Referral Rates for Intervention or Assessment : A Meta-Analysis of Racial Differences

We compare two statistical methods for combining event rates from several studies. Both methods treat each study as a separate stratum. The Peto-modified Mantel-Haenszel (Peto) method estimates a combined odds ratio assuming homogeneity across strata and provides a test for heterogeneity. The DerSimonian and Laird modified Cochran method (D&L) produces a weighted average of rate differences, where the weights allow for among-study variability. We analyse 22 meta-analyses from ten reports by both methods. The pooled estimates are divided by their standard errors to produce a Z-statistic. A t-test comparing Z-statistics from all 22 studies suggests that the D&L method tends to be more conservative [d(Peto - D&L) = 0.29, t = 2.53, p = 0.02]. For a subset of 14 non-heterogeneous studies, the difference is smaller and non-significant (d = 0.09, t = 0.72, p = 0.49). The results from the methods correlate well (r = 0.66 for all 22 studies, r = 0.95 for 14 non-heterogeneous studies). Thus, the presence of heterogeneity influences our conclusion. We discuss the statistical and scientific implications of these findings.