Mean & SD to % & number
Here are the calculaters to impute the proportion and number of responders (or remitters) from the mean and stanrdar deviation, assuming the normal distribution. This method has been developed using depression and anxiety meta-analyses (Furukawa TA et al., 2005) and validated with schizophrenia dataset (Samara et al., 2013) and insomnia dataset (Furukawa Y et al., 2024).
For example, if the upper limit of the normal range is 12 (say, the half the baseline HAM-D mean) and the number of patients in the group is 98 and the endpoint mean and SD of HAM-D is 15 and 6, then 30.8% of the group should be below 12 under the normal distribution assumption. Rounding the numbers you get 30 persons under 12.
目次
Negative outcomes
Positive outcomes
Some outcomes measure positive outcomes, with larger numbers meaning better outcomes (e.g., WHO-5, GAF, sleep efficiency). Below are the calculators for such outcomes.
In some cases, the change score is expressed in this direction. For example, 10-point improvement in PANSS is actually a decrease in PANSS, but can be expressed in a positive way. If the average change is 10 (SD=5), and you know that the change has to be greater than 8 in order to have 50% or greater change from baseline (because the baseline score is 16), then you enter 98 for the number of patients and 10 for the observed mean and 5 for SD, and 8 for the lower limit of the normal range. Then the number of patients responding is 64.
Reference
Furukawa TA, Cipriani A, Barbui C, Brambilla P, Watanabe N. Imputing response rates from means and standard deviations in meta-analyses. Int Clin Psychopharmacol. 2005;20(1):49-52. doi:10.1097/00004850-200501000-00010
Samara MT, Spineli LM, Furukawa TA, et al. Imputation of response rates from means and standard deviations in schizophrenia. Schizophr Res. 2013;151(1-3):209-214. doi:10.1016/j.schres.2013.10.029
Furukawa Y, Sakata M, Yamamoto R, et al. Components and Delivery Formats of Cognitive Behavioral Therapy for Chronic Insomnia in Adults: A Systematic Review and Component Network Meta-Analysis. JAMA Psychiatry. 2024;81(4):357-365. doi:10.1001/jamapsychiatry.2023.5060
名古屋市立大学医学部卒業後、南生協病院での初期研修を経て、東京大学医学部附属病院精神神経科、東京武蔵野病院で専攻研修。日本専門医機構認定精神科専門医、精神保健指定医。臨床と並行してメタアナリシスを中心とした臨床研究を主導。筆頭著者として、JAMA Psychiatry, British Journal of Psychiatry, Schizophrenia Bulletin, Psychiatry and Clinical Neuroscienceなどのトップジャーナルに論文を発表。不眠の認知行動療法 (CBT-I) などの心理療法や、精神科疾患の薬物療法について、臨床で抱いた疑問に取り組んでいる。メディア報道・講演など。
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