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A Closer Look at Decision and Analyst Error by Including Nonlinearities in Discrete Choice Models: Implications on Willingness-to-Pay Estimates Derived from Discrete Choice Data in Healthcare

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Abstract

Background

Most researchers in health economics cite random utility theory (RUT) when analysing discrete choice experiments (DCEs). Under RUT, the error term is associated with the analyst’s inability to properly capture the true choice processes of the respondent as well as the inconsistency or mistakes arising from the respondent themselves. Under such assumptions, it stands to reason that analysts should explore more complex nonlinear indirect utility functions, than currently used in healthcare, to strive for better estimates of preferences in healthcare.

Objective

To test whether complex indirect utility functions decrease error variance for models that either implicitly (i.e. the multinomial logit (MNL) model) or explicitly (i.e. entropy multinomial logit (EMNL) model) account for error variance in health(care)-related DCEs; and to determine the impact of complex indirect utility functions on willingness-to-pay (WTP) measures.

Methods

Using data from DCEs aimed at healthcare-related decisions, we empirically compared (1) complex and simple indirect utility specifications in terms of goodness of fit, (2) their impact on WTP measures, including confidence intervals (CIs) based on the Delta method, the Krinsky and Robb-procedure, and Bootstrapping, and (3) MNL and EMNL model results.

Results

Complex indirect utility functions had a better model fit than simple specifications (p < 0.05). WTP estimates were quite similar across alternative specifications. The Delta method produced the most narrow CIs. The EMNL model showed that respondents apply simplifying strategies when answering DCE questions.

Conclusion

Complex indirect utility functions reduce error arisen from researchers, which can have important implications for measures in healthcare such as the WTP, whereas EMNL provides insights into the behaviour of respondents when answering DCEs. Understanding how respondents answer DCE questions may allow researchers to construct DCEs that minimise scale differences, so that the decision error made across respondents is more homogeneous and therefore taken out as additional noise in the data. Hence, better estimates of preferences in healthcare can be provided.

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Notes

  1. We use the term indirect utility function as opposed to (direct) utility function deliberately. The original derivations of McFadden [4], which have led to the discrete choice models discussed herein, work within the framework of indirect utility functions that he identifies via Roy’s Identity. The derivation of models based on direct utility functions, whilst possible, result in an alternative modelling approach, based on the Kuhn–Tucker conditions (Kuhn and Tucker [7]).

  2. As in most studies, in this paper, we use the broad notion of the multinomial logit model as being a combination of multinomial logit and conditional logit. The original multinomial logit model uses only individual characteristics (also called covariates, for example gender) in the indirect utility functions, while the conditional logit model as proposed by McFadden [4] considers characteristics of the alternatives (such as cost). Often, both characteristics are included in the indirect utility functions.

  3. Equation 7 assumes constant marginal utility of income. Testing for this actually provides a test of whether the data are utility theoretic. If MUY is constant, the scatter plot of predicted utility against nominal cost should be linear [8]. We would not expect MUY to vary for costs that are small relative to disposable income.

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Acknowledgments

EW de Bekker-Grob designed and conducted the DCE studies, contributed to the analyses and drafted the manuscript. JM Rose conceived the idea for the study, performed the analyses, and drafted the manuscript. MCJ Bliemer contributed to the formulas and analyses, and contributed to the writing of the manuscript. EW de Bekker-Grob and JM Rose have full access to all of the data in the study and can take responsibility for the integrity of the data and the accuracy of the data analysis. EW de Bekker-Grob will act as the overall guarantor.

We would like to thank William Greene for his support with the Nlogit software, and Vereniging Trustfonds Erasmus University Rotterdam and the Department of Public Health, Erasmus MC – University Medical Centre Rotterdam for their financial support. EW de Bekker-Grob, JM Rose and MCJ Bliemer declare that they have no conflict of interest.

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Authors and Affiliations

  1. Department of Public Health, Erasmus MC, University Medical Centre Rotterdam, PO Box 2040, 3000 CA, Rotterdam, The Netherlands

    Esther W. de Bekker-Grob

  2. The University of Sydney Business School, The University of Sydney, Sydney, Australia

    John M. Rose & Michiel C. J. Bliemer

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  1. Esther W. de Bekker-Grob
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Correspondence to Esther W. de Bekker-Grob.

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de Bekker-Grob, E.W., Rose, J.M. & Bliemer, M.C.J. A Closer Look at Decision and Analyst Error by Including Nonlinearities in Discrete Choice Models: Implications on Willingness-to-Pay Estimates Derived from Discrete Choice Data in Healthcare. PharmacoEconomics 31, 1169–1183 (2013). https://doi.org/10.1007/s40273-013-0100-3

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