Outcome-dependent sampling for longitudinal binary response data based on a time-varying auxiliary variable

Area of Science:

• Biostatistics
• Epidemiology
• Longitudinal Data Analysis

Background:

• Outcome-dependent sampling (ODS) is crucial for rare disease research and infeasible prospective studies.
• ODS designs efficiently maximize statistical information in longitudinal settings with rare binary responses under resource constraints.

Purpose of the Study:

• To introduce a semi-parametric, sequential offsetted logistic regression (SOLR) approach for validly estimating marginal model parameters from ODS biased samples.
• To address challenges in longitudinal data analysis where a repeatedly measured binary response is rare.

Main Methods:

• Proposing SOLR, which estimates the auxiliary variable-response relationship using an offsetted logistic regression to adjust for biased sampling.
• Combining auxiliary variable model results with sampling probabilities to create a second offset for correcting the target model.
• Detailing asymptotic standard error estimates that incorporate uncertainty from the auxiliary variable model.

Main Results:

• The SOLR approach provides a valid method for estimating marginal model parameters in ODS studies.
• The study examines the properties of SOLR estimators and compares them with existing methods.
• Asymptotic standard errors are developed to account for the uncertainty in the auxiliary variable model.

Conclusions:

• SOLR offers a statistically sound method for analyzing longitudinal data collected via ODS, particularly with rare outcomes.
• The proposed method enhances the efficiency and validity of statistical inference in resource-limited observational studies.
• This work contributes to robust methodologies for handling complex sampling designs in biostatistical research.