Missing data may seriously compromise inferences from randomised clinical trials, especially if missing data are not handled appropriately. The potential bias due to missing data depends on the mechanism causing the data to be missing, and the analytical methods applied to amend the missingness. Therefore, the analysis of trial data with missing values requires careful planning and attention. The authors had several meetings and discussions considering optimal ways of handling missing data to minimise the bias potential. We also searched PubMed (key words: missing data; randomi*; statistical analysis) and reference lists of known studies for papers (theoretical papers; empirical studies; simulation studies; etc.) on how to deal with missing data when analysing randomised clinical trials. Handling missing data is an important, yet difficult and complex task when analysing results of randomised clinical trials. We consider how to optimise the handling of missing data during the planning stage of a randomised clinical trial and recommend analytical approaches which may prevent bias caused by unavoidable missing data. We consider the strengths and limitations of using of best-worst and worst-best sensitivity analyses, multiple imputation, and full information maximum likelihood. We also present practical flowcharts on how to deal with missing data and an overview of the steps that always need to be considered during the analysis stage of a trial. We present a practical guide and flowcharts describing when and how multiple imputation should be used to handle missing data in randomised clinical.

Objective To examine whether the association of inadequate or unclear allocation concealment and lack of blinding with biased estimates of intervention effects varies with the nature of the intervention or outcome. Design Combined analysis of data from three meta-epidemiological studies based on collections of meta-analyses. Data sources 146 meta-analyses including 1346 trials examining a wide range of interventions and outcomes. Main outcome measures Ratios of odds ratios quantifying the degree of bias associated with inadequate or unclear allocation concealment, and lack of blinding, for trials with different types of intervention and outcome. A ratio of odds ratios <1 implies that inadequately concealed or non-blinded trials exaggerate intervention effect estimates. Results In trials with subjective outcomes effect estimates were exaggerated when there was inadequate or unclear allocation concealment (ratio of odds ratios 0.69 (95% CI 0.59 to 0.82)) or lack of blinding (0.75 (0.61 to 0.93)). In contrast, there was little evidence of bias in trials with objective outcomes: ratios of odds ratios 0.91 (0.80 to 1.03) for inadequate or unclear allocation concealment and 1.01 (0.92 to 1.10) for lack of blinding. There was little evidence for a difference between trials of drug and non-drug interventions. Except for trials with all cause mortality as the outcome, the magnitude of bias varied between meta-analyses. Conclusions The average bias associated with defects in the conduct of randomised trials varies with the type of outcome. Systematic reviewers should routinely assess the risk of bias in the results of trials, and should report meta-analyses restricted to trials at low risk of bias either as the primary analysis or in conjunction with less restrictive analyses.

To explore whether reported methodologic quality affects estimated intervention effects in randomized trials and contributes to discrepancies between the results of large randomized trials and small randomized trials in meta-analyses. Meta-analyses of randomized trials that included at least one large trial (≥ 1000 participants) were included, regardless of the therapeutic area. Eligible meta-analyses were identified through electronic searches and bibliographies of relevant articles. Full-length randomized trials. Methodologic quality was assessed according to reported randomization, double blinding, and follow-up as separate components and by using the Jadad composite scale. Fourteen meta-analyses involving 190 randomized trials from eight therapeutic areas were included. Compared with large trials, intervention effects were exaggerated in small trials with inadequate allocation sequence generation (ratio of odds ratios, 0.46 [95% CI, 0.25 to 0.83]; P = 0.011), inadequate allocation concealment (ratio of odds ratios, 0.49 [CI, 0.27 to 0.86]; P = 0.014), and no double blinding (ratio of odds ratios, 0.52 [CI, 0.28 to 0.96]; P = 0.01). Large trials did not differ significantly from small trials with adequate generation of the allocation sequence, adequate allocation concealment, or adequate double blinding. No association was seen between reported follow-up and intervention effects. The Jadad scale provided no additional information because the scale and the quality components overlapped substantially. Inadequate generation of the allocation sequence, allocation concealment, and double blinding lead to exaggerated estimates of intervention benefit and may contribute to discrepancies between the results of large randomized trials and small randomized trials in meta-analyses.

Review from JAMA — Mortality in Randomized Trials of Antioxidant Supplements for Primary and Secondary Prevention — Systematic Review and Meta-analysis — ContextAntioxidant supplements are used for prevention of several diseases.ObjectiveTo assess the effect of antioxidant supplements on mortality in randomized primary and secondary prevention trials.Data Sources and Trial SelectionWe searched electronic databases and bibliographies published by October 2005. All randomized trials involving adults comparing beta carotene, vitamin A, vitamin C (ascorbic acid), vitamin E, and selenium either singly or combined vs placebo or vs no intervention were included in our analysis. Randomization, blinding, and follow-up were considered markers of bias in the included trials. The effect of antioxidant supplements on all-cause mortality was analyzed with random-effects meta-analyses and reported as relative risk (RR) with 95% confidence intervals (CIs). Meta-regression was used to assess the effect of covariates across the trials.Data ExtractionWe included 68 randomized trials with 232 606 participants (385 publications).Data SynthesisWhen all low- and high-bias risk trials of antioxidant supplements were pooled together there was no significant effect on mortality (RR, 1.02; 95% CI, 0.98-1.06). Multivariate meta-regression analyses showed that low-bias risk trials (RR, 1.16; 95% CI, 1.05-1.29) and selenium (RR, 0.998; 95% CI, 0.997-0.9995) were significantly associated with mortality. In 47 low-bias trials with 180 938 participants, the antioxidant supplements significantly increased mortality (RR, 1.05; 95% CI, 1.02-1.08). In low-bias risk trials, after exclusion of selenium trials, beta carotene (RR, 1.07; 95% CI, 1.02-1.11), vitamin A (RR, 1.16; 95% CI, 1.10-1.24), and vitamin E (RR, 1.04; 95% CI, 1.01-1.07), singly or combined, significantly increased mortality. Vitamin C and selenium had no significant effect on mortality.ConclusionsTreatment with beta carotene, vitamin A, and vitamin E may increase mortality. The potential roles of vitamin C and selenium on mortality need further study.

Most meta-analyses in systematic reviews, including Cochrane ones, do not have sufficient statistical power to detect or refute even large intervention effects. This is why a meta-analysis ought to be regarded as an interim analysis on its way towards a required information size. The results of the meta-analyses should relate the total number of randomised participants to the estimated required meta-analytic information size accounting for statistical diversity. When the number of participants and the corresponding number of trials in a meta-analysis are insufficient, the use of the traditional 95% confidence interval or the 5% statistical significance threshold will lead to too many false positive conclusions (type I errors) and too many false negative conclusions (type II errors). We developed a methodology for interpreting meta-analysis results, using generally accepted, valid evidence on how to adjust thresholds for significance in randomised clinical trials when the required sample size has not been reached. The Lan-DeMets trial sequential monitoring boundaries in Trial Sequential Analysis offer adjusted confidence intervals and restricted thresholds for statistical significance when the diversity-adjusted required information size and the corresponding number of required trials for the meta-analysis have not been reached. Trial Sequential Analysis provides a frequentistic approach to control both type I and type II errors. We define the required information size and the corresponding number of required trials in a meta-analysis and the diversity (D2) measure of heterogeneity. We explain the reasons for using Trial Sequential Analysis of meta-analysis when the actual information size fails to reach the required information size. We present examples drawn from traditional meta-analyses using unadjusted naïve 95% confidence intervals and 5% thresholds for statistical significance. Spurious conclusions in systematic reviews with traditional meta-analyses can be reduced using Trial Sequential Analysis. Several empirical studies have demonstrated that the Trial Sequential Analysis provides better control of type I errors and of type II errors than the traditional naïve meta-analysis. Trial Sequential Analysis represents analysis of meta-analytic data, with transparent assumptions, and better control of type I and type II errors than the traditional meta-analysis using naïve unadjusted confidence intervals.