A semiparametric Gumbel regression model for analyzing longitudinal data with non-normal tails

Area of Science:

• Biostatistics
• Epidemiology
• Medical Informatics

Background:

• Abnormal biomarker values, often in distribution tails, indicate disease. Early detection via biomarkers is vital for prevention.
• Traditional regression models may not adequately capture associations with extreme biomarker values.
• Accurate modeling of longitudinal biomarker data, including time effects and measurement error, is essential.

Purpose of the Study:

• To propose novel semiparametric Gumbel regression models for longitudinal continuous biomarker outcomes.
• To flexibly model time-dependent effects on biomarker levels and account for measurement error.
• To develop an efficient asymptotic variance estimator for regression parameters.

Main Methods:

• Utilized the Expectation-Maximization (EM) algorithm with a two-dimensional grid search for parameter estimation.
• Developed an efficient asymptotic variance estimator for regression parameters.
• Applied the proposed model alongside existing methods to a diabetes study dataset.

Main Results:

• The proposed semiparametric Gumbel regression model effectively handles longitudinal biomarker data with extreme values.
• The developed variance estimator demonstrated theoretical and simulated asymptotic unbiasedness.
• The model was successfully applied to investigate risk factors for diabetes using real-world data.

Conclusions:

• Semiparametric Gumbel regression models offer a robust approach for analyzing longitudinal biomarker data, particularly for identifying disease associations.
• The proposed methods enhance the ability to detect disease risk by accounting for biomarker distribution tails and measurement error.
• This approach holds promise for improving early disease detection and prevention strategies.