The most common data structures in the biomedical studies have been matched or unmatched designs. Data structures resulting from a hybrid of the two may create challenges for statistical inferences. The question may arise whether to use parametric or nonparametric methods on the hybrid data structure. The Early Treatment for Retinopathy of Prematurity study was a multicenter clinical trial sponsored by the National Eye Institute. The design produced data requiring a statistical method of a hybrid nature. An infant in this multicenter randomized clinical trial had high-risk prethreshold retinopathy of prematurity that was eligible for treatment in one or both eyes at entry into the trial. During follow-up, recognition visual acuity was accessed for both eyes. Data from both eyes (matched) and from only one eye (unmatched) were eligible to be used in the trial. The new hybrid nonparametric method is a meta-analysis based on combining the Hodges-Lehmann estimates of treatment effects from the Wilcoxon signed rank and rank sum tests. To compare the new method, we used the classic meta-analysis with the t-test method to combine estimates of treatment effects from the paired and two sample t-tests. We used simulations to calculate the empirical size and power of the test statistics, as well as the bias, mean square and confidence interval width of the corresponding estimators. The proposed method provides an effective tool to evaluate data from clinical trials and similar comparative studies.