I have a compilation of following data on 10 studies, all of which had 2 groups: a control group which received usual treatment and an active group which received an intervention. The subjects were followed up for one year and any adverse events were counted. The data is as follows:
study events_control total_control events_active total_active 'First et al' 25 100 38 200 'Second et al' 30 150 45 400 etc
Hence, in the first study, 25 of 100 in control group had events while 38 of 200 had events in active group. And so on.
How can I combine all these data to determine if events in active group were more or less than those in control group? Thanks for your help.
Edit: I was thinking of this option: since I have all the numbers, can I combine all 4 columns and get events in control and active groups and also total number of subjects with all studies taken together. Then I can compute overall odds ratio and its confidence interval.
Using this method 55/250 events occurred in the control group and 83/600 in active group, giving the overall OR is 0.57 with 95% CI of 0.39 and 0.83. These are not too different from the estimate of 0.536 (CI: 0.156, 0.916) using metafor package, as detailed in the excellent answer by @user33. Can this be a reasonable strategy? If not, what are the drawbacks?
Edit2: To take into account that data has come from different studies, can we use a mixed effects anova as follows:
aov(event_rate ~ treatment_type + Error(study_id/treatment_type), data=mydata)