Measurement error–tolerant Poisson regression for Valley Fever incidence prediction

The incidence of Valley Fever can be predicted using a Poisson regression model, which links the expected incidence count to influential covariates with model coefficients. In real-world practice, the estimated model coefficients are sensitive to the inevitable measurement errors in the covariates, which are usually manifested as classical errors and/or Berkson errors. While conventional methods have separately addressed each type of error, the joint consideration of both, referred to as mixture measurement error in this article, is currently absent from the existing literature, leaving model coefficient estimators with significant biases. This article presents a measurement-error tolerant Poisson regression to mitigate the impacts of the mixture measurement error in covariates of health-care data analysis. An error-structureadapted quasi-likelihood estimation method is proposed to enhance the accuracy of model estimation. The effectiveness of the proposed method is demonstrated through a numerical case study built upon a Valley Fever investigation, validating its improved estimation accuracy and robustness.