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

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.

[1]  Peter C Austin,et al.  Report Card on Propensity-Score Matching in the Cardiology Literature From 2004 to 2006: A Systematic Review , 2008, Circulation. Cardiovascular quality and outcomes.

[2]  B. Everitt,et al.  Statistical methods for rates and proportions , 1973 .

[3]  Peter C Austin,et al.  A critical appraisal of propensity‐score matching in the medical literature between 1996 and 2003 , 2008, Statistics in medicine.

[4]  Gary King,et al.  Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference , 2007, Political Analysis.

[5]  Jacob Cohen Statistical Power Analysis for the Behavioral Sciences , 1969, The SAGE Encyclopedia of Research Design.

[6]  H. Riedwyl,et al.  Standard Distance in Univariate and Multivariate Analysis , 1986 .

[7]  D. Rubin,et al.  The central role of the propensity score in observational studies for causal effects , 1983 .

[8]  Peter C. Austin,et al.  A report card on propensity-score matching in the cardiology literature from 2004 to 2006: results of a systematic review , 2008 .

[9]  Peter C Austin,et al.  A comparison of propensity score methods: a case‐study estimating the effectiveness of post‐AMI statin use , 2006, Statistics in medicine.

[10]  P D Cleary,et al.  Validating recommendations for coronary angiography following acute myocardial infarction in the elderly: a matched analysis using propensity scores. , 2001, Journal of clinical epidemiology.

[11]  Peter C Austin,et al.  A comparison of the ability of different propensity score models to balance measured variables between treated and untreated subjects: a Monte Carlo study , 2007, Statistics in medicine.

[12]  Peter C. Austin,et al.  A critical appraisal of propensity score matching in the medical literature from 1996 to 2003 , 2008 .

[13]  Peter C Austin,et al.  Propensity-score matching in the cardiovascular surgery literature from 2004 to 2006: a systematic review and suggestions for improvement. , 2007, The Journal of thoracic and cardiovascular surgery.