Correcting for selection bias in estimation of within-individual variance

Area of Science:

• Biostatistics
• Statistical modeling
• Population studies

Background:

• Within-individual variance is crucial for understanding biological and behavioral variability.
• Screening studies often involve repeated measures, but may introduce bias through selective observation.
• Existing variance estimators can be inaccurate when initial observations influence subsequent data collection.

Purpose of the Study:

• To identify and correct bias in the estimation of within-individual variance.
• To develop an unbiased estimator for situations with a selection cutoff based on initial observations.
• To extend the methodology to bivariate data with selection on a single variable.

Main Methods:

• Derivation of the expected value of the usual within-individual variance estimator.
• Application of the derived expected value to formulate an unbiased estimator.
• Generalization of the method to a bivariate case with selective observation on one variable.

Main Results:

• The standard estimator for within-individual variance is shown to be biased under selective screening.
• A novel, unbiased estimator for within-individual variance is derived.
• The unbiased estimation method is applicable to bivariate data with specific selection criteria.

Conclusions:

• The developed unbiased estimator corrects for bias introduced by screening procedures in repeated measures studies.
• This statistical approach enhances the accuracy of variance component estimation in observational studies.
• The findings have implications for fields utilizing screening and repeated measurements, such as clinical research and public health.