Modelling Budget Impact: Analytical Techniques When Limits on Cost-Sharing are Imposed on Skewed Health Expenditure Data

Decision-makers often request costing models of multi-tiered benefit programs, such as those involving different levels of cost-sharing at each tier of expenditure. This situation presents particular modelling problems as health expenditure data available from related programs are likely to be positively skewed with non-constant variance. Based on the results of a Monte Carlo simulation producing 50 log-normal expenditure distributions, this paper provides a method for working with such data to produce cost estimates that utilize a composite measure referred to as the anchored distance - a standardized measure of the range over which the tier is defined. This measure helps to determine a measure of central tendency of a tier equivalent to that of the tier's mean expenditure for the purposes of determining a unit price within each tier of a distribution of expenditures. The empirical results suggest that every one unit increase in the anchored distance results in a 26% shift to the left of the central tendency from the tier's median value. Further, this estimate is, on average, just 0.6% different from the actual mean price for the tier. This measure as well as that of a suggested measure of quantity are particularly useful as decision-makers vary the range over which cost-sharing is applied because they are simple to recalculate without requiring access to the complete expenditure data. This technique should assist economists who attempt to model statistically valid budget impact analyses using such data.