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A Primer on Marginal Effects—Part II: Health Services Research Applications

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Abstract

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.

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Acknowledgments

The authors have no conflicts of interest to declare.

The review and interpretation of findings are the sole responsibility of the authors. Eberechukwu Onukwugha drafted manuscript sections, conducted statistical analyses, revised the manuscript with input from all co-authors and serves as the overall guarantor for the work. Jason Bergtold conducted statistical analyses, drafted manuscript sections and reviewed, commented on, and edited all drafts of the manuscript. Rahul Jain conducted statistical analyses, drafted manuscript sections, reviewed, commented on, and edited all drafts of the manuscript.

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No funding was received for the preparation of this article.

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Authors and Affiliations

  1. Department of Pharmaceutical Health Services Research, University of Maryland School of Pharmacy, 220 Arch Street, 12th Floor, 21201, Baltimore, MD, USA

    E. Onukwugha

  2. Department of Agricultural Economics, Kansas State University, 304G Waters Hall, Manhattan, KS, 66506-4011, USA

    J. Bergtold

  3. HealthCore, Inc., 800 Delaware Avenue 5th Floor, Wilmington, DE, 19801, USA

    R. Jain

Authors
  1. E. Onukwugha
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  2. J. Bergtold
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  3. R. Jain
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Correspondence to E. Onukwugha.

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Onukwugha, E., Bergtold, J. & Jain, R. A Primer on Marginal Effects—Part II: Health Services Research Applications. PharmacoEconomics 33, 97–103 (2015). https://doi.org/10.1007/s40273-014-0224-0

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  • DOI: https://doi.org/10.1007/s40273-014-0224-0

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