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Title: Semiparametric Gumbel regression model for analyzing longitudinal data with non-normal tails Authors:  David Couper - University of North Carolina at Chapel Hill (United States)
Donglin Zeng - University of North Carolina at Chapel Hill (United States)
Noorie Hyun - Medical College of Wisconsin (United States) [presenting]
Abstract: Abnormal longitudinal values in biomarkers can be a sign of abnormal status or disease. Identifying new biomarkers for early and efficient disease detection is crucial for disease prevention. Compared to the majority of the healthy general population, abnormal values are located within the tails of the biomarker distribution. Thus, parametric regression models that accommodate abnormal values in biomarkers can be better for detecting the association between biomarkers and disease. We propose semiparametric Gumbel regression models for (1) longitudinal continuous biomarker outcomes, (2) flexibly modeling the time-effect on the outcome and (3) accounting for the measurement error in biomarker measurements. We adopted the EM algorithm in combination with a two-dimensional grid search to estimate regression parameters and a function of time-effect. We proposed an efficient asymptotic variance estimator for regression parameter estimates. The proposed estimator is asymptotically unbiased in both theory and simulation studies. We applied the proposed model and two other models to investigate associations between fasting blood glucose biomarkers and potential risk factors from a diabetes ancillary study to the Atherosclerosis Risk in Communities (ARIC) study. The real data application was illustrated by fitting the proposed regression model and by graphically evaluating the goodness-of-fit value.