Estimating Willingness to Pay for Online Health Services with Discrete-Choice Experiments

Abstract

Background

Research has outlined the benefits and costs of online health services, but these studies have typically focused on a specific geographic region or disease. Very few studies have estimated consumer demand for online health services.

Objective

This study estimated household’s willingness to pay (WTP) for the ability to receive remote diagnosis, treatment, monitoring and consultations online (telehealth).

Methods

WTP was estimated with a random utility model and household data from a US survey employing repeated discrete-choice experiments.

Results

The representative household was willing to pay $US4.39 per month for telehealth. This valuation increased to $US5.85 for households with higher opportunity costs, as measured by income, and to $US6.22 for households living more than 20 miles away from their nearest medical facility.

Conclusion

WTP estimates offer insights into the potential benefits from policies intended to promote the expansion of online health services into underserved areas. These include the Federal Communications Commission’s Rural Healthcare Pilot Program and the Department of Agriculture’s Distance Learning and Telemedicine Grants programme.

Appendices

Appendix A

1.1 Estimating the Standard Error of WTP Measures from Discrete Choice Experiments

Ignoring interactions, the utility model for Internet access choice is

$$U_{ij}^{*} = \beta_{p} p_{ij} + X_{ij}^{'} \beta_{a} + \beta_{s} b_{ij} + \varepsilon_{ij} , i = 1, \ldots , n;j = 1, \ldots , 8.$$

(1)

where p _ij is price, b _ij is Telehealth, and β _a is a K × 1 vector of attributes of the service other than price and Telehealth. The estimates of WTP for these attributes are $\hat{\varvec{\beta }}_{a} /\hat{\beta }_{p}$ and the estimated WTP for Telehealth is $\hat{\omega }_{b} = \hat{\beta }_{s} /\hat{\beta }_{p}$.

Since the estimates of willingness-to-pay are nonlinear functions of parameter estimates, their exact standard errors are unknown. While it would be possible to bootstrap the distribution of these estimators, since the normally distributed estimator of β _p is the denominator, the simulation would not converge to anything useful [23, 24]. Instead, we use linear approximation to the variance (sometimes known as the “delta method”). This approximation for elasticities has been examined in [25].

Define the (K + 1) × 1 vector

$$\hat{\varvec{\omega }} = ( \hat{\varvec{\beta }}_{a} \vdots \hat{\beta }_{s} )/\hat{\beta }_{p} .$$

(2)

Define the (K + 2) × 1 vector of parameter estimates $\hat{\varvec{\theta }} = \left( {\hat{\beta }_{p} \vdots \hat{\varvec{\beta }}_{a}^{\prime } \vdots \hat{\beta }_{s} } \right)^{\prime }$. Let ${\hat{\mathbf{\varSigma }}}$ be the estimated variance-covariance matrix of $\hat{\varvec{\theta }}$. The linear approximation to the variance of is $\hat{\varvec{\omega }}$

$$\hat{V}\left( {\hat{\varvec{\omega }}} \right) \approx \left[ {\frac{{\partial\varvec{\omega}}}{{\partial\varvec{\theta}}}} \right]^{'} {\hat{\mathbf{\varSigma }}}\left[ {\frac{{\partial\varvec{\omega}}}{{\partial\varvec{\theta}}}} \right]$$

(3)

where the derivatives are evaluated at the parameter estimates. The square root of the diagonal elements of $\hat{V}\left( {\hat{\varvec{\omega }}} \right)$ are the estimated standard errors of the estimates of WTP. These derivatives are

$$\frac{{\partial \hat{\varvec{\omega }}}}{{\partial \hat{\varvec{\theta }}}} = \left( {\begin{array}{*{20}c} { - \frac{{\hat{\beta }_{{a_{1} }} }}{{\hat{\beta }_{p}^{2} }}} & {\frac{1}{{\hat{\beta }_{p}^{{}} }}} & 0 & 0 & \cdots & 0 \\ { - \frac{{\hat{\beta }_{{a_{2} }} }}{{\hat{\beta }_{p}^{2} }}} & 0 & {\frac{1}{{\hat{\beta }_{p}^{{}} }}} & 0 & \cdots & 0 \\ \vdots & \vdots & {} & \vdots & {} & \vdots \\ { - \frac{{\hat{\beta }_{{a_{K} }} }}{{\hat{\beta }_{p}^{2} }}} & 0 & 0 & 0 & \cdots & 0 \\ { - \frac{{\hat{\beta }_{s} }}{{\hat{\beta }_{p}^{2} }}} & 0 & 0 & 0 & \cdots & {\frac{1}{{\hat{\beta }_{p}^{{}} }}} \\ \end{array} } \right).$$

(4)

Focusing on Telehealth, the estimated variance of the WTP for Telehealth from Eq. 3 is

$$V\left( {\hat{\omega }_{s} } \right) = \left( {\frac{{\hat{\beta }_{s}^{2} }}{{\hat{\beta }_{p}^{4} }}} \right)\hat{\sigma }_{pp} + 2\left( {\frac{{\hat{\beta }_{s} }}{{\hat{\beta }_{p}^{3} }}} \right)\hat{\sigma }_{ps} + \left( {\frac{1}{{\hat{\beta }_{p}^{2} }}} \right)\hat{\sigma }_{ss}$$

Appendix B

See Tables 5, 6 and 7.