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Imputing response rates from means and standard deviations in meta-analyses

Furukawa, Toshi A.a; Cipriani, Andreab; Barbui, Corradob; Brambilla, Paoloc; Watanabe, Norioa d

International Clinical Psychopharmacology: January 2005 - Volume 20 - Issue 1 - p 49-52

The principle of intention-to-treat analysis must be strictly applied to both individual randomized controlled trial and meta-analysis but, in doing so, would involve imputation of some missing data. There is little literature on how to perform this in the case of meta-analysis. For dichotomous outcome measures, one possible strategy is to carry out a sensitivity analysis based on the so-called best case/worst case analyses. For continuous outcomes, it may be possible to achieve this if we can dichotomise the continuous outcomes. Here, we empirically examined the appropriateness of converting continuous outcomes (expressed as mean±SD) into dichotomous outcomes (expressed as response rates) in four completed meta-analyses of depression and anxiety, assuming normal distribution of the continuous outcome measures. The agreement between the actually observed versus the imputed raw numbers of responders was indicated by an intraclass correlation coefficient of 0.97 (95% confidence interval 0.95–0.98). The pooled relative risks of the four meta-analyses based on the imputed values were virtually identical to those based on the actually observed values. When individual trials report the means±SDs of their outcome measures but fail to report response rates, it may therefore be possible to impute the response rates based on the means±SDs, and then submit the meta-analysis to worst case/best case analyses. This would allow a more robust and clinically interpretable estimation of the true, underlying treatment effect to be made.

aDepartment of Psychiatry, Nagoya City University Medical School, Mizuho-cho, Mizuho-ku, Nagoya, Japan

bDepartment of Medicine and Public Health, Section of Psychiatry and Clinical Psychology, University of Verona, Ospedale Policlinico, Verona, Italy

cDepartment of Pathology and Experimental and Clinical Medicine, Section of Psychiatry, University of Udine, Udine, Italy

dHealth Services Research Department, Institute of Psychiatry, King's College London, University of London, London, UK

Conflict of interest: T.A.F. has received fees for speaking and also several research grants from pharmaceutical companies that market antidepressants (paroxetine, fluvoxamine, milnacipran, trazodone, mianserin), antipsychotics (risperidone, olanzapine, quetiapine), nootropics (donepezil) and anxiolytics (loflazepate).

Correspondence and requests for reprints to Toshi A. Furukawa, Department of Psychiatry, Nagoya City University Medical School, Mizuho-cho, Mizuho-ku, Nagoya 467-8601, Japan

Tel: +81 52 853 8271; fax: +81 52 852 0837;


Received 11 October 2004 Accepted 1 November 2004

© 2005 Lippincott Williams & Wilkins, Inc.