Context: the random effects meta-analysis is of studies that measure visits to the doctor (visits), as a continuous variable (by reporting mean visits and respective standard deviations) or as a binary variable (visited a doctor y/n, which I'll call 'visited'). Outcomes were measured during a pre-treatment period (usually 12 months) and a post-treatment period (usually 12 months after the intervention), and all studies used a non-exposed comparison group that was given the same measures pre-test and post-test. An example of how the visited data is reported is as follows, where the % indicates the proportion of n that visited in the respective pre-test or post-test period:
treatment: T1) n=100, visited = 90% | T2) n=90, visited = 60% comparison: T1) n=100, visited = 90% | T2) n=90, visited = 70%
Current understanding: I have read on another QandA, as well as papers by Hassleblad & Hedges (1995) and Borenstein et al. (2009) cited within it, that it is possible to convert Odds ratios to Cohen's D (and subsequently Hedge's g) if certain assumptions are met. The difference here is that the outcome is measured pre-test and post-test, and so the comparison thats made for binary outcomes is the proportion of those who visited pre-test compared with the proportion of those who visited post-test (for both study groups). This difference is then compared between treatment and comparison groups. The advice that I have is that it would be possible to compute hedge's g from the binary studies, but that this is ultimately a different outcome to mean difference and so shouldn't be compared.
Problem: there are approximately 10 studies that report mean differences, and 10 studies that report the dichotomous differences. My questions are as follows: are these two measures (continuous visits, and visited) comparable given that treatment groups and controls were compared pre-test and post-test? If so, how can I convert them to a common effect size so that they can be meta-analysed? Are there any caveats worth noting given that the continuos data is count-data?