Is the Standardised Mean Difference a suitable Measure of Treatment Effect?

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Authors
Scholten R, de BE, Bouter L
Abstract
Introduction: In meta-analysis the results of individual studies are combined to give one overall estimate of treatment effect if the patients, interventions and outcomes in the various studies are sufficiently similar. However, if the studies addressed the same conceptual entity (e.g. depression), but applied different instruments or scales, the results cannot be combined directly. In such circumstances the result of each individual study can be standardised by calculating a standardised mean difference (SMD) which is the difference of the means of both treatment arms divided by the pooled standard deviation. In this way, the treatment effect in each study is expressed in standard units (instead of in original units) and the results of all studies can be combined by calculating a weighted standardised mean difference (WSMD). The interpretation of the (W)SMD, however, is less straightforward compared with the original measures of treatment effect. To address this problem, it is advocated to back transform the (W)SMDs by multiplying the (W)SMD with a "typical" standard deviation of the instrument of interest in order to enable the interpretation of the results in original units. The result of this back transformation, however, depends on the size of the "typical" standard deviation (and thus on what is considered "typical"). The main problem of the SMD (which is shared by other standardised measures) is that the SMD is a function of both the effect (the difference of the means) and the variance of the observations (or the consistency between patients) within studies. With simple examples it can easily been shown that back transformation of WSMDs produces "incorrect" and confusing results that impede a straightforward interpretation of the clinical relevance of the treatment effect.

Discussion: It is concluded that the (W)SMD has limited value as a clinically meaningful measure of treatment effect. Meta-analysts should be aware of the fact that the (W)SMD can only serve as a (qualitative) measure of strength of evidence against the null hypothesis.