### 12.6.3 Re-expressing SMDs by transformation to odds ratio

A transformation of a SMD to a (log) odds ratio is available, based on the assumption that an underlying continuous variable has a logistic distribution with equal standard deviation in the two intervention groups (Furukawa 1999, Chinn 2000). The assumption is unlikely to hold exactly and the results must be regarded as an approximation. The log odds ratio is estimated as

,

(or approximately 1.81×SMD) The resulting odds ratio can then be combined with an assumed control group risk to obtain an absolute risk reduction as in Section 12.5.4.3. These control group risks refer to proportions of people who have improved by some (unspecified) amount in the continuous outcome (‘responders’). Table 12.6.a shows some illustrative results from this method. These NNTs may be converted to people per thousand by using the formula 1000/NNT.