Percentages of 14,886 meta-analyses including no studies adequately powered to detect a target effect or including at least two adequately powered studies, where adequate power is defined as 80% or 50% in turn; and summary of median power within each meta-analysis.

<p>Percentages of 14,886 meta-analyses including no studies adequately powered to detect a target effect or including at least two adequately powered studies, where adequate power is defined as 80% or 50% in turn; and summary of median power within each meta-analysis.</p

The Impact of Study Size on Meta-analyses: Examination of Underpowered Studies in Cochrane Reviews

<div><p>Background</p><p>Most meta-analyses include data from one or more small studies that, individually, do not have power to detect an intervention effect. The relative influence of adequately powered and underpowered studies in published meta-analyses has not previously been explored. We examine the distribution of power available in studies within meta-analyses published in Cochrane reviews, and investigate the impact of underpowered studies on meta-analysis results.</p> <p>Methods and Findings</p><p>For 14,886 meta-analyses of binary outcomes from 1,991 Cochrane reviews, we calculated power per study within each meta-analysis. We defined adequate power as ≥50% power to detect a 30% relative risk reduction. In a subset of 1,107 meta-analyses including 5 or more studies with at least two adequately powered and at least one underpowered, results were compared with and without underpowered studies. In 10,492 (70%) of 14,886 meta-analyses, all included studies were underpowered; only 2,588 (17%) included at least two adequately powered studies. 34% of the meta-analyses themselves were adequately powered. The median of summary relative risks was 0.75 across all meta-analyses (inter-quartile range 0.55 to 0.89). In the subset examined, odds ratios in underpowered studies were 15% lower (95% CI 11% to 18%, P<0.0001) than in adequately powered studies, in meta-analyses of controlled pharmacological trials; and 12% lower (95% CI 7% to 17%, P<0.0001) in meta-analyses of controlled non-pharmacological trials. The standard error of the intervention effect increased by a median of 11% (inter-quartile range −1% to 35%) when underpowered studies were omitted; and between-study heterogeneity tended to decrease.</p> <p>Conclusions</p><p>When at least two adequately powered studies are available in meta-analyses reported by Cochrane reviews, underpowered studies often contribute little information, and could be left out if a rapid review of the evidence is required. However, underpowered studies made up the entirety of the evidence in most Cochrane reviews.</p> </div

Average differences in observed log odds ratios between underpowered () compared to adequately powered studies, in subset A of 1,107 meta-analyses, overall and within medical specialties, outcome types and intervention-comparison types.

1<p>Other medical specialties, semi-objective outcomes, subjective outcomes and non-pharmacological interventions defined in footnotes to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059202#pone-0059202-t002" target="_blank">Table 2</a>.</p>2<p>Comparison is less meaningful when comparing two active interventions since the a priori “better” active intervention is not taken into account.</p

Ratios comparing results obtained from adequately powered studies only with results obtained from all studies, in subset A of 1,107 meta-analyses: results shown are percentiles of the distribution of such ratios across meta-analyses.

1<p> in the all-studies meta-analysis in 256/1107 meta-analyses. In 199/256 (78%), also in the meta-analysis including adequately powered studies only. In 57/256 (22%), increased, but trivially, when underpowered studies were removed.</p

Meta-analytic power with respect to a 30% relative risk reduction (RRR30), based on the random-effects model, overall and by medical specialty, outcome type and intervention-comparison type.

1<p>Other medical specialties, semi-objective outcomes, subjective outcomes and non-pharmacological interventions defined in footnotes to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059202#pone-0059202-t002" target="_blank">Table 2</a>.</p

Drugs-related Death Rates Soon After Hospital-discharge for Ever-IDU Behavioral Risk-factor, SDMD Cohort, Scotland, 1996–2010.

<p>Drugs-related Death Rates Soon After Hospital-discharge for Ever-IDU Behavioral Risk-factor, SDMD Cohort, Scotland, 1996–2010.</p

Drugs-related Death Rates by Follow-up Era and Time Since Hospital-discharge: Adjusted Using Cox Proportional Hazards Regression With Calendar Time as the Underlying Time-scale, SDMD Cohort, Scotland, 1996–2010.

<p>Abbreviations: SDMD, Scottish Drugs Misuse Database; CI, Confidence Interval</p><p>Drugs-related Death Rates by Follow-up Era and Time Since Hospital-discharge: Adjusted Using Cox Proportional Hazards Regression With Calendar Time as the Underlying Time-scale, SDMD Cohort, Scotland, 1996–2010.</p

Drugs-related Death Rates by Follow-up Era and Time Since Hospital-discharge: Unadjusted, SDMD Cohort, Scotland, 1996–2010.

<p>Abbreviations: DRD, drugs-related death; SDMD, Scottish Drugs Misuse Database; Pys, Person-years; CI, Confidence Interval</p><p>Drugs-related Death Rates by Follow-up Era and Time Since Hospital-discharge: Unadjusted, SDMD Cohort, Scotland, 1996–2010.</p

Drugs-related Death Rates Soon After Hospital-discharge for Reported Misuse of Alcohol Behavioral Risk-factor, SDMD Cohort, Scotland, 1996–2010.

<p>Abbreviations: DRD, drugs-related death; SDMD, Scottish Drugs Misuse Database; Pys, Person-years; CI, Confidence Interval; IDU, Injecting Drug User</p><p>Drugs-related Death Rates Soon After Hospital-discharge for Reported Misuse of Alcohol Behavioral Risk-factor, SDMD Cohort, Scotland, 1996–2010.</p

Descriptive Statistics for outcomes by Follow-up Era, SDMD Cohort, Scotland, 1996–2010.

<p>Abbreviations: DRD, drugs-related death; SDMD, Scottish Drugs Misuse Database</p><p>^a Excluding DRD suicides which are included in the DRD total,</p><p>^b Restricted to individuals with first SDMD registration in 2006–2010 as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141073#pone.0141073.t001" target="_blank">Table 1(a)</a></p><p>Descriptive Statistics for outcomes by Follow-up Era, SDMD Cohort, Scotland, 1996–2010.</p