Weighted χ² tests for multiple group comparisons in observational studies

Abstract

Although ${\chi }^2$ test and F test are commonly used for multiple group comparisons in experimental data, these methods can not be directly used to examine group differences in observational studies because of the confounding factors. Since the seminal work by Rosenbaum and Rubin (1983), the inverse probability weighting (IPW) method has been applied to compare pairs among multiple treatment groups without controlling the family-wise error rate (FWER). In this article, we propose to examine whether there is an overall significant group difference using two weighted ${\chi }^2$ tests for categorical/continuous outcomes. Our extensive simulation studies show that the proposed methods can control the FWER, while the traditional tests have an inflated type I error rate. We apply the proposed weighted ${\chi }^2$ tests to investigate whether fruit/vegetable intakes are associated with heart attack using the 2015 Kentucky BRFSS dataset and to examine the effect of physical/recreational exercise on weight gain using the NHEFS dataset.

Keywords:

• Observational studies
• propensity score
• inverse probability weighting
• weighted tests

Acknowledgment

The authors would like to thank the Associate Editor and one anonymous reviewer for their constructive comments which led to this improved version.

Disclosure statement

No potential conflict of interest was reported by the author(s).