Non‐inferiority and clinical superiority of glucagon‐like peptide‐1 receptor agonists and sodium‐glucose co‐transporter‐2 inhibitors: Systematic analysis of cardiorenal outcome trials in type 2 diabetes

Figures

• 

  FIGURE 1. Statistical and clinical significance in non‐inferiority trials. Five hypothetical trials showed the logical inconsistency between the criteria for non‐inferiority and for superiority. Black dotted line shows the margin of 1 to determine statistical superiority, while the dotted magenta line indicates the margin of 1.3 commonly considered when investigating the non‐inferiority of the active medication to control in cardiorenal outcome trials in type 2 diabetes. A trial comparing an active versus control intervention with an hazards ratio (HR) of 0.95 (0.85‐1.06; second row) shows the non‐inferiority (upper bound of 95% confidence interval lower than 1.3) of the active compared with the control intervention; when inverting the roles and considering control versus active intervention, the HR is 1.05 (0.94‐1.18) and shows non‐inferiority of the control compared with the active intervention; therefore, in this trial each arm is clinically non‐inferior to the other and neither is clinically superior. A trial showing an HR of 0.90 (0.85‐0.95; first row) comparing active with control intervention shows both clinical non‐inferiority (upper bound of 95% confidence interval lower than 1.3)…

• 

  FIGURE 2. Posterior distribution and probabilities for a hypothetical trial. Top panel: Posterior hazard ratio distribution with mean 0.95 and 95% credible interval of 0.76‐1.15 (yellow circles on the x‐axis) in a simulated trial comparing active versus control treatment. The area under the curve A indicates the probability of values of hazard ratio ≤0.8: such probability (6.5%) can be determined in the bottom panel (cumulative density plot) as the value on the y‐axis corresponding to the hazard ratio of 0.8. Probability of values of hazard ratio ≤1.1 is 93.0%, corresponding to the sum of the three areas A + B + C. This plot shows how, in a Bayesian context, it is possible to quantify the probability that the magnitude of a treatment effect is smaller (or larger) than a specific threshold.

• 

  FIGURE 3. Bayesian treatment effect estimates. Each point corresponds to the estimate from a single iteration (10 000 for each trial and outcome); the box plot shows the median and interquartile range with spikes indicating the 95% credible interval; and the dotted magenta and green lines indicate the hazard ratio corresponding to the margin for clinical (1/1.3 = 0.769) and statistical (1) superiority, respectively, comparing active medication to placebo. Trials are sorted by drug class (blue, glucagon‐like peptide‐1 receptor agonists; orange, sodium‐glucose co‐transporter‐2 inhibitors) and alphabetically.

• 

  FIGURE 4. Statistical and clinical superiority of the active drug compared with placebo. Tornado plot showing the probability of statistical [grey; hazard ratio (HR) <1) and clinical (red; HR <0.769) superiority of the active drug compared with placebo; corresponding HRs reported in the original article are shown in the forest plot. Trials sorted by drug class, outcome (M, mortality; P, primary), and increasing probability of clinical superiority of the active drug. GLP‐1, glucagon‐like peptide‐1; SGLT2i, sodium‐glucose co‐transporter‐2.