Bias-corrected estimates for logistic regression models for complex surveys with application to the United States' Nationwide Inpatient Sample

For complex surveys with a binary outcome, logistic regression is widely used to model the outcome as a function of covariates. Complex survey sampling designs are typically stratified cluster samples, but consistent and asymptotically unbiased estimates of the logistic regression parameters can be obtained using weighted estimating equations (WEEs) under the naive assumption that subjects within a cluster are independent. Despite the relatively large samples typical of many complex surveys, with rare outcomes, many interaction terms, or analysis of subgroups, the logistic regression parameters estimates from WEE can be markedly biased, just as with independent samples. In this paper, we propose bias-corrected WEEs for complex survey data. The proposed method is motivated by a study of postoperative complications in laparoscopic cystectomy, using data from the 2009 United States' Nationwide Inpatient Sample complex survey of hospitals.