Marginal Analysis of Longitudinal Count Data in Long Sequences: Methods and Applications to A Driving Study

Area of Science:

• Statistics
• Biostatistics
• Longitudinal Data Analysis

Background:

• Traditional longitudinal data analysis methods are optimized for many subjects with few observations.
• The Naturalistic Teenage Driving Study (NTDS) presents a contrasting scenario: few subjects with extensive longitudinal data.
• Existing methods struggle with time-dependent covariates in low-count longitudinal data.

Purpose of the Study:

• To develop and evaluate statistical methodologies for marginal analysis of longitudinal count data with few, very long sequences.
• To address limitations of generalized estimating equations in specific longitudinal data scenarios.
• To propose a novel approach suitable for data structures like the NTDS.

Main Methods:

• Examination of standard generalized estimating equations (GEE) with different correlation structures.
• Exploration of a within-cluster resampling (WCR) approach using random subsamples.
• Development of a novel WCR method operating on separated blocks within subjects.

Main Results:

• Standard GEE methods were found unsatisfactory for low counts and time-dependent covariates.
• The proposed novel WCR method demonstrated superior performance compared to existing methods.
• Simulation experiments validated the effectiveness of the new WCR approach.

Conclusions:

• The novel within-cluster resampling method is effective for marginal analysis of longitudinal count data in scenarios with few, long sequences.
• This methodology offers a significant improvement over standard techniques for complex longitudinal datasets.
• The findings are directly applicable to studies like the NTDS.