Variance Estimation for Logistic Regression in Case-cohort Studies

Abstract

Background: The logistic regression analysis proposed by Schouten et al (Stat Med. 1993;12:1733–1745) has been a standard method in current statistical analysis of case-cohort studies, and it enables effective estimation of risk ratios from selected subsamples, with adjustment of potential confounding factors. Schouten et al (1993) also proposed the standard error estimate of the risk ratio estimator can be calculated using the robust variance estimator, and this method has been widely adopted. Methods and Results: The robust variance estimator does not account for the duplications of case and subcohort samples and generally has certain bias (ie, inaccurate confidence intervals and P-values are possibly obtained). To address the invalid statistical inference problem, we provide an alternative bootstrap-based valid variance estimator. Through simulation studies, the bootstrap method consistently provided more precise confidence intervals compared with those provided using the robust variance method, while retaining adequate coverage probabilities. Conclusion: The robust variance estimator has certain bias, and inadequate conclusions might be deduced from the resultant statistical analyses. The proposed bootstrap variance estimator can provide more accurate and precise interval estimates. The bootstrap method would be an alternative effective approach in practice to provide accurate evidence.

Keywords

• case-cohort design
• logistic regression
• risk ratio
• bias
• bootstrap