A primer on marginal effects-part II: health services research applications.

Marginal analysis evaluates changes in a regression function associated with a unit change in a relevant variable. The primary statistic of marginal analysis is the marginal effect (ME). The ME facilitates the examination of outcomes for defined patient profiles or individuals while measuring the change in original units (e.g., costs, probabilities). The ME has a long history in economics; however, it is not widely used in health services research despite its flexibility and ability to provide unique insights. This article, the second in a two-part series, discusses practical issues that arise in the estimation and interpretation of the ME for a variety of regression models often used in health services research. Part one provided an overview of prior studies discussing ME followed by derivation of ME formulas for various regression models relevant for health services research studies examining costs and utilization. The current article illustrates the calculation and interpretation of ME in practice and discusses practical issues that arise during the implementation, including: understanding differences between software packages in terms of functionality available for calculating the ME and its confidence interval, interpretation of average marginal effect versus marginal effect at the mean, and the difference between ME and relative effects (e.g., odds ratio). Programming code to calculate ME using SAS, STATA, LIMDEP, and MATLAB are also provided. The illustration, discussion, and application of ME in this two-part series support the conduct of future studies applying the concept of marginal analysis.