A positive association between anxiety disorders and cannabis use or cannabis use disorders in the general population- a meta-analysis of 31 studies

Background The aim of the current study was to investigate the association between anxiety and cannabis use/cannabis use disorders in the general population. Methods A total of N = 267 studies were identified from a systematic literature search (any time- March 2013) of Medline and PsycInfo databases, and a hand search. The results of 31 studies (with prospective cohort or cross-sectional designs using non-institutionalised cases) were analysed using a random-effects meta-analysis with the inverse variance weights. Lifetime or past 12-month cannabis use, anxiety symptoms, and cannabis use disorders (CUD; dependence and/or abuse/harmful use) were classified according to DSM/ICD criteria or scores on standardised scales. Results There was a small positive association between anxiety and either cannabis use (OR = 1.24, 95% CI: 1.06-1.45, p = .006; N = 15 studies) or CUD (OR = 1.68, 95% CI: 1.23-2.31, p = .001; N = 13 studies), and between comorbid anxiety + depression and cannabis use (OR = 1.68, 95% CI: 1.17-2.40, p = .004; N = 5 studies). The positive associations between anxiety and cannabis use (or CUD) were present in subgroups of studies with ORs adjusted for possible confounders (substance use, psychiatric illness, demographics) and in studies with clinical diagnoses of anxiety. Cannabis use at baseline was significantly associated with anxiety at follow-up in N = 5 studies adjusted for confounders (OR = 1.28, 95% CI: 1.06-1.54, p = .01). The opposite relationship was investigated in only one study. There was little evidence for publication bias. Conclusion Anxiety is positively associated with cannabis use or CUD in cohorts drawn from some 112,000 non-institutionalised members of the general population of 10 countries.

. Exclusion criteria applied to N=267 studies .. The mathematical approach to meta-analysis in this document is based on Borenstein et al., 2009 [1].

Computation of odds ratio (OR) and its 95% confidence interval (95%CI)
The odds ratios (OR) were not reported in some studies and were computed according to the following formulae based on the number of cases (letters A-D) in the following groups ('cannabis user' or 'cannabis user with cannabis use disorder (CUD)', 'non-user' or 'no CUD', 'anxiety' or 'anxiety+depression', 'no anxiety' or 'no diagnosis') below [1,  The OR for anxiety (vs. no anxiety) in cannabis users (vs. non-users or CUD vs. no CUD) was computed as follows [1, p. 36]: The OR for cannabis use (vs. no use or CUD vs. no CUD) in anxiety (vs. no anxiety) was computed as follows: The formulae indicate that both ORs are equivalent.
Since the OR is limited on its lower end (it cannot be negative) but can take on any positive value, its distribution is skewed [2]. Thus, to maintain symmetry and obtain an approximately normal distribution, the 95%CI was computed based on the log (natural logarithmic, ln) scale using the values from the contingency table above as follows [2]:

Computation of standardised mean difference (Cohen's d) and its conversion to OR
Some studies reported the severity of anxiety scores based on standardised scales in user and non-user (or CUD and no CUD) groups. Based on mean (M), standard deviation (SD) of scores and group size (N) in each group the standardised mean difference (Cohen's d) and its variance (V d ) were computed in these studies as follows [1, p. 26-27]: The d and V d were converted into the log OR scale as follows [1, p. 47

Combining of data in independent groups to compute Cohen's d
One study reported the severity of anxiety scores separately for boys and girls in non-user, user and user with CUD groups. Thus, the mean (M) and the standard deviation (SD) of scores for boys and girls had to be combined into a single score in each group (non-user, user and user with CUD).
The total sample size per group (N 1+2 ) was the sum of N 1 (number of boys) and N 2 (number of girls) in that group. The combined mean severity of anxiety score for boys (M 1 ) and girls (M 2 ) in each group (M 1+2 ) was computed as follows [1, p. 222]: The combined standard deviation of the mean severity of anxiety scores for boys (SD 1 ) and girls (SD 2 ) in each group (SD 1+2 ) was computed as follows [1, p. 222]: Based on the single M, SD, and N values per group, the standardised mean difference, Cohen's d, was computed for the difference between users -non-users and CUD -non-users as explained under subsection 2 of this document.
Combining OR from studies with dependent data (using the same cases/data sets) If the same cases were used in different studies or same studies provided two estimates of ORs based on the same cases then a mean of such ORs and its variance were computed. Because the same cases were used it was assumed that the ORs were dependent and thus the correlation between them is r=1. This approach is conservative in that it overestimates the variance of the mean OR and thus increases the length of the 95%CI [1, p. 232]. The two ORs and their 95%CIs were first converted into a log scale as follows [1, p. 36, 3]: Then, an arithmetic mean (LogOR combined ) of LogOR 1 and LogOR 2 was computed. Next, the variance of each OR was computed separately as follows [3]: The two individual estimates of variance (V LogOR1 and V LogOR2 ) for both ORs were combined into one variance estimate (V LogORcombined ) using r=1 as follows [1, p. 228 Next, the within-study variance for each study was computed as follows [3]: The weight of each study (W LogOR ) was computed according to the random-effects model as follows [1, where V LogOR is the within-study variance of LogOR and T 2 is the between-study variance which was computed according to the method of moments also known as the DerSimonian and Laird method [4] and using df=k-1 (k=number of studies) as follows: The overall mean weighted effect size (M LogOR ) of all studies and its variance (V MLogOR ) were computed as follows: The lower and upper bounds of the log 95% CI of M LogOR (LogLower MLogOR and LogUpper MLogOR ) were computed as follows: Next, the z-score for M LogOR was computed to test the null-hypothesis that M LogOR =1 (meaning that there is no association between anxiety and cannabis use/CUD) according to the following formula: In the final step of the analysis the overall mean weighted effect size (M LogOR ) and its 95%CI were antiloged as follows [1, p. 97]:

Publication bias analyses in Comprehensive Meta-Analysis (CMA) software
Publication bias refers to an overestimation of the overall mean weighted effect size in meta-analysis due to inclusion of studies based on large sample sizes and/or large effect sizes [1,Chapter 30]. Such studies are more likely to be published and thus are easier to locate during a systematic search than studies based on smaller samples and/or small (often not statistically significant) effect sizes that are either not published at all or published in smaller (often non-English language) journals that are not included in major databases [1,Chapter 30].
Publication bias in the current study was assessed using methods available in the Comprehensive Meta-Analysis (CMA) software, version 2.2 (Biostat Inc., Englewood, NJ, USA). The theoretical number of null-studies (with OR=1) required to remove the statistical significance of the overall mean weighted OR in meta-analysis was computed using Rosenthal's Fail-Safe N [5]. The smaller the Fail-Safe N, the more likely it is that publication bias is present in meta-analysis.
Publication bias can also be assessed visually using a funnel plot of LogOR vs. SEM [6]. According to the funnel plot, the distribution of all effect sizes around the overall mean weighted LogOR should resemble a symmetrical funnel. Since the Y-axis is reversed (smaller SEM values on top, larger on the bottom of the plot), it was expected that larger studies with smaller variability would be found towards the top of the plot, close to and on both sides of the overall mean weighted LogOR. The small studies with larger variability would be found towards the bottom of the plot and they would spread wider away from and on both sides of the overall mean weighted LogOR. Such symmetrical funnel plot would indicate that some studies in the current meta-analysis show that anxiety and cannabis use/CUD are positively associated while others show either no association or a negative association. Any deviation from such symmetry towards the right or the left of the overall mean weighted LogOR would indicate presence of publication bias in the current analysis.
Because a visual inspection of the funnel plot is subjective, the Duval and Tweedie's Trim-and-Fill analysis [7] was used to test for symmetry in such plot using mathematical assumptions of symmetry.
Specifically, first the extreme studies from one side of the plot are removed ('trimmed') until the plot becomes symmetrical. This procedure adjusts the overall mean weighted LogOR. Then, the studies are added ('filled') back onto the plot and a mirror image of each one is produced and added to the opposite side of the plot to maintain symmetry. This procedure corrects the variance of the new estimate of the overall mean weighted LogOR. Publication bias is present if mostly the smaller studies towards the bottom of the plot are missing from the analysis and the adjusted overall mean weighted effect size differs from the original overall mean weighted effect size (for example, the effect size changes direction and/or its 95%CI overlaps with the line of no effect following the adjustment for missing studies).
Finally, the results of two more methods were inspected in the current analysis. However, both methods are unreliable because they are based on the standard null-hypothesis testing and have low power (and thus high Type II error) if the number of studies in the analysis is low. Specifically, the Begg and Mazumdar Rank Order Correlation (Kendall's tau b) was used to investigate the relationship between the standardised effect sizes vs. SEM in each study [8] and the Egger's regression [9] was used to predict the standardised effect size with 1/SEM. Publication bias is present if smaller studies differ systematically (significantly) from the larger studies. In this case, either the correlation is statistically significant and/or the intercept of the regression line significantly deviates from zero causing the asymmetry of the funnel plot [9].