Influence function based variance estimation and missing data issues in case-cohort studies

Area of Science:

• Epidemiology
• Biostatistics
• Survival Analysis

Background:

• Cox proportional hazards models require many cases for efficient relative risk estimation.
• The case-cohort design, proposed by Prentice (1986), enhances efficiency by measuring covariates on all cases and a random cohort sample.
• Existing estimation and sampling methods for case-cohort designs have been further developed.

Purpose of the Study:

• To formalize Barlow's (1994) variance estimation approach for case-cohort designs.
• To derive a robust variance estimator using influence functions.
• To adapt methods for missing covariate data in case-cohort studies.

Main Methods:

• Formalization of Barlow's (1994) variance estimation approach.
• Derivation of a robust variance estimator based on influence functions.
• Development of methods to handle missing covariate information, including chance missingness and design-dependent missingness.
• Adaptation of S-plus code for estimating influence function variances with missing covariates.

Main Results:

• A robust variance estimator applicable to various case-cohort estimators was derived.
• Influence functions were derived for estimators using observed sampling fractions instead of known probabilities.
• Modifications for handling missing covariate data were discussed and implemented in code.
• The utility of the methods was demonstrated using esophageal and gastric cancer case-cohort studies.

Conclusions:

• The proposed robust variance estimator enhances the analysis of case-cohort studies.
• The methods provide practical solutions for design and analytic challenges, particularly with missing covariate data.
• The adapted code facilitates the estimation of influence function variances in complex epidemiological studies.