Using the Standardized Difference to Compare the Prevalence of a Binary Variable Between Two Groups in Observational Research

• Published in: Communications in statistics. Simulation and computation Vol. 38; no. 6; pp. 1228 - 1234
• Main Author: Austin, Peter C.
• Format: Journal Article
• Language: English
• Published: Colchester Taylor & Francis Group 14.05.2009; Taylor & Francis
• Subjects: 62P; Balance; Correlation; Distribution theory; Exact sciences and technology; Matching; Mathematics; Multivariate analysis; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Observational study; Probability and statistics; Probability theory and stochastic processes; Propensity-score matching; Sciences and techniques of general use; Standardized difference; Statistics; Correlation coefficient; Correlation; Observational study; Propensityscore matching; Statistical association; Multivariate analysis; Covariate; Mean estimation; Relative risk; Statistical method; Matching; Medical science; Standardized difference; Dichotomous variable; 62P; Correlation analysis; Distribution function; Numerical simulation; Application; Balance
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610910902859574

Researchers are increasingly using the standardized difference to compare the distribution of baseline covariates between treatment groups in observational studies. Standardized differences were initially developed in the context of comparing the mean of continuous variables between two groups. However, in medical research, many baseline covariates are dichotomous. In this article, we explore the utility and interpretation of the standardized difference for comparing the prevalence of dichotomous variables between two groups. We examined the relationship between the standardized difference, and the maximal difference in the prevalence of the binary variable between two groups, the relative risk relating the prevalence of the binary variable in one group compared to the prevalence in the other group, and the phi coefficient for measuring correlation between the treatment group and the binary variable. We found that a standardized difference of 10% (or 0.1) is equivalent to having a phi coefficient of 0.05 (indicating negligible correlation) for the correlation between treatment group and the binary variable.