Nonparametric Willingness-To-pay Measures and Confidence Statements

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Technical Notes

Nonparametric Willingness-to-pay

Measures and Confidence StatementsMAGNUS TAMBOUR, PhD, NIKLAS ZETHRAEUS, PhD

Willingness to pay (WTP) for a health care program can be estimated in contingentvaluation (CV) studies by a nonparametric approach. The nonparametric approach isfree from distributional assumptions, which is a strength compared with parametricregression-based approaches. However, using a nonparametric approach it is not clear how to obtain confidence statements for WTP estimates, for example, when testinghypotheses regarding differences in mean WTP for different subsamples. The authorspropose a procedure that allows statistical testing and confidence interval estimationby employing bootstrap techniques. The method is easy to implement and has lowcomputational costs with modern personal computers. The method is applied to datafrom a CV study where the WTP for hormone replacement therapy was investigated.The mean WTP was estimated for the full sample and separately for women with mildand severe menopausal symptoms. Using the proposed method, the mean WTP wassignificantly higher in the group with severe symptoms. Key w o r d s : bootstrap; eco-nomic evaluation; hormone replacement therapy: nonparametric; willingness to pay.(Med Decis Making 1998;18:330-336)

Different methods for eliciting monetary values of health care programs have been presented in theliterature., The expressed-preference approach, orcontingent-valuation (CV) method, is one way to ob-tain benefit measures of health care programs. Inthe CV method, survey methods are used to inves-tigate the willingness to pay (WTP) for a good or aservice. The CV method was originally developed inthe environmental field to measure the value of changes in the environment, but recently a numberof health care applications have been presented. 3-13

Contingent-valuation questions can be dividedinto open-ended questions and closed-ended ques-tions. Because there are problems with open-endedquestions (e.g., starting point bias when using bid-ding games? the current recommendation is to useclosed-ended CV questions. 15-16 The CV methodbased on closed-ended questions (or open-endedquestions) is itself not without problems, and vari-ous issues remain to be solved. For example, therelationship between hypothetical and real money

Received April 8, 1997, from the Stockholm School of Econom-tcs, Stockholm, Sweden. Revision accepted for publication Jan-uary 8, 1998. Supported by the National Corporation of SwedishPharmacies (NCSP) The conclusions and opinions expressedherein are those of the authors.

Address correspondence and reprint requests to Dr. Tam-bow: Centre for Health Economics, Stockholm School of Economics, PO Box 6501, S-113 83 Stockholm, Sweden. e-mail: [email protected] .

payments needs to be tested further. Another meth-odologic issue, which we address here, is how toobtain confidence statements for the mean WTP.

Parametric or nonparametric approaches can beused to estimate the mean WTP from dichotomouschoice (closed-ended) CV questions. A parametricapproach necessitates assumptions regarding func-tional form. 17-19 The main advantage of nonpara-metric estimators is that they are robust againstfunctional misspecification. The nonparametric ap-proach also has the virtue that the mean WTP isusually simple to estimate. For the parametric ap-proach, different methods have been proposed toaccount for uncertainty in the mean WTP measuredue to sample variation. 21,22 However, it is perhapsless clear how to obtain confidence statements formean WTP estimates using a nonparametric ap-proach. The purpose of this article is to propose aprocedure based on bootstrap techniques that al-lows statistical testing and confidence-interval esti-mation for the mean WTP where the estimator isbased on the nonparametric approach developed by Kristrom. 20 This procedure makes it possible notonly to estimate confidence intervals for the meanWTP in the whole sample in a CV study, but also totest whether there are significant differences inmean WTP between different subsamples. The ap-proach requires no assumptions regarding para-metric functional form, but the computational in-tensity of the bootstrap technique precludes its


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VOL 18/NO 3, JUL-SEP 1998 Nonparametric Willingness-to-pay Measures l 333

Table 1 l Shares of Yes Answers by Price; Original Values and Adjusted Values after Smoothing

Price (Krone) Total Original Total Adjusted Severe Original Severe Adjusted Mild Original Mild Adjusted

100 0.88 0.88 1 .00500 0.80 0.80 0.86

1,000 0.70 0.70 1 .oo1,500 0.60 0.60 0.752,000 0.50 0.50 0.503,000 0.23 0.28 0.255,000 0.33 0.28 0.50

10,000 0.18 0.18 0.50

1 .oo 0.80 0.800.92 0.75 0.750.92 0.40 0.500.75 0.55 0.500.50 0 . 5 0 0.500.39 0.20 0.200.39 0.17 0.170.39 0.00 0.00

terviewed the women after their consultations with

the clinic doctor. In order to classily each womanas having mild or severe symptoms, she was askedto read a description of mild and severe symptomsused in a study by Daly et a1.,25 and to choose thealternative that best corresponded to her own symp-toms before taking HRT. The interview consisted of three parts. In the first part, the woman was askedto indicate her health status before starting HRT andher present health status with HRT, on a rating scale

(RS) between 0 (dead) and 100 (full health). In thesecond part, the woman was asked to indicate herhealth status before starting HRT and her presenthealth status with HRT, based on the time-tradeoff (TT0) method. In the third part of the interview, theWTP for HRT was investigated by the CV methodbased on a closed-ended approach, i.e., each indi-vidual was asked whether or not she would be will-ing to pay a specific price.

In the questionnaire, the woman was askedwhether she would continue her current HRT if shehad to pay p Swedish krone (August 1997: 16 = 12.0Swedish krone, = 8.0 Swedish krone) per monthout of her own income. The price (p) was randomly varied between 100 and 10,000 Swedish krone ineight different subsamples (J = 81 and each individ-ual was offered one of these prices. The eight dif-ferent prices were 100; 500; 1,000; 1,500; 2,000; 3,000;

5,000, and 10,000 Swedish krone. The formulation of the WTP question is given in appendix B.

In the estimation of the mean WTP, we assume,as mentioned above, that no one accepts to pay ahigher price than the maximum of 10,000 Swedish

krone used in the study (b = 10,000). We also as-

sume that each woman would continue her HRT if the price were 0 (a = 01. The mean WTP was esti-mated for the whole sample and separately for thetwo subsamples with mild and severe menopausalsymptoms, respectively. To obtain a non-increasingfunction of the yes answers in p, smoothing wasnecessary for the entire sample as well as for thegroups with mild and severe symptoms. Table 1shows the original as well as the adjusted ratio val-

ues after smoothing was carried out. The mean treatment duration at the time for the

interview was three years, and the response rate was100%. Eighty-five women were being treated with es-trogen in combination with a progestin, while 19women were receiving estrogen alone. The meanage of the entire patient group was 52.2 years (range45-65 years), whereas the mean ages of the womenwith mild and severe menopausal symptoms were

52.0 (range 45-60) and 52.4 (range 45-65) years, re-spectively (table 2). Table 2 shows large increases inthe quality-of-life scores of the two groups in termsof increases in RS and TTO. The socioeconomic fac-tors income, age, and household size are almost thesame in the two groups, whereas the women withmild symptoms had a higher level of education.

Based on the Ayer curve represented by the curvein figure 1, the mean WTP was estimated. The mean

monthly WTP for all the women (full sample1 was3,508 Swedish krone. For women suffering mild andsevere menopausal symptoms, the mean WTPs forHRT were 2,346 and 4,838 Swedish krone, respec-tively. These are point estimates on the mean WTP

Table 2 l Mean Values of Background Variables for all Women and for Women with Mild and Severe Menopausal Symptoms,Respectively

No. ATTO ARS Age Income?All women 104 0.29 0.37 52.2 27,840Mild symptoms 56 0.18 0.26 52.0 28,839Severe symptoms 48 0.42 0.5 52.4 26,649pvaluesg: 0.00 0.00 0.77 0.36

*The difference in the quality-of-life score with and without hormone-replacement therapy.tPer month pre-tax household income.SCoded 0 for primary education and 1 for secondary and university or higher education.gBased on t-tests of mean differences between the mild- and severe-symptom groups.

Household Size Educationz2.15 0.552.14 0.712.17 0.350.90 0.00


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334 l Tambour, Zethraeus MEDICAL DECISION MAKING

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0.90

0.80

0.70F 0 . 6 0y

j 0 . 5 0

0.405 0 . 3 09 0.20

Fz0.10

x\-\

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-\\

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Price S per month)

for HRT, which indicates a large difference in meanWTPs between the two groups. One explanation of the high WTP for HRT is that there is a considerableincrease in the quality of life from using HRT interms of changes in the TTO and RS, as indicated in

Table 2. To account for uncertainty due to the sample var-

iation, a confidence interval for the true mean WTPcan be constructed using the outlined bootstrap ap-proach. The bootstrap approach also makes it pos-sible to test whether there is a statistically significantdifference in the mean WTPs between the groupswith severe and mild menopausal symptoms.

BOOTSTRAP RESULTS

In this subsection we report confidence intervals

for mean WTP. First, a confidence interval for themean WTP was estimated using the whole sample.

The same procedure was then used for the two sub-samples of women with severe and mild symptoms,respectively. Finally, to investigate whether therewas a significant difference in mean WTPs betweenwomen suffering from mild and severe symptoms,we estimated a bootstrap confidence interval for thedifference in the mean WTPs. The results are re-

ported in table 3. The first row shows the results for the full sample.

The original estimate shows a mean WTP of about3,500 Swedish krone per month, which Zethraeus etal. concluded is well above the estimated treatmentcosts. The bootstrap results show that even thelower bound of the mean WTP exceeds the treat-ment costs. An analysis of the uncertainty due to

FIGURE 1. The relationship betweenthe price level and the proportion ofwomen willing to pay each price. Fullsample and subsamples with mild andsevere symptoms. N (full sample) =104 [n mild = 56, nkevere 481.

sampling variation as reported in table 3 couldtherefore strengthen the results in a cost-benefitstudy. For the two subsamples, the original esti-mates are as expected, in the sense that the womenwho had severe symptoms were willing to pay morethan the women with mild symptoms. The originalpoint estimates indicate that the women who hadsevere symptoms were willing to pay twice as muchas the women with mild symptoms. As the last rowin table 3 shows, this difference is statistically sig-nificant. It should be noted that it is not enough touse the confidence intervals for the two groups andcompare the upper bound for the mild-symptomsgroup with the lower bound for the severe-symp-toms group in order to conclude whether or not thedifference between the groups is significant.

Finally, it should also be noted that other factors

Table 3 l 95% Confidence Intervals for Mean Willingnessto Pay WTP)*

All women (n = 104)

Lower Bound

2,539

Original

3,508

Upper Bound

4,813

Women with mild symp-toms (n = 56) 1,444 2,346 3,870

Women with severe symp-toms (n = 48) 3,092 4,838 6,767

Difference in WTP, severe- mild 313 2,492 4,409

*Lower and upper bootstrap bias-corrected confidence intervals andoriginal mean WTP estimates.


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VOL 18/NO 3, JUL-SEP 1998

not controlled for may explain some of the differ-ence between the WTPs of the women with mildand severe symptoms. The background variablesthat differed significantly between the two groupswere the education, RS, and TTO variables, whichindicate a higher education level and less gain inquality of life for women with mild symptoms. So-cioeconomic factors such as income, age, andhousehold size did not differ significantly betweenthe two groups.

Summary and ConclusionsCost-benefit analysis with WTP estimates used as

benefit measures is one approach to the evaluationof health care programs. Estimates of mean WTPcan be obtained from CV studies by parametric ornonparametric techniques. We propose for this pur-pose a bootstrap procedure that allows statisticaltesting and confidence interval estimation for non-parametric mean WTP estimates.

The bootstrap approach can also be applied using other assumptions regarding the tails of the distri-bution and the behaviors associated with the pricesin the bid groups. Instead of using linear interpo-lation, cubic splines could have been used. Otherupper and lower limits of integration could alsohave been used.

The method was applied to data from a SwedishCV study of HRT. It was possible to conclude thatthe lower bound of the confidence interval was wellabove the treatment costs for this program. In acomplete stochastic analysis, one should, of course,also estimate confidence intervals for the cost mea-sure, but this was not possible in the study fromwhich the data were taken. The results also showedthat there was a significant difference between themean WTPs of women with severe and mild symp-toms. Such conclusions cannot be drawn using thenonparametric estimates alone. Bootstrap tech-niques offer a comprehensive tool for stochasticanalysis for the nonparametric WTP measure.

The authors thank Magnus Johannesson for helpful commentsabout the manuscript.

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Nonparametric Willingness-To-pay Measures and Confidence Statements