The effects of excluding patients from the analysis in randomised controlled trials: meta-epidemiological study

Abstract

Objective: To examine whether excluding patients from the analysis of randomised trials are associated with biased estimates of treatment effects and higher heterogeneity between trials.

Design: Meta-epidemiological study based on a collection of meta-analyses of randomised trials.

Data sources: 14 meta-analyses including 167 trials that compared therapeutic interventions with placebo or non-intervention control in patients with osteoarthritis of the hip or knee and used patient reported pain as an outcome.

Methods: Effect sizes were calculated from differences in means of pain intensity between groups at the end of follow-up, divided by the pooled standard deviation. Trials were combined by using random effects meta-analysis. Estimates of treatment effects were compared between trials with and trials without exclusions from the analysis, and the impact of restricting meta-analyses to trials without exclusions was assessed.

Results: 39 trials (23%) had included all patients in the analysis. In 128 trials (77%) some patients were excluded from the analysis. Effect sizes from trials with exclusions tended to be more beneficial than those from trials without exclusions (difference -0.13, 95% confidence interval -0.29 to 0.04). However, estimates of bias between individual meta-analyses varied considerably (tau(2)=0.07). Tests of interaction between exclusions from the analysis and estimates of treatment effects were positive in five meta-analyses. Stratified analyses indicated that differences in effect sizes between trials with and trials without exclusions were more pronounced in meta-analyses with high between trial heterogeneity, in meta-analyses with large estimated treatment benefits, and in meta-analyses of complementary medicine. Restriction of meta-analyses to trials without exclusions resulted in smaller estimated treatment benefits, larger P values, and considerable decreases in between trial heterogeneity.

Conclusion: Excluding patients from the analysis in randomised trials often results in biased estimates of treatment effects, but the extent and direction of bias is unpredictable. Results from intention to treat analyses should always be described in reports of randomised trials. In systematic reviews, the influence of exclusions from the analysis on estimated treatment effects should routinely be assessed.

Fig 1 Identification of meta-analyses in osteoarthritis

Fig 2 Difference in effect sizes between 128 trials with and 39 trials without exclusions of patients from analysis. A negative difference in effect sizes indicates that trials with exclusions of patients from analysis show more beneficial treatment effects. P values are for interaction between exclusions from analysis and effect sizes. NSAIDs=non-steroidal anti-inflammatory drugs; TENS=transcutaneous electrical nerve stimulation

Fig 3 Differences in effect sizes between 128 trials with and 39 trials without exclusions of patients from analysis stratified according to four characteristics of meta-analyses. See table 1 for a description of meta-analyses according to these characteristics. A τ² <0.06 indicates low between trial heterogeneity and a τ² ≥0.06 high between trial heterogeneity. An effect size >−0.5 indicates a small benefit of the experimental intervention and an effect size ≤−0.5 a large benefit. Meta-analyses are ordered according to year of publication. A negative difference in effect sizes indicates that trials with exclusions of patients from analysis show a more beneficial treatment effect. Variability in bias between-meta-analyses is expressed as heterogeneity variance τ²

Fig 4 Effect sizes, between trial heterogeneity τ², precision, and P values of overall treatment benefits compared between overall meta-analyses including trials with and without exclusions of patients (x axis) and restricted meta-analyses including trials without exclusions of patients only (y axis). Dashed line indicates that estimates are identical. P values are derived from Wilcoxon rank tests for paired observations