Random-effects models were conducted in which the OR for each substance outcome was weighted by the inverse variance of the OR. Heterogeneity of effect sizes was estimated using the standard Cochran Q test, which approximates a χ2 distribution with k–1 df, where k is the number of effect sizes and indicates the degree of consistency of findings across studies.23 A nonsignificant Q test statistic suggests that the pooled OR represents a unitary effect. When the P value associated with the Q statistic was equal or less than.10, random-effects metaregression analyses were conducted to determine whether the study characteristics described could explain variability across studies. Publication bias was assessed via the Egger24 and Begg25 tests. Leave-one-out sensitivity analyses were conducted when heterogeneous effect sizes were observed. In addition, we examined whether any of the moderator variables predicted significant variance in the effect sizes with significant heterogeneity. The meta-analysis statistical analyses were performed using STATA statistical software (release 11; StataCorp LP).
