Fixed budgets as a cost containment measure for pharmaceuticals

Abstract

In Västerbotten County, Sweden, there are two health centers which (in contrast to all other health centers in the region) bear strict responsibility over their pharmaceutical budget. This study examined whether the prices and quantities of pharmaceuticals prescribed by physicians working at these health centers differ significantly from those prescribed by physicians at health centers with open-ended budgets. Estimation results using matching methods, which allows us to compare similar patients at the different health centers, show that the introduction of fixed pharmaceutical budgets did not affect physicians’ prescription behavior, indicating that fixed budgets may not be an efficient measure to reduce costs. Another explanation is that the health centers under study already had taken measures to contain costs, making it hard to further reduce costs.

Appendix: balancing tests

To guarantee that propensity score matching eliminates all the bias for which the observables can account, the observables must be independent of the treatment assignment conditioned on the propensity score. Several different tests of this condition have been proposed in the literature. These have differing limitations, and little is known about their statistic properties. Our analysis employed two balancing tests. The first was a Hotelling T² test of the joint null hypothesis of equal means between treatment and control groups. This test can, however, fail to reject the null hypothesis even if X is dependent on treatment assignment, conditioned on the propensity score. One example of this is the case of some variables having higher values in the treated group than in the matched group, for high values of the propensity score but lower values for low values of the propensity score. The second balancing test we conduct is a regression based test described by Smith and Todd (unpublished). For each variable used in estimating the propensity score we estimate the following regression:

$$ \begin{aligned} X_{k} = \beta _{0} + \beta _{1} \hat{P}{\left( X \right)} + \beta _{2} \hat{P}{\left( X \right)}^{2} + \beta _{3} \hat{P}{\left( X \right)}^{3} + \beta _{4} \hat{P}{\left( X \right)}^{4} + \beta _{5} D + \beta _{6} D\hat{P}{\left( X \right)} & \\ + \beta _{7} D\hat{P}{\left( X \right)}^{2} + \beta _{8} D\hat{P}{\left( X \right)}^{3} + \beta _{9} D\hat{P}{\left( X \right)}^{4} + \varepsilon {\text{ }}{\text{,}} & \\ \end{aligned} $$

where D is an indicator variable which takes the value one if the observation is treated. To test whether D provides additional information about X conditioned on P(X) we tested the joint null hypothesis that all the coefficients of the terms involving D equal 0. A shortcoming to this test is that the choice of the order of the polynomial may affect the result. The results of the tests appear in Table 6. The Hotelling test rejects balance for three of the subsamples for Moröbacke. The results from the regression based test show that between 10% and 33% of the independent variables remain unbalanced conditioned on the propensity score, in all models.

Table 6 P values on the Hotelling test for balancing; the percentages of the variables which are unbalanced at the level of P<0.05%