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Addressing missing responses and categorical covariates in binary regression modeling: an integrated framework
Pradhan, Vivekananda
Pradhan, Vivekananda
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2024
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Abstract
In the field of applied statistics, the challenge of missing data in binary regression analyses is pervasive. Common strategies, such as complete case analysis (CC), frequently fall short, particularly in smaller datasets where they can induce bias. Traditionally, methods to tackle missing data have been divided, focusing on either missing covariates or missing responses, but seldom both. This limitation is prominent in sectors such as biomedical research, where both the response variables and covariates often suffer from missingness. This thesis presents an expectation maximization (EM) algorithm that proficiently handles missing data at both the response and covariate levels. It is predicated on the assumption that covariate data are missing at random (MAR), while responses are considered nonignorable. Additionally, it incorporates a bias correction method inspired by Firth (1993) to improve model fitting, particularly in contexts of small sample sizes. Through simulation studies and the examination of real data, the effectiveness and utility of our approach are substantiated. Our findings underscore its potential to significantly enhance the precision and reliability of binary regression analyses in scenarios plagued by missing data. The thesis culminates in proposing an exact likelihood method for fitting binary logistic regression models with missing covariates. This method has been validated through comprehensive simulations and data analyses, affirming its viability.
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