Original ArticleImputing missing standard deviations in meta-analyses can provide accurate results
Introduction
Conduct of a systematic review or a meta-analysis involves comprehensive search of relevant randomized controlled trials (RCTs) and their quantitative or qualitative synthesis. To pool results on a continuous outcome measure of the identified RCTs quantitatively, one needs both means and standard deviations (SDs) on that outcome measure for each RCT.
Many reports of RCTs, however, fail to provide SDs for their continuous outcomes. It is sometimes possible to use P or t or F values, reported in the original RCTs, to calculate exact SDs [1]. When none of these is available, it is recommended that one should contact primary authors [2]. However, the yield is very often very low; some are incontactable, some never respond, and others report that the data are discarded, lost or irretrievable because there are no longer any computers to read the tapes.
Some meta-analysts then resort to substitution of SDs of known outcome measures by those reported in other studies, either from another meta-analysis or from other studies in the same meta-analysis. But the validity of such practices has never been empirically examined.
The present article therefore aims to examine empirically the validity of borrowing SDs from other studies when individual RCTs fail to report SDs in a meta-analysis, by simulating the above-mentioned two imputation methods for SDs in two meta-analyses on antidepressants that we have conducted [3], [4]. Systematic reviews for depression are particularly suitable for this purpose, because Hamilton Rating Scale for Depression [5] (HRSD) is the de facto standard in symptom assessment and is used in many depression trials identified for overviews.
Section snippets
Imputation from a previous meta-analysis
We used the pooled SD for the 17-item HRSD and 21-item HRSD from a comprehensive meta-analysis of all three-armed trials for depression involving an investigational drug, an active comparison drug, and placebo [6] for two reasons. We are unaware of any other meta-analysis that dealt with the whole range of antidepressants along with placebo for depression. We argue that such a meta-analysis would provide a more impartial estimate of SDs for ratings scales than, for example, a meta-analysis
Characteristics of individual RCTs in the two meta-analyses
Of 133 RCTs pooled to examine the overall efficacy for fluoxetine vs. other antidepressants, 108 used HRSD, 8 used Montgomery-Asberg Depression Rating Scale (MADRS) [13], and 14 used other scales. Of the first group, 36 used 17-item HRSD, 39 used 21-item HRSD, and the remaining 33 used other or unknown versions of HRSD. Moreover, of the 36 studies that used HRSD-17, only 24 reported SDs; of the 39 which used HRSD-21, only 15 reported SDs. We therefore compared the meta-analytic results for 39
Discussion
Few studies to date have dealt with the problem of missing variance estimates for continuous variables in meta-analyses, although apparently the problem is annoyingly common. For example, in a systematic review of sodium reduction on blood pressure, fewer than half of the identified trials (10 out of 26 identified trials) published a variance estimate or information to allow one to derive it [14]. In the comprehensive meta-analysis of three-armed studies involving antidepressants [6], the
References (18)
- et al.
Meta-analysis in clinical trials
Control Clin Trials
(1986) - et al.
Variance imputation for overviews of clinical trials with continuous response
J Clin Epidemiol
(1992) - et al.
Publication and related bias in meta-analysis: power of statistical tests and prevalence in the literature
J Clin Epidemiol
(2000) - et al.
Statistics with confidence
(2000) - et al.
Cochrane reviewers' handbook. 4.2.0
(2003) - et al.
Amitriptyline versus other types of pharmacotherapy for depression (Cochrane Review)
- et al.
Fluoxetine versus other types of pharmacotherapy for depression
A rating scale for depression
J Neurol Neurosurg Psychiatry
(1960)- et al.
Antidepressant treatment of depression: a metaanalysis
Can J Psychiatry
(1996)
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