Presentation: Corrected Bias Reduction for Generalized Linear Models
Speaker: Andrew Humbert, Graduate Student, UW Biostatistics
Abstract: Dichotomous variables are frequently used to measure health outcomes. Generalized linear models (GLM) are one popular method to analyze the relationship between covariates and the outcome. By specifying a log link function, GLMs can be used to estimate relative risk, which are often preferred for their interpretability over odds ratios. Because of issues in fitting algorithms, a Poisson working distribution is often assumed despite knowing the data truly follows a binomial distribution. Asymptotically, the estimates are still consistent and the standard errors (when using a robust estimation method) reliable. However, this is not necessarily true in the finite sample setting. Due to the curvature of the score functions used in GLMs, the parameter estimates are biased. Firth proposes a corrective method for correctly specified GLMs that shifts the score function to produce estimates with reduced bias. However, this method does not account for the incongruity of the model. Failing to account for this incongruity leads to poor bias reduction performance and can even increase the bias. Our corrected bias reduction (CBR) method address the incongruity present in this type of model, and adjusts the score function taking this into consideration.