A method for combining matched and unmatched binary data: Application to randomized, controlled trials of photocoagulation in the treatment of diabetic retinopathy

A method for combining matched and unmatched data is described and was applied to the results of randomized, controlled trials of photocoagulation in the treatment of diabetic retinopathy. A pooled estimate from the matched and unmatched studies war obtained by adaptation of the Mantel-Haenszel method, where the strata were unmatched studies and matched pairs within studies. A test of significance was based on the Mantel-Haenszel chi-square statistic, the latter also being used to calculate test-based confidence intervals. A test of homogeneity was performed by combining Mantel-Haenszel chi-square statistics from the matched and unmatched studies. By these methods, the combined estimate of the risk of deterioration of visual acuity for those receiving photocoagulation (relative to a risk of unity for those not receiving photocoagulation) was 0.37 (95 per cent confidence interval 0.29-0.46). The chi-square statistic (1 df) for an effect of treatment was 87.75 (p < 0.0001). The chi-square statistic for homogeneity of relative risk among studies was 11.20 (4 df, p < 0.05). However, this result was influenced disproportionately by one small matched study.