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

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

SUBMITTER: Chen W

PROVIDER: S-EPMC6013902 | biostudies-other | 2018 Jun

REPOSITORIES: biostudies-other

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

Chen Wansu W Qian Lei L Shi Jiaxiao J Franklin Meredith M

BMC medical research methodology 20180622 1

<h4>Background</h4>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.<h4>Methods</h4>In this simulation study, the statistical performance of the two models was compared when the log link function was misspecified or the response ...[more]

PMID: 29929477

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Project description:BackgroundThe odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR.MethodsWe propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial.ResultsIn simulation studies, confidence intervals for the OR were 56-65% as wide (geometric model), 75-79% as wide (Poisson model), and 61-69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression.ConclusionsMore precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions.

Dataset Information

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

Publications

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

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