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. 2024 Feb 14;53(2):dyae030.
doi: 10.1093/ije/dyae030.

M-estimation for common epidemiological measures: introduction and applied examples

Rachael K Ross  1 , Paul N Zivich  2   3 , Jeffrey S A Stringer  4 , Stephen R Cole  3
Affiliations

M-estimation for common epidemiological measures: introduction and applied examples

Rachael K Ross et al. Int J Epidemiol. .

Abstract

M-estimation is a statistical procedure that is particularly advantageous for some comon epidemiological analyses, including approaches to estimate an adjusted marginal risk contrast (i.e. inverse probability weighting and g-computation) and data fusion. In such settings, maximum likelihood variance estimates are not consistent. Thus, epidemiologists often resort to bootstrap to estimate the variance. In contrast, M-estimation allows for consistent variance estimates in these settings without requiring the computational complexity of the bootstrap. In this paper, we introduce M-estimation and provide four illustrative examples of implementation along with software code in multiple languages. M-estimation is a flexible and computationally efficient estimation procedure that is a powerful addition to the epidemiologist's toolbox.

Keywords: M-estimation; data fusion; estimating equations; logistic regression; standardization.

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Conflict of interest statement

None declared.

References

    1. Cole SR, Chu H, Greenland S.. Maximum likelihood, profile likelihood, and penalized likelihood: a primer. Am J Epidemiol 2014;179:252–60. - PMC - PubMed
    1. Stefanski LA, Boos DD.. The calculus of M-estimation. Am Stat 2002;56:29–38.
    1. Naimi AI, Cole SR, Kennedy EH.. An introduction to g methods. Int J Epidemiol 2017;46:756–62. - PMC - PubMed
    1. Hernán MA, Robins JM.. Causal Inference: What If. Boca Raton: Chapman & Hall/CRC, 2020.
    1. Cole SR, Edwards JK, Breskin A. et al. Illustration of two fusion designs and estimators. Am J Epidemiol 2022;192:467–74. - PMC - PubMed