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Comparative Study
. 2018 Jun 22;18(1):63.
doi: 10.1186/s12874-018-0519-5.

Comparing performance between log-binomial and robust Poisson regression models for estimating risk ratios under model misspecification

Wansu Chen  1 , Lei Qian  2 , Jiaxiao Shi  2 , Meredith Franklin  3
Affiliations
Comparative Study

Comparing performance between log-binomial and robust Poisson regression models for estimating risk ratios under model misspecification

Wansu Chen et al. BMC Med Res Methodol. .

Abstract

Background: Log-binomial and robust (modified) Poisson regression models are popular approaches to estimate risk ratios for binary response variables. Previous studies have shown that comparatively they produce similar point estimates and standard errors. However, their performance under model misspecification is poorly understood.

Methods: In this simulation study, the statistical performance of the two models was compared when the log link function was misspecified or the response depended on predictors through a non-linear relationship (i.e. truncated response).

Results: Point estimates from log-binomial models were biased when the link function was misspecified or when the probability distribution of the response variable was truncated at the right tail. The percentage of truncated observations was positively associated with the presence of bias, and the bias was larger if the observations came from a population with a lower response rate given that the other parameters being examined were fixed. In contrast, point estimates from the robust Poisson models were unbiased.

Conclusion: Under model misspecification, the robust Poisson model was generally preferable because it provided unbiased estimates of risk ratios.

Keywords: Link function misspecification; Log-binomial regression; Model misspecification; Risk ratio; Robust (modified) Poisson regression.

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Conflict of interest statement

Ethics approval and consent to participate

The asthma study mentioned in the “A motivating example” Section was approved by the Institutional Review Board of Kaiser Permanente Southern California.

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no competing interests.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures

Fig. 1
Fig. 1
Percentage bias in log(RR) scale. a From left to right: increasing intercept(scenario I→II →III); b From left to right: increasing coefficient of β2 (scenario IV→III→V); c From left to right: change of link function (scenarios III, VI and VII). Red lines: Robust Poison; Blue lines: Log-binomial
Fig. 2
Fig. 2
Distribution of P(Y = 1). Y-axis: Percent; X-axis: P(Y = 1). a From left to right: increasing intercept (scenario I→II→III); b From left of right: increasing coefficient of β2 (scenarion IV→III→V); c From left to right: change of link function (scenarios III, VI and VII)
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