Delta inflation: a bias in the design of randomized controlled trials in critical care medicine

Abstract

Introduction: Mortality is the most widely accepted outcome measure in randomized controlled trials of therapies for critically ill adults, but most of these trials fail to show a statistically significant mortality benefit. The reasons for this are unknown.

Methods: We searched five high impact journals (Annals of Internal Medicine, British Medical Journal, JAMA, The Lancet, New England Journal of Medicine) for randomized controlled trials comparing mortality of therapies for critically ill adults over a ten year period. We abstracted data on the statistical design and results of these trials to compare the predicted delta (delta; the effect size of the therapy compared to control expressed as an absolute mortality reduction) to the observed delta to determine if there is a systematic overestimation of predicted delta that might explain the high prevalence of negative results in these trials.

Results: We found 38 trials meeting our inclusion criteria. Only 5/38 (13.2%) of the trials provided justification for the predicted delta. The mean predicted delta among the 38 trials was 10.1% and the mean observed delta was 1.4% (P < 0.0001), resulting in a delta-gap of 8.7%. In only 2/38 (5.3%) of the trials did the observed delta exceed the predicted delta and only 7/38 (18.4%) of the trials demonstrated statistically significant results in the hypothesized direction; these trials had smaller delta-gaps than the remainder of the trials (delta-gap 0.9% versus 10.5%; P < 0.0001). For trials showing non-significant trends toward benefit greater than 3%, large increases in sample size (380% - 1100%) would be required if repeat trials use the observed delta from the index trial as the predicted delta for a follow-up study.

Conclusions: Investigators of therapies for critical illness systematically overestimate treatment effect size (delta) during the design of randomized controlled trials. This bias, which we refer to as "delta inflation", is a potential reason that these trials have a high rate of negative results."Absence of evidence is not evidence of absence."

Figure 1

Plot of observed versus predicted delta (with associated 95% confidence intervals for observed delta) of 38 trials included in the analysis. Point estimates of treatment effect (deltas) are represented by green circles for non-statistically significant trials and red triangles for statistically significant trials. Numbers within the circles and triangles refer to the trials as referenced in Additional file 1. The blue 'unity line' with a slope equal to one indicates perfect concordance between observed and predicted delta; for visual clarity and to reduce distortions, the slope is reduced to zero (and the x-axis is horizontally expanded) where multiple predicted deltas have the same value and where 95% confidence intervals cross the unity line. If predictions of delta were accurate and without bias, values of observed delta would be symmetrically scattered above and below the unity line. If there is directional bias, values will fall predominately on one side of the line as they do in the figure.