Can income-based co-payment rates improve disparity? The case of the choice between brand-name and generic drugs

Background Higher income population tend to prefer brand-name to generic drugs, which may cause disparity in access to brand-name drugs among income groups. A potential policy that can resolve such disparity is imposing a greater co-payment rate on high-income enrollees. However, the effects of such policy are unknown. We examined how patients’ choice between brand-name and generic drugs are affected by the unique income-based co-payment rates in Japan; 10% for general enrollees and 30% for those with high income among the elderly aged 75 and over. Methods We drew on cross-sectional price variation among commonly prescribed 311 drugs using health insurance claims data from a large prefecture in Japan between October 2013 and September 2014 to identify between-income-group differences in responses to differentiated payments. Results Running 311 multivariate logistic regression models controlling individual demographics, the median estimate indicated that high-income group was 3% (odds ratio = 0.97) less likely to choose a generic drug than the general-income group and the interquartile estimates ranged 0.92–1.02. The multivariate feasible generalized least squares model indicated high-income group’s higher likelihood to choose brand-name drugs than the general-income group without co-payment rate differentiation (p < 0.001). Such gap in the likelihood was attenuated by 0.4% (p = 0.027) with an US$1 increase in the difference in additional payment/month for brand-name drugs between income groups — no gap with US$10 additional payment/month. This attenuation was observed in drugs for chronic diseases only, not for acute diseases. Conclusions Income-based co-payment rates appeared to reduce disparity in access to brand-name drugs across income groups, in addition to reducing total medical expenditure among high-income group who shifted from brand-name drugs to generic ones due to larger drug price differences.


Appendix. Conceptual Model for Drug Choice and Calibration Studies for Utility Difference between Income Groups by Specifying the Utility Function and Income
We model patient 's utility from brand-name and generic drug k as follows: where , denote patient 's utilities from brand-name and generic versions, is patient i's co-payment rate, and , are the prices of brand-name and generic version of drug .
is the income of patient . (•) is the patient's utility function for a monetary outcome.
Since we focus on patients' choice after receiving a prescription, we assume there is no outside option besides choosing a brand-name or generic version of the drug. If − + > − + holds, the patient will choose the brand-name drug, and vice versa. Our interest is the difference between and by a patient's income status.
Furthermore, we aim to reveal the varying effects of price differences on patients' choice on the basis of income status.
We consider a simple setting. Assume there are two types of patients with high-and generalincome ( = ℎ, , respectively), and = (= ) holds, that is, the utility function is common across enrollees, irrespective of income. The generic version of drug k is more likely to be chosen by the high-income group than the general counterpart if the following relationship holds: where ( ) indicates the probability of event . Figure A1 illustrates our model.  report the value of ( ) − ( − ) for = ℎ, columns 3 and 4 for = . We report this amount for several values of and . As we can see from this result, whether ( ) − ( − ) is larger for = ℎ or = depends on the form of the utility function and income related term . When = 1, ( ) − ( − ) tend to be larger in the higher 4 income group in our setting of income. In contrast, when = 2, 3, the results suggest that this comparison in size heavily depends on income of each group.
Our calibration results suggest that whether the size of ( ) − ( − ) is larger for high-or general-income enrollees remains controversial and the size can be substantial. In other words, there is no clear implication for how the difference in probability of choosing generic drugs between high-and general-income groups responds to price changes and the difference may be sizeable such that equal probability cannot be achieved within a realistic co-payment rate setting.
In addition, it is important to know the distributions of , to elucidate the differences in preferences for brand-name drugs by income status. By empirically assessing these aspects, we can determine whether differentiating co-payment rates can contribute to the equal probability of high-and general-income groups choosing generic drugs.

Appendix. Details of the Patients' Choice Model and Empirical Strategy
We describe the relations between our empirical methods and an underlying patients' choice model. We denote the patient 's utility from choosing each version of the drug and introduce time dimension t: where we assume that the patient's utility function is time-invariant.
We decompose ( = , ) as follows: where denotes brand-name drug and indicates generic drugs; is the drug-versionspecific time-invariant preference toward version j; is a dummy variable that equals 1 if patient 's co-payment rate is 30%, which also indicates a relatively high income; is a vector for other individual characteristics; and is an error term for an unobservable taste shock.
Coefficient is the change in preference for version j caused by being in the high-income group instead of the general-income group. We allow each patient's preference to differ by their income level and other observable characteristics. Let Note that can be interpreted as the difference in preference for the generic version relative to the brand-name version between the high-and general-income groups. Assuming ( ) − U( − ) = ′( ) by linear approximation, we rewrite the condition for the generic version to be chosen as: Here, recall that we assume two types of patients with high or general income adjusted to the price of generic drugs , . Finally, the condition can be written as Assuming that and are exogenous error terms with type-I extreme value distribution, this condition motivates us to conduct a logistic regression for each drug as follows: where dependent variable is a dummy variable that equals 1 if a generic version of drug is dispensed for patient at prescription timing . We include a set of covariates for such as age, sex, amount of drug prescribed at , area of patient's residence, total medical expenditure in a month including prescription timing t but excluding spending on drugs, and total spending on drugs besides drug in a month including prescription timing . is an intercept (we rewrite ′ + as ). Since individuals tend to receive a prescription for the same drug repeatedly, we employ a generalized estimating equation (GEE) approach to account for the clustering responses among the same individuals. To model the within-individual correlation, we choose a working correlation matrix to have an exchangeable structure.
Our central estimate of interest is . If this coefficient is smaller than 0 (i.e., the odds ratio is less than 1), being in the high-income group reduces the probability of choosing generic drugs, despite the higher out-of-pocket prices. From the above argument, comprises two components: is the difference in utility loss from the high price of a brandname version between high-and general-income groups and is difference in preference for a generic drug between high-and general-income groups. We focus on the role of these components in the choice of versions.
We analyze the relationship between estimated coefficients and price difference between the brand-name and generic drugs. We define price difference as the product of price difference per unit dose and average daily dose. To analyze the relationship, we regress the estimated coefficient on price difference. We introduce certain assumptions to interpret our results from the regressions.
Assumption 1. The difference in utility loss from the price difference per one yen between highand general-income groups, ( ′( ) − ′ ), is the same across drugs .
Although this assumption is untestable using our data, the drugs included in our analysis are commonly prescribed drugs. Therefore, we consider this assumption to be reasonable as the income level would not largely differ among such drugs.
Assumption 2a. The difference in preference for generic drugs between high-and generalincome groups, , is heterogeneous with mean π. In addition, is mean-independent of , that is, E( − π| ) = 0 holds.
It is natural that the preference for generic drugs is heterogeneous among drugs. Although the conditional mean-zero assumption may be strong, we make this assumption for inference. To relax this assumption to a certain extent, we later allow mean π to differ among the types of drugs.
Under assumptions 1 and 2a, the price coefficient can be interpreted as ′( ) − ′ and the intercept as π.
Next, we regress on price difference and drug category dummies. To interpret the results from this regression, we relax Assumption 2a and instead, propose the following assumption.
Assumption 2b. The difference in preference for generic drugs between the high-and generalincome groups, , is heterogeneous with mean π in each drug category, . In addition, we assume mean independence between and within each drug category , that is, Instead of Assumption 2a, we allow the mean level of preference to differ by drug category. Again, under assumptions 1 and 2b, the price coefficient can be interpreted as ′( ) − ′ and the intercept as of the reference category in the regression.

Appendix. FGLS Estimation
We describe the FGLS estimation procedure which follows the previous literature on estimating regression models where the dependent variables are estimates. Our model of interest is: where we rearrange the terms = ′( ) − ′( ) and + = . We introduced Assumption 1 to drop index k in the terms and . From Assumption 2, is assumed to be mean-zero conditional on and let the variance be . Now, as s are estimated in our model, let the estimates be . Let = + .
In addition, assume that ( ) = . We assume that the estimate of the for each observation is independent of the others, in other words, we assume ( , ) = 0 where k ≠ l. By substituting this equation we obtain: (2005), we first calculate residuals from OLS regression. Then, we can obtain a consistent estimator for as:

Following Lewis & Linzer
Assuming that we have consistent estimators for , which is the standard errors from the logistic regression, we may substitute the standard errors in the equation above without harming consistency of . Note that the variance-covariance matrix for v = ( , , … , )′ is: By substituting estimates for and , we can conduct FGLS estimation using this matrix as the weighting matrix. O U (x)