Artikel
Comparison of standardized difference and z-difference as balance measures
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Autoren
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Alexandra Strobel
- Martin-Luther-University Halle-Wittenberg, Halle (Saale), Germany
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Andreas Wienke
- Martin-Luther University Halle-Wittenberg, Institute of Medical Epidemiology, Biostatistics and Informatics, Halle (Saale), Germany
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Oliver Kuß
- Deutsches Diabetes-Zentrum (DDZ), Leibniz-Zentrum für Diabetes-Forschung an der Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany
| Veröffentlicht: | 6. September 2024 |
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Gliederung
Text
Background: In the realm of analyzing non-randomized clinical trials through, a necessary consideration lies in assessing the balance of covariates between treatment groups. One famous way to deal with baseline imbalance is Propensity Score Matching (PSM) . Various statistical metrics have been introduced to compare covariate balance in a PS matched trial, with the standardized difference (SMD) being a commonly employed measure [1]. Typically, SMD values are expressed in absolute terms and compared against a predetermined threshold, often set at 0.1. However, the practice of comparing absolute values with fixed cutoffs yields limitations, in particular, it makes the expected value of the SMD depending on the sample size. Alternative measures, like the z-difference [2], offer advantages in terms of interpretability and comparability.
Methods: We compare the mathematical properties of two balance metrics, the SMD and the z-difference, when presented in absolute terms. Our analysis is complemented by a small-scale simulation study and an empirical investigation.
Results: We illustrate that while the absolute covariate-specific value of SMD is irrespective of sample size, its distribution is influenced by variations in sample size. Consequently, when presenting SMD in absolute terms, the expected value depends on the sample size, thus questioning the validity of the commonly utilized cutoff. Conversely, the distribution of z-differences is not affected by the sample size. Furthermore, an aggregate measure for global balance, the sum of squared z-differences, can be defined which also remains resilient to changes in sample size.
Conclusion: Our findings suggest exercising caution when measuring balance in clinical trials by the SMD in absolute terms and advise against relying on fixed cutoffs for comparison. Instead, we propose embracing z-differences as they provide more resilient and readily interpretable measures of balance in PS matched trials.
The authors declare that they have no competing interests.
The authors declare that an ethics committee vote is not required.
References
- 1.
- Austin PC. Balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity-score matched samples. Stat Med. 2009;28(25):3083-3107.
- 2.
- Kuss O. The z-difference can be used to measure covariate balance in matched propensity score analyses. J Clin Epidemiol. 2013;66(11):1302-1307.
