Abstract
BackgroundLog-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.MethodsIn 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).ResultsPoint 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.ConclusionUnder model misspecification, the robust Poisson model was generally preferable because it provided unbiased estimates of risk ratios.
Highlights
Log-binomial and robust Poisson regression models are popular approaches to estimate risk ratios for binary response variables
Generalized linear models (GLM) originate from a significant extension of traditional linear regression models [14]. They consist of a random component that specifies the conditional distribution of the response variable (Y) from an exponential family given the values of the explanatory variables X1,X2,···,Xk, a linear predictor component that is a linear function of the predictors, ƞ=β0+β1X1+β2X2+···+βkXk, where β=(β0,β1,...,βk)T is the vector of the parameters, and a smooth invertible link function that transforms the expectation of the response variable, μ ≡ E(Y), to the linear predictors: g(μ)=ƞ=β0+β1X1+β2X2+···βkXk
Our findings suggest that 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 for even a small proportion of observations
Summary
Log-binomial and robust (modified) Poisson regression models are popular approaches to estimate risk ratios for binary response variables. When events are common, odds ratios always overestimate risk ratios [1] Zhang and Yu [2] suggested a correction for odds ratios to give a risk ratio in studies of common outcomes This method was subsequently shown to result in inconsistent point estimates as well as invalid confidence intervals [3]. In medical and public health research, log-binomial and robust Poisson regression models are widely used to directly estimate risk ratios for both common and rare outcomes. They can be used to estimate the effect of clinical characteristics (e.g. obesity, smoking, history of stroke, exercise, or diet) on a health condition
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