Conditional power, predictive power and probability of success in clinical trials with continuous, binary and time-to-event endpoints

Assessment of study success using conditional power (CP), the predictive power of success (PPoS) and probability of success (PoS) is becoming increasingly common for resource optimization and adaption of trials in clinical investigation. Determination of these measures is often a non-trivial mathematical task. Further, the terminologies used across the literature are not consistent, and there is no consolidated presentation on this. Lastly, certain types of trials received more attention where others (e.g., single-arm trial with time-to-event endpoints) were completely ignored. We attempted to fill these gaps. This paper first provides a detailed derivation of CP, PPoS and PoS in a general setting with normally distributed test statistics and normal prior. Subsequently, expressions for these measures are obtained for continuous, binary, and time-to-event endpoints in single-arm and two-arm trial settings. We have discussed both clinical success and trial success. Importantly, we have derived the expressions for CP, PPoS and PoS in a single-arm trial with a time-to-event endpoint that was never addressed in the literature to our knowledge. In that discussion, we have also shown that commonly recommended 1/d consistently under-estimates the variance of log(median) and alternative expression for variance was derived. We have also presented the PPoS calculation for the binomial endpoint with a beta prior. Examples are given along with the comparison of CP and PPoS. Expressions presented in this paper are implemented in LongCART package in R. An R shiny app is also available at https://ppos.herokuapp.com/ .

Estimating Conditional Power for Sequential Monitoring of Covariate Adaptive Randomized Designs: The Fractional Brownian Motion Approach

Conditional power based on classical Brownian motion (BM) has been widely used in sequential monitoring of clinical trials, including those with the covariate adaptive randomization design (CAR). Due to some uncontrollable factors, the sequential test statistics under CAR procedures may not satisfy the independent increment property of BM. We confirm the invalidation of BM when the error terms in the linear model with CAR design are not independent and identically distributed. To incorporate the possible correlation structure of the increment of the test statistic, we utilize the fractional Brownian motion (FBM). We conducted a comparative study of the conditional power under BM and FBM. It was found that the conditional power under FBM assumption was mostly higher than that under BM assumption when the Hurst exponent was greater than 0.5.

Conditional power of antidepressant network meta-analysis

Background Conditional power of network meta-analysis (NMA) can support the planning of randomized controlled trials (RCTs) assessing medical interventions. Conditional power is the probability that updating existing inconclusive evidence in NMA with additional trial(s) will result in conclusive evidence, given assumptions regarding trial design, anticipated effect sizes, or event probabilities. Methods The present work aimed to estimate conditional power for potential future trials on antidepressant treatments. Existing evidence was based on a published network of 502 RCTs conducted between 1979-2018 assessing acute antidepressant treatment in major depressive disorder (MDD). Primary outcomes were efficacy in terms of the symptom change on the Hamilton Depression Scale (HAMD) and tolerability in terms of the dropout rate due to adverse events. The network compares 21 antidepressants consisting of 231 relative treatment comparisons, 164 (efficacy) and 127 (tolerability) of which are currently assumed to have inconclusive evidence. Results Required sample sizes to achieve new conclusive evidence with at least 80% conditional power were estimated to range between N = 894 - 4190 (efficacy) and N = 521 - 1246 (tolerability). Otherwise, sample sizes ranging between N = 49 - 485 (efficacy) and N = 40 - 320 (tolerability) may require stopping for futility based on a boundary at 20% conditional power. Optimizing trial designs by considering multiple trials that contribute both direct and indirect evidence, anticipating alternative effect sizes or alternative event probabilities, may increase conditional power but required sample sizes remain high. Antidepressants having the greatest conditional power associated with smallest required sample sizes were identified as those on which current evidence is low, i.e., clomipramine, levomilnacipran, milnacipran, nefazodone, and vilazodone, with respect to both outcomes. Conclusions The present results suggest that conditional power to achieve new conclusive evidence in ongoing or future trials on antidepressant treatments is low. Limiting the use of the presented conditional power analysis are primarily due to the estimated large sample sizes which would be required in future trials as well as due to the well-known small effect sizes in antidepressant treatments. These findings may inform researchers and decision-makers regarding the clinical relevance and justification of research in ongoing or future antidepressant RCTs in MDD.

Smoothing Corrections for Improving Sample Size Recalculation Rules in Adaptive Group Sequential Study Designs

Background An adequate sample size calculation is essential for designing a successful clinical trial. One way to tackle planning difficulties regarding parameter assumptions required for sample size calculation is to adapt the sample size during the ongoing trial.This can be attained by adaptive group sequential study designs. At a predefined timepoint, the interim effect is tested for significance. Based on the interim test result, the trial is either stopped or continued with the possibility of a sample size recalculation. Objectives Sample size recalculation rules have different limitations in application like a high variability of the recalculated sample size. Hence, the goal is to provide a tool to counteract this performance limitation. Methods Sample size recalculation rules can be interpreted as functions of the observed interim effect. Often, a “jump” from the first stage's sample size to the maximal sample size at a rather arbitrarily chosen interim effect size is implemented and the curve decreases monotonically afterwards. This jump is one reason for a high variability of the sample size. In this work, we investigate how the shape of the recalculation function can be improved by implementing a smoother increase of the sample size. The design options are evaluated by means of Monte Carlo simulations. Evaluation criteria are univariate performance measures such as the conditional power and sample size as well as a conditional performance score which combines these components. Results We demonstrate that smoothing corrections can reduce variability in conditional power and sample size as well as they increase the performance with respect to a recently published conditional performance score for medium and large standardized effect sizes. Conclusion Based on the simulation study, we present a tool that is easily implemented to improve sample size recalculation rules. The approach can be combined with existing sample size recalculation rules described in the literature.