Differing types of medical prevention appeal to different individuals

Nicolas Bouckaert; Erik Schokkaert

doi:10.1007/s10198-015-0709-6

The European Journal of Health Economics

April 2016, Volume 17, Issue 3, pp 317–337 | Cite as

Differing types of medical prevention appeal to different individuals

Authors
Authors and affiliations

Nicolas BouckaertEmail author
Erik Schokkaert

Original Paper

First Online: 19 July 2015

Received: 21 January 2015

Accepted: 22 June 2015

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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.

Keywords

Screening Vaccination Prevention Expected utility Behavioral economics

JEL Classification

D81 I12

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Notes

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).

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).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

	Min	Max	Mean	Standard deviation
Breast cancer screening	0	1	0.540	(0.498)
Dental prevention	0	1	0.405	(0.491)
Influenza vaccination	0	1	0.327	(0.469)
Cholesterol screening	0	1	0.532	(0.499)
Blood pressure screening	0	1	0.694	(0.461)
Blood sugar screening	0	1	0.537	(0.499)
Number of GP visits	0	98	4.586	(7.173)
GP quality index	0	1	0.253	(0.234)
SAH: very good or excellent	0	1	0.290	(0.454)
SAH: good	0	1	0.381	(0.486)
SAH: fair	0	1	0.239	(0.427)
SAH: poor	0	1	0.090	(0.286)
ADL index	0	1	0.036	(0.134)
Mobility index	0	1	0.175	(0.268)
BMI	11	78	26.529	(4.436)
Grip strength dominant hand (average of two attempts)	0	91	29.551	(15.006)
Prob. death in 10 years	5.14e$-$08	1	0.122	(0.211)
Age below 40	0	1	0.002	(0.044)
Age between 40 and 44	0	1	0.007	(0.082)
Age between 45 and 49	0	1	0.026	(0.158)
Age between 50 and 54	0	1	0.168	(0.374)
Age between 55 and 59	0	1	0.185	(0.388)
Age between 60 and 64	0	1	0.166	(0.372)
Age between 65 and 69	0	1	0.145	(0.352)
Age between 70 and 74	0	1	0.120	(0.325)
Age between 75 and 79	0	1	0.091	(0.287)
Age between 80 and 84	0	1	0.058	(0.234)
Age 85 and over	0	1	0.033	(0.180)
Gender: male	0	1	0.443	(0.497)
Gender: female	0	1	0.557	(0.497)
Nationality: native	0	1	0.980	(0.140)
Nationality: EU citizen (not native)	0	1	0.012	(0.111)
Nationality: outside EU	0	1	0.007	(0.086)
Has partner	0	1	0.748	(0.434)
Schooling: primary	0	1	0.325	(0.468)
Schooling: lower secondary	0	1	0.179	(0.384)
Schooling: upper secondary	0	1	0.305	(0.460)
Schooling: university	0	1	0.191	(0.393)
House owner	0	1	0.730	(0.444)
Smoked in the past	0	1	0.472	(0.499)
Smokes currently	0	1	0.197	(0.398)
Diagnosed cancer (except breasts)	0	1	0.039	(0.195)
Breast cancer: incidence (per 1000 cases)	0.077	5	2.794	(0.883)
Breast cancer: mortality (per 1000 cases)	0.012	2	0.777	(0.463)
Breast cancer: target group	0	1	0.724	(0.447)
Breast cancer: prob. receiving invitation letter	0	1	0.381	(0.444)
Breast cancer: pop.-based program complete	0	1	0.542	(0.498)
Influenza: target group (age)	0	1	0.528	(0.499)
Influenza: target group (illness)	0	1	0.259	(0.438)
Influenza: subsidized vaccination	0	1	0.334	(0.472)
Influenza: free vaccination	0	1	0.292	(0.455)

Database: SHARE, wave 1 and wave 2

Table 8

Determinants in the take-up of prevention: sample restricted to individuals aged 50 years and over

Variables	Breast cancer		Dental		Influenza		Cholesterol		Blood pressure		Blood sugar
	Screening		Prevention		Vaccination		Screening		Screening		Screening
	Marginal effects (SE)		Marginal effects (SE)		Marginal effects (SE)		Marginal effects (SE)		Marginal effects (SE)		Marginal effects (SE)
Self-assessed health (Ref. = very good/excellent)
SAH: good	0.005	(0.011)	−0.010	(0.005)**	0.042	(0.008)***	0.080	(0.020)***	0.090	(0.019)***	0.084	(0.017)***
SAH: fair	0.003	(0.013)	−0.024	(0.006)***	0.075	(0.009)***	0.092	(0.024)***	0.127	(0.026)***	0.101	(0.021)***
SAH: poor	−0.029	(0.020)	−0.026	(0.010)***	0.095	(0.015)***	0.125	(0.037)***	0.162	(0.041)***	0.160	(0.029)***
Objective health indicators
ADL index	−0.081	(0.043)*	−0.043	(0.024)*	0.006	(0.030)	0.052	(0.090)	−0.049	(0.113)	0.123	(0.069)*
Mobility index	0.021	(0.021)	−0.024	(0.012)**	0.047	(0.016)***	0.061	(0.047)	0.205	(0.056)***	0.075	(0.036)**
BMI	−0.001	(0.001)	−0.004	(0.001)***	0.002	(0.001)***	0.007	(0.002)***	0.000	(0.002)	0.006	(0.002)***
Grip strength dominant hand	0.001	(0.001)	0.000	(0.000)	−0.001	(0.000)***	0.000	(0.001)	0.000	(0.001)	0.001	(0.001)
Importance of the future
Prob. death in 10 years	−0.058	(0.025)**	−0.017	(0.012)	−0.011	(0.016)	−0.012	(0.057)	0.084	(0.070)	−0.050	(0.044)
Income (Ref. = decile 1)
Decile 2	−0.022	(0.019)	−0.003	(0.011)	−0.030	(0.016)**	−0.007	(0.033)	0.008	(0.034)	−0.031	(0.028)
Decile 3	−0.024	(0.019)	−0.017	(0.011)	0.003	(0.016)	−0.013	(0.033)	−0.003	(0.034)	−0.003	(0.029)
Decile 4	−0.002	(0.019)	−0.001	(0.010)	0.000	(0.016)	0.058	(0.035)*	0.017	(0.036)	0.054	(0.030)*
Decile 5	−0.002	(0.020)	0.002	(0.010)	0.004	(0.015)	0.060	(0.039)	0.015	(0.038)	0.074	(0.034)**
Decile 6	0.044	(0.020)**	0.007	(0.010)	0.003	(0.015)	0.036	(0.040)	−0.005	(0.039)	0.030	(0.035)
Decile 7	0.033	(0.020)	0.042	(0.010)***	0.028	(0.015)*	0.027	(0.040)	0.026	(0.040)	0.033	(0.035)
Decile 8	0.047	(0.021)**	0.041	(0.010)***	0.023	(0.015)	0.047	(0.039)	0.021	(0.038)	0.061	(0.034)*
Decile 9	0.039	(0.021)*	0.055	(0.010)***	0.027	(0.015)*	0.066	(0.039)*	0.033	(0.039)	0.053	(0.034)
Decile 10	0.045	(0.020)**	0.052	(0.010)***	0.027	(0.015)*	0.055	(0.040)	0.046	(0.039)	0.066	(0.035)*
Breast cancer specific
Diagnosed cancer (except breasts)	0.082	(0.025)***
Dental specific
Dentures			−0.117	(0.005)***
Trouble biting			−0.049	(0.006)***
No. of observations	10,614		47,085		20,619		3810		3130		5407

Averaged marginal effects from probit regressions are reported with robust standard errors. For dental prevention, standard errors are clustered at the individual level. All regressions control for education, nationality, gender, age, partner, past and current smoker, house owner, country dummies by wave

Database: SHARE, wave 1 and wave 2

Significance levels: * p < 0.10, ** p < 0.05, *** p < 0.01

Table 9

Determinants in the take-up of prevention: with controls for GP visits and GP quality

Variables	Breast cancer		Dental		Influenza		Cholesterol		Blood pressure		Blood sugar
	Screening		Prevention		Vaccination		Screening		Screening		Screening
	Marginal effects (SE)		Marginal effects (SE)		Marginal effects (SE)		Marginal effects (SE)		Marginal effects (SE)		Marginal effects (SE)
GP indicators
Number of GP visits	0.002	(0.001)**	0.002	(0.001)***	0.004	(0.001)***	0.010	(0.003)***	0.029	(0.004)***	0.010	(0.002)***
GP quality index	0.063	(0.022)***	0.025	(0.015)	0.129	(0.015)***	0.476	(0.037)***	0.489	(0.043)***	0.466	(0.031)***
Self-assessed health (Ref. = very good/excellent)
SAH: good	0.007	(0.012)	−0.007	(0.008)	0.028	(0.008)***	0.062	(0.019)***	0.048	(0.019)**	0.067	(0.017)***
SAH: fair	−0.006	(0.015)	−0.034	(0.010)***	0.051	(0.010)***	0.056	(0.026)**	0.052	(0.027)*	0.056	(0.022)***
SAH: poor	−0.021	(0.023)	−0.016	(0.017)	0.056	(0.016)***	0.059	(0.040)	0.032	(0.045)	0.071	(0.032)**
Objective health indicators
ADL index	−0.078	(0.051)	−0.052	(0.041)	0.014	(0.036)	−0.026	(0.100)	−0.146	(0.123)	0.094	(0.077)
Mobility index	−0.007	(0.024)	−0.066	(0.019)***	0.013	(0.018)	−0.045	(0.049)	0.117	(0.059)**	0.011	(0.039)
BMI	−0.002	(0.001)**	−0.004	(0.001)***	0.001	(0.001)**	0.006	(0.002)***	−0.001	(0.002)	0.004	(0.002)***
Grip strength dominant hand	0.000	(0.001)	0.001	(0.000)*	−0.001	(0.000)*	0.001	(0.001)	0.001	(0.001)	0.002	(0.001)*
Importance of the future
Prob. death in 10 years	−0.083	(0.031)***	−0.009	(0.022)	−0.031	(0.020)	0.014	(0.066)	0.097	(0.080)	−0.021	(0.050)
Income (Ref. = decile 1)
Decile 2	−0.024	(0.021)	0.004	(0.017)	−0.032	(0.018)**	−0.008	(0.032)	0.004	(0.034)	−0.037	(0.028)
Decile 3	−0.014	(0.021)	−0.027	(0.017)	−0.003	(0.017)	−0.003	(0.033)	−0.009	(0.034)*	0.006	(0.029)
Decile 4	0.001	(0.021)	0.003	(0.016)	0.010	(0.017)	0.059	(0.034)*	0.021	(0.035)	0.058	(0.030)*
Decile 5	0.003	(0.022)	−0.008	(0.016)	0.009	(0.017)	0.060	(0.038)	0.006	(0.036)	0.082	(0.033)**
Decile 6	0.054	(0.023)**	−0.002	(0.017)	0.008	(0.017)	0.049	(0.039)	0.018	(0.039)	0.036	(0.034)
Decile 7	0.024	(0.023)	0.015	(0.016)	0.026	(0.017)	0.042	(0.039)	0.020	(0.038)	0.043	(0.034)
Decile 8	0.060	(0.023)***	0.029	(0.016)*	0.029	(0.017)*	0.058	(0.038)	0.016	(0.037)	0.075	(0.033)**
Decile 9	0.045	(0.023)*	0.014	(0.016)	0.030	(0.017)*	0.084	(0.038)**	0.055	(0.037)	0.074	(0.033)**
Decile 10	0.064	(0.023)***	0.020	(0.016)	0.019	(0.017)	0.074	(0.039)*	0.067	(0.037)*	0.076	(0.034)**
Breast cancer specific
Diagnosed cancer (except breasts)	0.081	(0.028)***
Dental specific
Dentures			−0.113	(0.008)***
Trouble biting			−0.026	(0.009)***
No. of observations	8853		16,874		16,774		3728		3108		5164

Averaged marginal effects from probit regressions are reported with robust standard errors. For dental prevention, standard errors are clustered at the individual level. All regressions control for education, nationality, gender, age, partner, past and current smoker, house owner, country dummies by wave

Database: SHARE, wave 1 and wave 2

Significance levels: * p < 0.10, ** p < 0.05, *** p < 0.01

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Authors and Affiliations

Nicolas Bouckaert
- 1
Email author
Erik Schokkaert
- 1
- 2

1.Department of EconomicsKU LeuvenLeuvenBelgium
2.COREUniversité catholique de LouvainLouvain-la-NeuveBelgium

Differing types of medical prevention appeal to different individuals

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