9.4.6  Combining dichotomous and continuous outcomes

Occasionally authors encounter a situation where data for the same outcome are presented in some studies as dichotomous data and in other studies as continuous data. For example, scores on depression scales can be reported as means or as the percentage of patients who were depressed at some point after an intervention (i.e. with a score above a specified cut-point). This type of information is often easier to understand and more helpful when it is dichotomized. However, deciding on a cut-point may be arbitrary and information is lost when continuous data are transformed to dichotomous data.

 

There are several options for handling combinations of dichotomous and continuous data. Generally, it is useful to summarize results from all the relevant, valid studies in a similar way, but this is not always possible. It may be possible to collect missing data from investigators so that this can be done. If not, it may be useful to summarize the data in three ways: by entering the means and standard deviations as continuous outcomes, by entering the counts as dichotomous outcomes and by entering all of the data in text form as ‘Other data’ outcomes.

 

There are statistical approaches available which will re-express odds ratios as standardized mean differences (and vice versa), allowing dichotomous and continuous data to be pooled together. Based on an assumption that the underlying continuous measurements in each intervention group follow a logistic distribution (which is a symmetrical distribution similar in shape to the normal distribution but with more data in the distributional tails), and that the variability of the outcomes is the same in both treated and control participants, the odds ratios can be re-expressed as a standardized mean difference according to the following simple formula (Chinn 2000):

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The standard error of the log odds ratio can be converted to the standard error of a standardized mean difference by multiplying by the same constant (√3/ π = 0.5513). Alternatively standardized mean differences can be re-expressed as log odds ratios by multiplying by π/√3 = 1.814. Once standardized mean differences (or log odds ratios) and their standard errors have been computed for all studies in the meta-analysis, they can be combined using the generic inverse-variance method in RevMan. Standard errors can be computed for all studies by entering the data in RevMan as dichotomous and continuous outcome type data, as appropriate, and converting the confidence intervals for the resulting log odds ratios and standardized mean differences into standard errors (see Chapter 7, Section 7.7.7.2).