Abstract
Marginal analysis evaluates changes in an objective 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 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 paper, the first in a two-part series, introduces and illustrates the calculation of the ME for a variety of regression models often used in health services research. Part One includes a review of prior studies discussing MEs, followed by derivation of ME formulas for various regression models including linear, logistic, multinomial logit model (MLM), generalized linear model (GLM) for continuous data, GLM for count data, two-part model, sample selection (two-stage) model, and parametric survival model. Prior theoretical papers in health services research reported the derivation and interpretation of ME primarily for the linear and logistic models, with less emphasis on count models, survival models, MLM, two-part models, and sample selection models. These additional models are relevant for health services research studies examining costs and utilization. Part Two of the series will focus on the methods for estimating and interpreting the ME in applied research. The illustration, discussion, and application of ME in this two-part series support the conduct of future studies applying the marginal concept.
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Acknowledgments
The authors are grateful for the research assistance provided by Richard Wooldridge and Dinci Pennap. The authors are grateful to Samuel Kofi Ampaabeng, Ph.D., for his review of and feedback on the online Technical Appendix. All remaining errors are the authors’ responsibility.
The authors have no conflicts of interest to declare.
The review and interpretation of findings are the sole responsibility of the authors. Eberechukwu Onukwugha contributed to the conceptual framework, drafted manuscript sections, revised the manuscript with input from all co-authors, and serves as the overall guarantor for the work. Jason Bergtold drafted manuscript sections and reviewed, commented on, and edited all drafts of the manuscript. Rahul Jain contributed to the conceptual framework, drafted manuscript sections, reviewed, commented on, and edited all drafts of the manuscript.
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Onukwugha, E., Bergtold, J. & Jain, R. A Primer on Marginal Effects—Part I: Theory and Formulae. PharmacoEconomics 33, 25–30 (2015). https://doi.org/10.1007/s40273-014-0210-6
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DOI: https://doi.org/10.1007/s40273-014-0210-6