Zero-Inflated Poisson Models with Measurement Error in the Response

Abstract

Zero-inflated count data arise frequently from genomics studies. Analysis of such data is often based on a mixture model which facilitates excess zeros in combination with a Poisson distribution, and various inference methods have been proposed under such a model. Those analysis procedures, however, are challenged by the presence of measurement error in count responses. In this article, we propose a new measurement error model to describe error-contaminated count data. We show that ignoring the measurement error effects in the analysis may generally lead to invalid inference results, and meanwhile, we identify situations where ignoring measurement error can still yield consistent estimators. Furthermore, we propose a Bayesian method to address the effects of measurement error under the zero-inflated Poisson model and discuss the identifiability issues. We develop a data-augmentation algorithm that is easy to implement. Simulation studies are conducted to evaluate the performance of the proposed method. We apply our method to analyze the data arising from a prostate adenocarcinoma genomic study.

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“…Instead, we generated the data through computer simulation using R, following these steps: The beta values and conditions were used in Lalonde's (2014) study, which have been shown to greatly affect the relative bias, error rate, and power of the models. Some studies also consider the potential impact of measurement errors in the response variable, a complication Zhang and Yi (2023) addressed in their work on ZIP models. Their methodology provides a foundation for dealing with measurement errors.…”

mbDecoda: A debiased approach to compositional data analysis for microbiome surveys

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