# Estimating the price elasticity of demand through value-based formulary designs

In 2010, Premera Blue Cross (Premera), a large nonprofit health plan in the Pacific Northwest implemented a value-based formulary design for its beneficiaries.   In essence, enrollees could purchase high-value treatments for low copayments and low-value treatments for higher copayments.  Can we use this change from more standard to value-base formulary designs to estimate the price elasticity of demand?

This is exactly what Yeung et al. (2018) attempt to do.  In the study, the “value” used for the value-based formulary was defined based on incremental cost-effectiveness ratios (ICERs).  Each drug was defined along three dimensions: active ingredient, dosage form, and brand-generic status. Premera’s change from standard cost-sharing benefit design to a value-based formulary was an exogenous shift in prices that could be used to measure the price elasticity of demand.

The price elasticity of demand measures the change in quantity of pharmaceuticals demanded when the price increases by 10%. The authors use a two-part model to estimate this elasticity parameter.  First, they use a probit regression to estimate the probability of a fill, where the explanatory variables were drug copay, drug fixed effects, drug fixed effects-drug copayment interactions, plan type, time trend, season and patient demographics.  In the second part of the model, the authors use “a generalized linear model with a logarithmic link function and a Poisson distribution to estimate the number of days’ supply.”  The authors then explain how these are used to determine the price elasticity of demand:

Then, based on the estimated models [i.e., the two-part models described above], we utilize the method of recycled predictions along with the factual (or counterfactual) copayment to predict the factual (or counterfactual) medication utilization in the VBF group for each part of the two‐part model. We then multiply the recycled predictions from the two parts to obtain the final conditional predicted mean factual (or counterfactual) values.

Using this approach, the authors find that the price elasiticty of demand is -0.16.  In other words, a doubling of copayment faced by the enrollees in this study is expected to reduce the quarterly number of fills of a medication by 16%.  This figure is similar to the number from in the RAND Health Insurance Experiment (RAND HIE).  However, there was some heterogeneity in these results.

…we find that for VBF Tier 1 drugs, which represent good value, price elasticity was larger for those that experienced price decreases but smaller for those that experienced price increases. Similarly, for drugs placed in higher VBF tiers, which represent lower value, price increases were associated with much higher price elasticities.

Price elasticities for branded drugs were larger in magnitude (-0.76) compared to generic medications (-0.03). The authors find that VBF improves social welfare.  However, their approach requires that the CEA conducted by the health plan must fully capture all sources of value. This assumption is unlikely to hold since the plan CEA was from a payer rather than societal perceptive.  Further, CEA that measures value for the average patient may miss significant patient heterogeneity due to patient effect modifiers or treatment preferences (e.g., preferences of efficacy vs. safety, dosing schedule, mode of administration).

One interesting note is that the paper’s findings imply that patients respond to prices.  While this makes perfect sense to an eocnomist, subsequent  patient focus groups found that “…beneficiaries were not aware of the new value‐based copayment tiering process.” Source:

## 1 Comment

1. Sarath says:

Hi,
Can you please share the full text of the article. Appreciate for your time and consideration.