scholarly journals Statistical Issues and Lessons Learned From COVID-19 Clinical Trials With Lopinavir-Ritonavir and Remdesivir (Preprint)

2020 ◽  
Author(s):  
Guosheng Yin ◽  
Chenyang Zhang ◽  
Huaqing Jin
Keyword(s):  
Clinical Trials ◽  
Sample Size ◽  
Error Rate ◽  
Recovery Time ◽  
Type I Error ◽  
Lessons Learned ◽  
Type I ◽  
Statistical Issues ◽  
The Difference ◽  
Mean Time

BACKGROUND Recently, three randomized clinical trials on coronavirus disease (COVID-19) treatments were completed: one for lopinavir-ritonavir and two for remdesivir. One trial reported that remdesivir was superior to placebo in shortening the time to recovery, while the other two showed no benefit of the treatment under investigation. OBJECTIVE The aim of this paper is to, from a statistical perspective, identify several key issues in the design and analysis of three COVID-19 trials and reanalyze the data from the cumulative incidence curves in the three trials using more appropriate statistical methods. METHODS The lopinavir-ritonavir trial enrolled 39 additional patients due to insignificant results after the sample size reached the planned number, which led to inflation of the type I error rate. The remdesivir trial of Wang et al failed to reach the planned sample size due to a lack of eligible patients, and the bootstrap method was used to predict the quantity of clinical interest conditionally and unconditionally if the trial had continued to reach the originally planned sample size. Moreover, we used a terminal (or cure) rate model and a model-free metric known as the restricted mean survival time or the restricted mean time to improvement (RMTI) to analyze the reconstructed data. The remdesivir trial of Beigel et al reported the median recovery time of the remdesivir and placebo groups, and the rate ratio for recovery, while both quantities depend on a particular time point representing local information. We use the restricted mean time to recovery (RMTR) as a global and robust measure for efficacy. RESULTS For the lopinavir-ritonavir trial, with the increase of sample size from 160 to 199, the type I error rate was inflated from 0.05 to 0.071. The difference of RMTIs between the two groups evaluated at day 28 was –1.67 days (95% CI –3.62 to 0.28; <i>P</i>=.09) in favor of lopinavir-ritonavir but not statistically significant. For the remdesivir trial of Wang et al, the difference of RMTIs at day 28 was –0.89 days (95% CI –2.84 to 1.06; <i>P</i>=.37). The planned sample size was 453, yet only 236 patients were enrolled. The conditional prediction shows that the hazard ratio estimates would reach statistical significance if the target sample size had been maintained. For the remdesivir trial of Beigel et al, the difference of RMTRs between the remdesivir and placebo groups at day 30 was –2.7 days (95% CI –4.0 to –1.2; <i>P</i>&lt;.001), confirming the superiority of remdesivir. The difference in the recovery time at the 25th percentile (95% CI –3 to 0; <i>P</i>=.65) was insignificant, while the differences became more statistically significant at larger percentiles. CONCLUSIONS Based on the statistical issues and lessons learned from the recent three clinical trials on COVID-19 treatments, we suggest more appropriate approaches for the design and analysis of ongoing and future COVID-19 trials.

scholarly journals Statistical Issues and Lessons Learned From COVID-19 Clinical Trials With Lopinavir-Ritonavir and Remdesivir

10.2196/19538 ◽  
2020 ◽  
Vol 6 (3) ◽  
pp. e19538
Author(s):  
Guosheng Yin ◽  
Chenyang Zhang ◽  
Huaqing Jin
Keyword(s):  
Clinical Trials ◽  
Sample Size ◽  
Error Rate ◽  
Recovery Time ◽  
Type I Error ◽  
Lessons Learned ◽  
Type I ◽  
Statistical Issues ◽  
The Difference ◽  
Mean Time

Background Recently, three randomized clinical trials on coronavirus disease (COVID-19) treatments were completed: one for lopinavir-ritonavir and two for remdesivir. One trial reported that remdesivir was superior to placebo in shortening the time to recovery, while the other two showed no benefit of the treatment under investigation. Objective The aim of this paper is to, from a statistical perspective, identify several key issues in the design and analysis of three COVID-19 trials and reanalyze the data from the cumulative incidence curves in the three trials using more appropriate statistical methods. Methods The lopinavir-ritonavir trial enrolled 39 additional patients due to insignificant results after the sample size reached the planned number, which led to inflation of the type I error rate. The remdesivir trial of Wang et al failed to reach the planned sample size due to a lack of eligible patients, and the bootstrap method was used to predict the quantity of clinical interest conditionally and unconditionally if the trial had continued to reach the originally planned sample size. Moreover, we used a terminal (or cure) rate model and a model-free metric known as the restricted mean survival time or the restricted mean time to improvement (RMTI) to analyze the reconstructed data. The remdesivir trial of Beigel et al reported the median recovery time of the remdesivir and placebo groups, and the rate ratio for recovery, while both quantities depend on a particular time point representing local information. We use the restricted mean time to recovery (RMTR) as a global and robust measure for efficacy. Results For the lopinavir-ritonavir trial, with the increase of sample size from 160 to 199, the type I error rate was inflated from 0.05 to 0.071. The difference of RMTIs between the two groups evaluated at day 28 was –1.67 days (95% CI –3.62 to 0.28; P=.09) in favor of lopinavir-ritonavir but not statistically significant. For the remdesivir trial of Wang et al, the difference of RMTIs at day 28 was –0.89 days (95% CI –2.84 to 1.06; P=.37). The planned sample size was 453, yet only 236 patients were enrolled. The conditional prediction shows that the hazard ratio estimates would reach statistical significance if the target sample size had been maintained. For the remdesivir trial of Beigel et al, the difference of RMTRs between the remdesivir and placebo groups at day 30 was –2.7 days (95% CI –4.0 to –1.2; P<.001), confirming the superiority of remdesivir. The difference in the recovery time at the 25th percentile (95% CI –3 to 0; P=.65) was insignificant, while the differences became more statistically significant at larger percentiles. Conclusions Based on the statistical issues and lessons learned from the recent three clinical trials on COVID-19 treatments, we suggest more appropriate approaches for the design and analysis of ongoing and future COVID-19 trials.

scholarly journals Statistical Issues and Lessons Learned from COVID-19 Clinical Trials with Lopinavir-Ritonavir and Remdesivir

2020 ◽  
Author(s):  
Guosheng Yin ◽  
Chenyang Zhang ◽  
Huaqing Jin
Keyword(s):  
Clinical Trials ◽  
Sample Size ◽  
Type I Error ◽  
Bootstrap Method ◽  
Lessons Learned ◽  
Type I ◽  
Target Sample Size ◽  
Statistical Issues ◽  
The Difference ◽  
Mean Time

AbstractBackgroundSince the outbreak of the novel coronavirus disease 2019 (COVID-19) in December 2019, it has rapidly spread in more than 200 countries or territories with over 8 million confirmed cases and 440,000 deaths by June 17, 2020. Recently, three randomized clinical trials on COVID-19 treatments were completed, one for lopinavir-ritonavir and two for remdesivir. One trial reported that remdesivir was superior to placebo in shortening the time to recovery, while the other two showed no benefit of the treatment under investigation. However, several statistical issues in the original design and analysis of the three trials are identified, which might shed doubts on their findings and the conclusions should be evaluated with cautions.ObjectiveFrom statistical perspectives, we identify several issues in the design and analysis of three COVID-19 trials and reanalyze the data from the cumulative incidence curves in the three trials using more appropriate statistical methods.MethodsThe lopinavir-ritonavir trial enrolled 39 additional patients due to insignificant results after the sample size reached the planned number, which led to inflation of the type I error rate. The remdesivir trial of Wang et al. failed to reach the planned sample size due to a lack of eligible patients, while the bootstrap method was used to predict the quantity of clinical interest conditionally and unconditionally if the trial had continued to reach the originally planned sample size. Moreover, we used a terminal (or cure) rate model and a model-free metric known as the restricted mean survival time or the restricted mean time to improvement (RMTI) in this context to analyze the reconstructed data due to the existence of death as competing risk and a terminal event. The remdesivir trial of Beigel et al. reported the median recovery time of the remdesivir and placebo groups and the rate ratio for recovery, while both quantities depend on a particular time point representing local information. We reanalyzed the data to report other percentiles of the time to recovery and adopted the bootstrap method and permutation test to construct the confidence intervals as well as the P values. The restricted mean time to recovery (RMTR) was also computed as a global and robust measure for efficacy.ResultsFor the lopinavir-ritonavir trial, with the increase of sample size from 160 to 199, the type I error rate was inflated from 0.05 to 0.071. The difference of terminal rates was −8.74% (95% CI [-21.04, 3.55]; P=.16) and the hazards ratio (HR) adjusted for terminal rates was 1.05 (95% CI [0.78, 1.42]; P=.74), indicating no significant difference. The difference of RMTIs between the two groups evaluated at day 28 was −1.67 days (95% CI [-3.62, 0.28]; P=.09) in favor of lopinavir-ritonavir but not statistically significant. For the remdesivir trial of Wang et al., the difference of terminal rates was −0.89% (95% CI [-2.84, 1.06]; P=.19) and the HR adjusted for terminal rates was 0.92 (95% CI [0.63, 1.35]; P=.67). The difference of RMTIs at day 28 was −0.89 day (95% CI [-2.84, 1.06]; P=.37). The planned sample size was 453, yet only 236 patients were enrolled. The conditional prediction shows that the HR estimates would reach statistical significance if the target sample size had been maintained, and both conditional and unconditional prediction delivered significant HR results if the trial had continued to double the target sample size. For the remdesivir trial of Beigel et al., the difference of RMTRs between the remdesivir and placebo groups up to day 30 was −2.7 days (95% CI [-4.0, −1.2]; P<.001), confirming the superiority of remdesivir. The difference in recovery time at the 25th percentile (95% CI [-3, 0]; P=.65) was insignificant, while the differences manifested to be statistically significant at larger percentiles.ConclusionsBased on the statistical issues and lessons learned from the recent three clinical trials on COVID-19 treatments, we suggest more appropriate approaches for the design and analysis for ongoing and future COVID-19 trials.

scholarly journals Controlling the family-wise error rate in multi-arm, multi-stage trials

2017 ◽  
Vol 14 (3) ◽  
pp. 237-245 ◽  
Author(s):  
Luis A Crouch ◽  
Lori E Dodd ◽  
Michael A Proschan
Keyword(s):  
Clinical Trials ◽  
Sample Size ◽  
Error Rate ◽  
Type I Error ◽  
Type I ◽  
Simple Method ◽  
Family Wise Error Rate ◽  
Expected Sample Size ◽  
Multi Stage ◽  
The Family

Background and aims: Multi-arm, multi-stage trials have recently gained attention as a means to improve the efficiency of the clinical trials process. Many designs have been proposed, but few explicitly consider the inherent issue of multiplicity and the associated type I error rate inflation. It is our aim to propose a straightforward design that controls family-wise error rate while still providing improved efficiency. Methods: In this article, we provide an analytical method for calculating the family-wise error rate for a multi-arm, multi-stage trial and highlight the potential for considerable error rate inflation in uncontrolled designs. We propose a simple method to control the error rate that also allows for computation of power and expected sample size. Results: Family-wise error rate can be controlled in a variety of multi-arm, mutli-stage trial designs using our method. Additionally, our design can substantially decrease the expected sample size of a study while maintaining adequate power. Conclusion: Multi-arm, multi-stage designs have the potential to reduce the time and other resources spent on clinical trials. Our relatively simple design allows this to be achieved while weakly controlling family-wise error rate and without sacrificing much power.

Alternative models and randomization techniques for Bayesian response-adaptive randomization with binary outcomes

2021 ◽  
pp. 174077452110101
Author(s):  
Jennifer Proper ◽  
John Connett ◽  
Thomas Murray
Keyword(s):  
Logistic Regression ◽  
Sample Size ◽  
Error Rate ◽  
Adaptive Design ◽  
Type I Error ◽  
Probability Model ◽  
Binary Outcomes ◽  
Type I ◽  
Operating Characteristics ◽  
Type I Error Rate

Background: Bayesian response-adaptive designs, which data adaptively alter the allocation ratio in favor of the better performing treatment, are often criticized for engendering a non-trivial probability of a subject imbalance in favor of the inferior treatment, inflating type I error rate, and increasing sample size requirements. The implementation of these designs using the Thompson sampling methods has generally assumed a simple beta-binomial probability model in the literature; however, the effect of these choices on the resulting design operating characteristics relative to other reasonable alternatives has not been fully examined. Motivated by the Advanced R2 Eperfusion STrategies for Refractory Cardiac Arrest trial, we posit that a logistic probability model coupled with an urn or permuted block randomization method will alleviate some of the practical limitations engendered by the conventional implementation of a two-arm Bayesian response-adaptive design with binary outcomes. In this article, we discuss up to what extent this solution works and when it does not. Methods: A computer simulation study was performed to evaluate the relative merits of a Bayesian response-adaptive design for the Advanced R2 Eperfusion STrategies for Refractory Cardiac Arrest trial using the Thompson sampling methods based on a logistic regression probability model coupled with either an urn or permuted block randomization method that limits deviations from the evolving target allocation ratio. The different implementations of the response-adaptive design were evaluated for type I error rate control across various null response rates and power, among other performance metrics. Results: The logistic regression probability model engenders smaller average sample sizes with similar power, better control over type I error rate, and more favorable treatment arm sample size distributions than the conventional beta-binomial probability model, and designs using the alternative randomization methods have a negligible chance of a sample size imbalance in the wrong direction. Conclusion: Pairing the logistic regression probability model with either of the alternative randomization methods results in a much improved response-adaptive design in regard to important operating characteristics, including type I error rate control and the risk of a sample size imbalance in favor of the inferior treatment.

Use of interval estimations in design and evaluation of multiregional clinical trials with continuous outcomes

2018 ◽  
Vol 28 (7) ◽  
pp. 2179-2195 ◽  
Author(s):  
Chieh Chiang ◽  
Chin-Fu Hsiao
Keyword(s):  
Clinical Trials ◽  
Sample Size ◽  
Type I Error ◽  
Interval Estimation ◽  
Error Rates ◽  
New Drugs ◽  
Sample Size Determination ◽  
Type I ◽  
Size Determination ◽  
Interval Estimators

Multiregional clinical trials have been accepted in recent years as a useful means of accelerating the development of new drugs and abridging their approval time. The statistical properties of multiregional clinical trials are being widely discussed. In practice, variance of a continuous response may be different from region to region, but it leads to the assessment of the efficacy response falling into a Behrens–Fisher problem—there is no exact testing or interval estimator for mean difference with unequal variances. As a solution, this study applies interval estimations of the efficacy response based on Howe’s, Cochran–Cox’s, and Satterthwaite’s approximations, which have been shown to have well-controlled type I error rates. However, the traditional sample size determination cannot be applied to the interval estimators. The sample size determination to achieve a desired power based on these interval estimators is then presented. Moreover, the consistency criteria suggested by the Japanese Ministry of Health, Labour and Welfare guidance to decide whether the overall results from the multiregional clinical trial obtained via the proposed interval estimation were also applied. A real example is used to illustrate the proposed method. The results of simulation studies indicate that the proposed method can correctly determine the required sample size and evaluate the assurance probability of the consistency criteria.

Sample Size Reassessment in Non-inferiority Trials

2011 ◽  
Vol 50 (03) ◽  
pp. 237-243 ◽  
Author(s):  
T. Friede ◽  
M. Kieser
Keyword(s):  
Sample Size ◽  
Error Rate ◽  
Type I Error ◽  
Nuisance Parameters ◽  
Type I ◽  
Nominal Significance Level ◽  
Significance Level ◽  
Type I Error Rate ◽  
Planning Phase ◽  
Nominal Significance

SummaryObjectives: Analysis of covariance (ANCOVA) is widely applied in practice and its use is recommended by regulatory guidelines. However, the required sample size for ANCOVA depends on parameters that are usually uncertain in the planning phase of a study. Sample size recalculation within the internal pilot study design allows to cope with this problem. From a regulatory viewpoint it is preferable that the treatment group allocation remains masked and that the type I error is controlled at the specified significance level. The characteristics of blinded sample size reassessment for ANCOVA in non-inferiority studies have not been investigated yet. We propose an appropriate method and evaluate its performance.Methods: In a simulation study, the characteristics of the proposed method with respect to type I error rate, power and sample size are investigated. It is illustrated by a clinical trial example how strict control of the significance level can be achieved.Results: A slight excess of the type I error rate beyond the nominal significance level was observed. The extent of exceedance increases with increasing non-inferiority margin and increasing correlation between outcome and covariate. The procedure assures the desired power over a wide range of scenarios even if nuisance parameters affecting the sample size are initially mis-specified.Conclusions: The proposed blinded sample size recalculation procedure protects from insufficient sample sizes due to incorrect assumptions about nuisance parameters in the planning phase. The original procedure may lead to an elevated type I error rate, but methods are available to control the nominal significance level.

scholarly journals Assessment of Type I Error Rates and Power of Common Analysis Methods in Murine Obesity-Related Study: ‘Plasmode-Based’ Simulation (P13-011-19)

2019 ◽  
Vol 3 (Supplement_1) ◽  
Author(s):  
Keisuke Ejima ◽  
Andrew Brown ◽  
Daniel Smith ◽  
Ufuk Beyaztas ◽  
David Allison
Keyword(s):  
Sample Size ◽  
Error Rate ◽  
Type I Error ◽  
Error Rates ◽  
T Test ◽  
Small Samples ◽  
Type I ◽  
Type I Error Rates ◽  
Type I Error Rate ◽  
Weight Distributions

Abstract Objectives Rigor, reproducibility and transparency (RRT) awareness has expanded over the last decade. Although RRT can be improved from various aspects, we focused on type I error rates and power of commonly used statistical analyses testing mean differences of two groups, using small (n ≤ 5) to moderate sample sizes. Methods We compared data from five distinct, homozygous, monogenic, murine models of obesity with non-mutant controls of both sexes. Baseline weight (7–11 weeks old) was the outcome. To examine whether type I error rate could be affected by choice of statistical tests, we adjusted the empirical distributions of weights to ensure the null hypothesis (i.e., no mean difference) in two ways: Case 1) center both weight distributions on the same mean weight; Case 2) combine data from control and mutant groups into one distribution. From these cases, 3 to 20 mice were resampled to create a ‘plasmode’ dataset. We performed five common tests (Student's t-test, Welch's t-test, Wilcoxon test, permutation test and bootstrap test) on the plasmodes and computed type I error rates. Power was assessed using plasmodes, where the distribution of the control group was shifted by adding a constant value as in Case 1, but to realize nominal effect sizes. Results Type I error rates were unreasonably higher than the nominal significance level (type I error rate inflation) for Student's t-test, Welch's t-test and permutation especially when sample size was small for Case 1, whereas inflation was observed only for permutation for Case 2. Deflation was noted for bootstrap with small sample. Increasing sample size mitigated inflation and deflation, except for Wilcoxon in Case 1 because heterogeneity of weight distributions between groups violated assumptions for the purposes of testing mean differences. For power, a departure from the reference value was observed with small samples. Compared with the other tests, bootstrap was underpowered with small samples as a tradeoff for maintaining type I error rates. Conclusions With small samples (n ≤ 5), bootstrap avoided type I error rate inflation, but often at the cost of lower power. To avoid type I error rate inflation for other tests, sample size should be increased. Wilcoxon should be avoided because of heterogeneity of weight distributions between mutant and control mice. Funding Sources This study was supported in part by NIH and Japan Society for Promotion of Science (JSPS) KAKENHI grant.

scholarly journals Maximum type I error rate inflation from sample size reassessment when investigators are blind to treatment labels

2015 ◽  
Vol 35 (12) ◽  
pp. 1972-1984 ◽  
Author(s):  
Magdalena Żebrowska ◽  
Martin Posch ◽  
Dominic Magirr
Keyword(s):  
Sample Size ◽  
Error Rate ◽  
Type I Error ◽  
Type I ◽  
Type I Error Rate
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