792259_supp_mat – Supplemental material for Design of non-inferiority randomized trials using the difference in restricted mean survival times

<p>Supplemental material, 792259_supp_mat for Design of non-inferiority randomized trials using the difference in restricted mean survival times by Isabelle R Weir and Ludovic Trinquart in Clinical Trials</p

Probabilities that each antidepressant drug is the best according to network meta-analyses of data from 74 FDA-registered trials or 51 published trials with published effect sizes.

<p>For instance, for mirtazapine, the probability of being the best was 7.3% and 30.2% according to network-meta-analysis of the 74 FDA-registered trials and 51 published trials with published effect sizes, respectively. Drugs for which the probability of being the best was <5% for both published and FDA data are not labeled (blue area).</p

Probabilities of being the best among competing antidepressant agents when reporting bias affects one specific agent.

<p>The first stacked bar at the left corresponds to the network meta-analysis free of reporting biases (ie, with the data from the 74 FDA-registered trials). The other stacked bars correspond to the 12 network meta-analyses in which reporting bias hypothetically affects one specific agent in turn. For instance, for mirtazapine, we used the 6 published trials (out of 10 FDA-registered trials), with published effect sizes, and data from the 64 FDA-registered trials for the other 11 agents, which resulted in an incomplete FDA network of 70 trials; the probability of mirtazapine being the best was 80.6% with data from the incomplete FDA network and 7.3% with data from the 74 FDA-registered trials. For the sake of clarity, we presented in each analysis the 3 drugs with the 3 highest probabilities of being the best among competing antidepressant agents. Bup: Bupropion; Cit: Citalopram; Dul : Duloxetine ; Esc: Escitalopram; Flu: Fluoxetine; Mir: Mirtazapine ; Nef: Nefazodone ; Par: Paroxetine; Par CR: Paroxetine CR; Ser: Sertraline; Ven: Venlafaxine; VenXR: Venlafaxine XR.</p

Box plot of the 10,000 calculated samples sizes based on the conventional approach.

<p>These sample sizes are used for the situation of mean theoretical odds ratio = 1.5. The dotted line represents 300 patients, which corresponds to the number of patients involved in the meta-experiment.</p

Simulation study with a non-null treatment effect.

<p>Theoretical distributions are used to draw the true treatment effects and success rates in the control group for only one trial with the conventional approach and for each of the 3 trials with the meta-experiment. The log odds ratio <i>θ</i> is drawn from a normal distribution with mean log(1.5) and SD 0.1. The success rate in the control group <i>p</i>_<i>c</i> is drawn from a beta distribution with mean 30% and SD 10%. With the conventional approach, relative errors are simulated to deduce the postulated hypothesis in designing the trial. The sample size 2n is calculated to ensure 80% power. A trial of size 2n is simulated from the true treatment effect and success rate, and analyzed. With the meta-experiment approach, the same theoretical distributions are used to draw 3 treatments effects <i>θ</i>¹, <i>θ</i>² and <i>θ</i>³, and 3 success rates and . 3 trials with sample size 100 each are simulated from the 3 treatment effects and success rates. Then the data are meta-analyzed in a random-effects model, allowing for variation between the results of the 3 trials.</p

Statistical performance of conventional and meta-experiment approaches to determining sample size (1 trial vs 3 trials).

<p>(a) For a treatment effect (mean theoretical odds ratio (OR) = 1.5), power and coverage of the 95% confidence interval (95% CI) are estimated. (b) For no treatment effect (mean theoretical OR = 1), the type I error rate is estimated. For both scenarios, box plots of 95% CIs are presented. Results were derived from a simulation study with 10,000 runs for an expected mean success of 30% for the control group (i.e., considering a Beta distribution with mean 30% and SD 10%), and SD = 0.1 for the theoretical log OR.</p

Summary effect sizes for the 12 comparisons of each antidepressant agent and placebo.

<p>Weighted mean effect-size values for each drug were derived using a random-effects model with the method of DerSimonian and Laird. N: number of trials; SMD (95%CI): summary standardized mean difference of drug vs. placebo derived from random effects meta-analysis (95% confidence interval); Τ² (SE): between-trial variance as a measure of heterogeneity in meta-analysis (standard error); NA: not assessable.</p

Star-shaped networks of comparisons of data from 74 US Food and Drug Administration (FDA)-registered trials of 12 antidepressants and their 51 related publications.

<p>The central node represents the placebo, and each leaf node represents an antidepressant agent. Each node diameter is proportional to the number of patients who received the antidepressant agent; each connecting line width is proportional to the number of trials that addressed the comparison.</p

Scatterplot of estimates of relative efficacy for 66 pair-wise comparisons of the 12 antidepressant agents with one another derived from network meta-analyses of data from 74 FDA-registered trials and their 51 trial publications.

<p>Data are effect sizes. Positive effect sizes indicate that drug A has higher efficacy than drug B. The two areas above the uppermost dotted line (labeled +100%) and below the lowest dotted line (labeled −100%) correspond to cases in which an effect size derived from the network meta-analysis of the 51 published trials differed in absolute value from that derived from the network meta-analysis of the 74 FDA-registered trials by at least 100%. The two areas between the 2 upper dotted lines (labeled +50%) and between the 2 lower dotted lines (labeled −50%) correspond to cases in which an effect size derived from the network meta-analysis of the 51 published trials differed in absolute value from that derived from the network meta-analysis of the 74 FDA-registered trials by at least 50%. Red-colored points refer to cases in which agent B was superior to agent A by one network meta-analysis and A was superior to B by the other network meta-analysis.</p

Flow diagram of the study selection.

<p>RCT, randomized controlled trial; SR, systematic review; MA, meta-analysis.</p