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. Howe...

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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
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Abstract	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.
AbstractList	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. 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 oovariates 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.
Author	Austin, Peter C.
Author_xml	– sequence: 1 givenname: Peter C. surname: Austin fullname: Austin, Peter C. email: peter.austin@ices.on.ca organization: Institute for Clinical Evaluative Sciences
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Cites_doi	10.1093/pan/mpl013 10.1080/00031305.1986.10475403 10.1002/sim.2580 10.1002/sim.3150 10.1016/S0895-4356(00)00321-8 10.1161/CIRCOUTCOMES.108.790634 10.1002/0471445428 10.1016/j.jtcvs.2007.07.021 10.1002/sim.2328 10.1093/biomet/70.1.41
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SubjectTerms	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
Title	Using the Standardized Difference to Compare the Prevalence of a Binary Variable Between Two Groups in Observational Research
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