearly while the disorder needs more than a year to develop to the late stage of the disorder, the prevention decision is taken in period 1 and potential curative treatment occurs in period 2. The consequence of this discrepancy is again that the future matters for a non-fatal disease, and that the marginal effects (w.r.t. \({\beta} ;{p_{x,2}};{V_{2}}\)) go in the same direction as described for a fatal disease.

  11. The details of the calculations are given in “Appendix 1”.

  12. Similar arguments are given in Maurer [22] and Mullahy [23].

  13. The American Cancer Society [1] distinguishes between 4 cancer stages. If breast cancer is detected and treated early (stage 1 or 2), the 5 year survival rate is nearly 100 %, whereas survival rates drop to 20 % if cancer is detected in stage 4.

  14. It should be noted however that mortality varies substantially by influenza virus type and age group. Most of the influenza- and pneumonia-related deaths occur among adults aged 65 or more. Hadler et al. [15] suggest case fatality rates per age group for seasonal influenza of 0.001–0.004 % in the age group of 0–17 years olds, 0.003–0.011 % for adults between 18 and 64 and 0.11–0.44 % for those aged 65 or more.

  15. Cardiovascular diseases are the main cause of death in Western countries. In the US, the incidence of heart diseases in 2012 is 18 and 30 % for non-institutionalized individuals aged above 45 and 65, respectively [3]. The mortality rate over the entire population in 2010 is 0.5 and 1.2 %, for individuals aged above 45 and 65, respectively [24].

  16. Belkar et al. [2] show that neglecting to distinguish between “aware” and “unaware” individuals may lead to a selection effect. However, they also show that the problem is not very serious if “censoring is modest and positive dependence between awareness and choice is substantial” (p. 44). This is likely to be the case with our data.

  17. We set preventive dental care equal to one if individuals reported visiting a dentist in the last 12 months for preventive use or prevention and treatment combined. The value is set to zero if the individual has not seen a dentist or has seen him/her only for treatment. Our empirical results are similar when using an alternative specification with a value equal to one if the dentist is contacted for prevention use only and zero otherwise.

  18. All other SHARE data discussed below were collected using a computer assisted personal interviewing (CAPI) program. A self-administered drop-off questionnaire can be biased, since lower socio-economic groups tend to be underrepresented. Therefore, the answers to the drop-off questionnaire might not be representative of the population. However, Jusot et al. point out that prevalence rates obtained in the drop-off questionnaire correspond to available published OECD population data for most countries [18].

  19. The activity questions that are used (yes/no): are you able to... dress?, walk across a room?, bathe or shower?, eat?, get in and out of bed? use the toilet?

  20. The mobility questions that are used (yes/no): Are you able to... walk 100 m?, get up from a chair after sitting for long periods?, climb stairs?, reach your arms above shoulder level?, carry weights over 5 kg?

  21. There exists some doubt as to whether or not the answers to survival questions have predictive value for real longevity [33]. Moreover, skeptics point at a heaping of responses at focal-point values of 0, 50, or 100 %, hinting at biased response [6]. On the other hand, an individual has access to superior information about herself than is incorporated in a life table. For a discussion, see e.g., [26] or [43]. Peracchi and Perotti [26] using SHARE data and Smith et al. [30] using HRS data find evidence that subjective beliefs about longevity relate to observed survival patterns. For our purpose, it is not crucial whether or not individual beliefs are an accurate reproduction of reality, since the prevention decisions of individuals will be influenced by their subjective beliefs including biases.

  22. One of the reasons for using this decile information is that the income variable is defined differently in waves 1 and 2 of SHARE. In wave 1 it is reported before taxes and contributions, in wave 2 it is reported after taxes and contributions. To check the robustness of our findings we also introduced the two wave-specific income variables as separate variables in our regressions. In that way, we allow for the possibility that the income effects are different in the two waves (possibly because of the change in definition). Our empirical results and conclusions (see below) remain very similar (results available on request).

  23. We create dummies for highest educational degree: primary education (ISCED 0–1), lower secondary education (ISCED 2), upper secondary education (ISCED 3–4), higher vocational education and university degree (ISCED 5–6).

  24. By population-based screening, we refer to an organized screening program (with a specified target group, a specific screening test, intervals, quality assurance, monitoring and other procedures) managed by an organization at a national or regional level. In addition to the high degree of organization, every eligible individual served by the screening program is individually identified and personally invited to attend screening. Opportunistic screening on the other hand refers to screening outside an organized program and without personal invitation. The initiative to perform a screening examination is taken either by the individual or the health care provider. Opportunistic screening may or may not be performed according to the public screening policy (if one exists), e.g., it may be applied to individuals outside the targeted population or according to a different screening technique.

  25. It takes time to set up a population-based program. By implementation status, we refer to the progress made in this process. The starting point is a planning phase, followed by a pilot project, a rollout over the entire region/country and finally a completed population-based screening program.

  26. We give some examples. If there are regional differences within a country (e.g., in implementation status of a screening program), this information is matched to the individuals living in these different regions. If a country implements a specific target group (e.g., women between 50 and 69 years old), a woman in that country belonging to that target group will get a value 1 for the corresponding variable, while the other women get a value zero.

  27. VENICE is an acronym for Vaccine European New Integrated Collaboration Effort.

  28. A similar position is taken by Howard [16, p. 893].

  29. Some authors have used information in the third wave of SHARE to analyze the influence of reported past behavior in regard to (non-)participation in breast cancer screening [42, 43] and in dental prevention [21].

  30. The strongest arguments against using the expected utility model can be found in Oster et al. [25]. However, they analyze medical testing decisions for Huntington’s disease—where at this moment no curative treatment is available.

  31. Examples in the literature are Bradford et al. [5] for time preferences and Carman and Kooreman [8] for subjective probabilities.

  32. If the time horizon is longer, as in the multi-period model, the effects of \({p_{2}}\) become more complex (results can be obtained from the author on request). Given that the individual can choose to participate in prevention in period 2 as well, she can counter partly the utility loss due to an increased risk of illness.

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Acknowledgments

Comments from Chiara Canta, Sverre Grepperud, Henri Ghesquiere, Tom Van Ourti, Erwin Ooghe, Geert Dhaene, Magne Mogstad, two anonymous referees, and participants at the Public Economics seminar in Leuven, the Ecore summer school and the EHEW 14 conference in Lyon are gratefully acknowledged. Nicolas Bouckaert is grateful to the Research Foundation—Flanders for providing a research fellowship. This paper uses data from SHARELIFE release 1, as of November 24th 2010 or SHARE release 2.3.1, as of July 29th 2010. The SHARE data collection has been primarily funded by the European Commission through the 5th framework programme (project QLK6-CT-2001- 00360 in the thematic programme Quality of Life), through the 6th framework programme (Projects SHARE-I3, RII-CT- 2006-062193, COMPARE, CIT5-CT-2005-028857, and SHARELIFE, CIT4-CT-2006-028812) and through the 7th framework programme (SHARE-PREP, 211909 and SHARE-LEAP, 227822). Additional funding from the U.S. National Institute on Aging (U01 AG09740-13S2, P01 AG005842, P01 AG08291, P30 AG12815, Y1-AG-4553-01 and OGHA 04-064, IAG BSR06-11, R21 AG025169) as well as from various national sources is gratefully acknowledged (see www.share-project.org/t3/share/index.php for a full list of funding institutions).

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Appendices

Appendix 1: First-order Taylor expansion

We start from Eq. (32) and perform a Taylor expansion around \({y_{1}}\), for secondary prevention, this gives:

$$\begin{aligned} \frac{\partial \Delta {\text {EU}}_{1}}{\partial y_{1}} &= v_{y}(y_{1})p_{1}\times se-v_{yy}(y_{1})[c_{\alpha } \\&\times \,(1-p_{1}(1-se))+c_{e}\times p_{1}\times se] \\&-\,I(nf)[v_{y}(y_{1})p_{1}\times se-v_{yy}(y_{1}) \\&\times \,(c_{\alpha }\times p_{1}(1-se)+c_{l}\times p_{1}\times se)] \end{aligned}$$

and for primary prevention:

$$\begin{aligned} \frac{\partial \Delta {\text {EU}}_{1}}{\partial y_{1}} &= v_{y}(y_{1})p_{1}\times se-v_{yy}(y_{1})\left[ c_{\alpha }(1-p_{1}(1-se))\right] \\&-\,I(nf)[v_{y}(y_{1})p_{1}\times se-v_{yy}(y_{1}) \\&\times \,(c_{\alpha }\times p_{1}(1-se)+c_{l}\times p_{1}\times se)] \end{aligned}$$

Since \(v_{y}({y_{1}})>0\) and \(v_{{yy}} (y_{1} ) \le 0\), the effect will always be positive for a fatal disease. For a non-fatal disease, we derive the following Taylor condition for secondary prevention:

$$\begin{aligned} \frac{\partial \Delta {\text {EU}}_{1}}{\partial y_{1}} &= -v_{yy}(y_{1})[c_{\alpha }+p_{1}\times se\times (c_{e}-c_{l})] \\ \frac{\partial \Delta {\text {EU}}_{1}}{\partial y_{1}} & \geqslant 0\Leftrightarrow c_{\alpha }\geqslant p_{1}\times se\times (c_{l}-c_{e}) \end{aligned}$$

and for primary prevention:

$$\begin{aligned} \frac{\partial \Delta {\text {EU}}_{1}}{\partial y_{1}} &= -v_{yy}(y_{1})\left[ c_{\alpha }-p_{1}\times se\times c_{l}\right] \\ \frac{\partial \Delta {\text {EU}}_{1}}{\partial y_{1}} &\geqslant 0\Leftrightarrow c_{\alpha }\geqslant p_{1}\times se\times c_{l} \end{aligned}$$

Appendix 2: Comparative static results

Characteristics of the testing procedure

Starting from Eq. (18), we derive for secondary prevention:

$$\begin{aligned} \frac{\partial \Delta {\text {EU}}_{1}}{\partial se}=p_{1}(u^{P}-u^{FN})>0 \end{aligned}$$

where the conclusion about the sign follows from Eq. (20). An improvement of the effectiveness of prevention, without additional monetary or psychological costs, always makes prevention more attractive. For primary prevention, we have

$$\begin{aligned} \frac{\partial \Delta {\text {EU}}_{1}}{\partial se}=p_{1}(u^{TN}-u^{FN})>0\quad {\text { for }} \quad ef=se \end{aligned}$$

The comparative static results are straightforward for the “cost” parameters α and \({c_{\alpha }}.\) We have \(\frac{{\partial u^{{xx}} }}{{\partial z}} < 0\), for \(z = (\alpha ,c_{\alpha } )\) and for \(xx=(P,TN,FN)\). We therefore conclude that

$$\begin{aligned} \frac{\partial \Delta {\text {EU}}_{1}}{\partial \alpha }< & {} 0 \\ \frac{\partial \Delta {\text {EU}}_{1}}{\partial c_{\alpha }}< & {} 0 \end{aligned}$$

As could be expected, increased costs make preventive effort less attractive. If an increase in α leads to an increase in \({c_{\alpha }}\), the negative effects are reinforced. If, on the other hand, a policy change increases α, and, at the same time, se, positive and negative effects should be weighed against each other.

Characteristics of the disease

The effect of a change in \({p_{1}}\) is less straightforward. Taking the derivative of Eq. (17), we get for secondary prevention:

$$\begin{aligned} \frac{\partial \Delta {\text {EU}}_{1}}{\partial p_{1}} &= \left[ u^{\rm HE}-u^{TN}\right] +[se\times u^{P} \\&+\,(1-se)u^{FN}-u^{S}] \nonumber \\ &= [v(y_{1})-v(y_{1}-c_{\alpha })] \nonumber \\&+\,se[v(y_{1}-c_{\alpha }-c_{e})+w(h_{1},e) \nonumber \\&+\,\beta (1-{p_{x,2}}){V_{2}}] \nonumber \\&+\,I(nf)[v(y_{1}-c_{\alpha }-c_{l})-v(y_{1}-c_{l}) \nonumber \\&-\,se(v(y_{1}-c_{\alpha }-c_{l})+w(h_{1},l) \nonumber \\&+\,\beta (1-{p_{x,2}}){V_{2}})] \nonumber \end{aligned}$$
(35)

which has an obvious interpretation. The relative ranking of utility states in Eq. (20) shows clearly that if the individual is healthy (states \(u^{{{\text{HE}}}} ,u^{{TN}}\)), participation in prevention leads to additional costs and a utility loss, while if she is ill (states \(u^{S} ,u^{P} ,u^{{FN}}\)), it depends on the underlying parameters, such as the costs and the efficiency of the preventive procedures, whether prevention leads to a gain or a loss. As \({p_{1}}\) increases there is a shift away from the utility loss when healthy, towards the utility gain or loss when sick. The former leads to a positive effect on participation in prevention, captured by the first term in Eq. (35), while the latter may result in a positive or a negative effect on preventive behavior, captured by the second term in Eq. (35). The positive effect will dominate, i.e., \(\frac{{\partial \Delta {\text{EU}}_{1} }}{{\partial p_{1} }} > 0\), for a fatal disease and for preventive procedures with a high sensitivity se and/or low screening costs \({c_{\alpha }}\). For primary prevention (with \(ef=se\)), the partial effect is similar, but \({u^{P}}\) is replaced by \({u^{TN}}\), which ceteris paribus leads to a higher marginal effect:

$$\begin{aligned} \frac{\partial \Delta {\text {EU}}_{1}}{\partial p_{1}}= & {} \left[ u^{\rm HE}-u^{TN}\right] +[se\times u^{TN} \\&+\,(1-se)u^{FN}-u^{S}] \end{aligned}$$

We can also draw conclusions about the effect of \({p_{2}}\) on the probability of taking a preventive test in period 1. As noted before, it will only have an impact for fatal diseases. In that case, we get from Eqs. (27) and (31) that

$$\begin{aligned} \frac{\partial \Delta {\text {EU}}_{1}}{\partial p_{2}}=-p_{1}\times se\times \beta (1-{p_{x,2}})\left( v(y_{2})+w(h_{2},0)\right) <0 \end{aligned}$$

The intuition is obvious. Future utility \({V_{2}}\) unambiguously decreases as \({p_{2}}\) increases, since the individual is less likely to be healthy and more likely to be dead. As a result \(\Delta {\text{EU}}_{1}\) decreases and prevention becomes less interesting. This is in accordance with the conclusions from Eq. (31).Footnote 32

A last characteristic of the disease is the treatment cost, represented in the model by \({c_{e}}\) and \({c_{l}}\). Starting from Eqs. (28) and (28′), we get:

$$\begin{aligned} \frac{\partial \Delta {\text {EU}}_{1}}{\partial c_{e}}& =-p_{1}\times se\times v_{y}(y_{1}-c_{\alpha }-c_{e})\leqslant 0 \\ \frac{\partial \Delta {\text {EU}}_{1}}{\partial c_{l}}& = I(nf)\times p_{1}[v_{y}(y_{1}-c_{l}) \\&-\,(1-se)v_{y}(y_{1}-c_{\alpha }-c_{l})] \end{aligned}$$

An increase in the cost of early treatment only matters for secondary prevention. It leads to a reduction in \(\Delta {\text{EU}}_{1}\) and, consequently, lowers the incentives for preventive action. Higher curative (late stage) treatment costs have no effect for fatal diseases, since no cure is available. For non-fatal diseases the effect is ambiguous, since the costs can occur both in case of participation (state \({u^{FN}}\)) as in case of non-participation (state \({u^{S}}\)). However, if se is high enough and/or \({c_{\alpha }}\) low, more expensive curative treatment increases the incentives for preventive effort. That was only to be expected. Prevention is the only possibility to avoid the larger cost, but this cost avoidance can only work if prevention is reasonably effective (se high enough) and screening costs are limited.

Appendix 3: Additional empirical results

See Tables 7, 8 and 9.

Table 7 Descriptive statistics
Table 8 Determinants in the take-up of prevention: sample restricted to individuals aged 50 years and over
Table 9 Determinants in the take-up of prevention: with controls for GP visits and GP quality

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Bouckaert, N., Schokkaert, E. Differing types of medical prevention appeal to different individuals. Eur J Health Econ 17, 317–337 (2016). https://doi.org/10.1007/s10198-015-0709-6

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