Maximum type 1 error rate inflation in multiarmed clinical trials with adaptive interim sample size modifications.

Consider a parallel group trial for the comparison of an experimental treatment to a control, where the second-stage sample size may depend on the blinded primary endpoint data as well as on additional blinded data from a secondary endpoint. For the setting of normally distributed endpoints, we demonstrate that this may lead to an inflation of the type I error rate if the null hypothesis holds for the primary but not the secondary endpoint. We derive upper bounds for the inflation of the type I error rate, both for trials that employ random allocation and for those that use block randomization. We illustrate the worst-case sample size reassessment rule in a case study. For both randomization strategies, the maximum type I error rate increases with the effect size in the secondary endpoint and the correlation between endpoints. The maximum inflation increases with smaller block sizes if information on the block size is used in the reassessment rule. Based on our findings, we do not question the well-established use of blinded sample size reassessment methods with nuisance parameter estimates computed from the blinded interim data of the primary endpoint. However, we demonstrate that the type I error rate control of these methods relies on the application of specific, binding, pre-planned and fully algorithmic sample size reassessment rules and does not extend to general or unplanned sample size adjustments based on blinded data.

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. 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. 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. 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.

Considerations of sample size in medical research

Sample size calculations for gene expression microarray and NGS-RNA-Seq experiments are challenging because the overall power depends on unknown quantities as the proportion of true null hypotheses and the distribution of the effect sizes under the alternative. We propose a two-stage design with an adaptive interim analysis where these quantities are estimated from the interim data. The second stage sample size is chosen based on these estimates to achieve a specific overall power. The proposed procedure controls the power in all considered scenarios except for very low first stage sample sizes. The false discovery rate (FDR) is controlled despite of the data dependent choice of sample size. The two-stage design can be a useful tool to determine the sample size of high-dimensional studies if in the planning phase there is high uncertainty regarding the expected effect sizes and variability.

In phase II platform trials, ‘many-to-one’ comparisons are performed when K experimental treatments are compared with a common control to identify the most promising treatment(s) to be selected for Phase III trials. However, when sample sizes are limited, such as when the disease of interest is rare, only a single Phase II/III trial addressing both treatment selection and confirmatory efficacy testing may be feasible. In this paper, we suggest a two-step safety selection and testing procedure for such seamless trials. At the end of the study, treatments are first screened on the basis of safety, and those deemed to be sufficiently safe are then taken forwards for efficacy testing against a common control. All safety and efficacy evaluations are therefore performed at the end of the study, when for each patient all safety and efficacy data are available. If confirmatory conclusions are to be drawn from the trial, strict control of the family-wise error rate (FWER) is essential. However, to avoid unnecessary losses in power, no type I error rate should be “wasted” on comparisons which are no longer of interest because treatments have been dropped due to safety concerns. We investigate the impact on power and FWER control of multiplicity adjustments which correct efficacy tests only for the number of safe selected treatments instead of adjusting for all K null hypotheses the trial begins testing. We derive conditions under which strict control of the FWER can be achieved. Procedures using the estimated association between safety and efficacy outcomes are developed for the case when the correlation between endpoints is unknown. The operating characteristics of the proposed procedures are assessed via simulation.

Random norming aids analysis of non-linear regression models with sequential informative dose selection

ABSTRACTSample size estimation (SSE) is an important issue in the planning of clinical studies. While larger studies are likely to have sufficient power, it may be unethical to expose more patients than necessary to answer a scientific question. Budget considerations may also cause one to limit the study to an adequate size to answer the question at hand. Typically at the planning stage, a statistically based justification for sample size is provided. An effective sample size is usually planned under a pre-specified type I error rate, a desired power under a particular alternative and variability associated with the observations recorded. The nuisance parameter such as the variance is unknown in practice. Thus, information from a preliminary pilot study is often used to estimate the variance. However, calculating the sample size based on the estimated nuisance parameter may not be stable. Sample size re-estimation (SSR) at the interim analysis may provide an opportunity to re-evaluate the uncertainties using accrued data and continue the trial with an updated sample size. This article evaluates a proposed SSR method based on controlling the variability of nuisance parameter. A numerical study is used to assess the performance of proposed method with respect to the control of type I error. The proposed method and concepts could be extended to SSR approaches with respect to other criteria, such as maintaining effect size, achieving conditional power, and reaching a desired reproducibility probability.

Adaptive sample size redetermination (SSR) for clinical trials consists of examining early subsets of on-trial data to adjust prior estimates of statistical parameters and sample size requirements. Blinded SSR, in particular, while in use already, seems poised to proliferate even further because it obviates many logistical complications of unblinded methods and it generally introduces little or no statistical or operational bias. On the other hand, current blinded SSR methods offer little to no new information about the treatment effect (TE); the obvious resulting problem is that the TE estimate scientists might simply 'plug in' to the sample size formulae could be severely wrong. This paper proposes a blinded SSR method that formally synthesizes sample data with prior knowledge about the TE and the within-treatment variance. It evaluates the method in terms of the type 1 error rate, the bias of the estimated TE, and the average deviation from the targeted power. The method is shown to reduce this average deviation, in comparison with another established method, over a range of situations. The paper illustrates the use of the proposed method with an example.

Sample size re-estimation in adaptive enrichment design

A three-arm comparative clinical endpoint bioequivalence (BE) study is often used to establish bioequivalence (BE) between a locally acting generic drug (T) and reference drug (R), where superiority needs to be established for T and R over Placebo (P) and equivalence needs to be established for T vs. R. Sometimes, when study design parameters are uncertain, a fixed design study may be under- or over-powered and result in study failure or unnecessary cost. In this paper, we propose a two-stage adaptive clinical endpoint BE study with unblinded sample size re-estimation, standard or maximum combination method, optimized allocation ratio, optional re-estimation of the effect size based on likelihood estimation, and optional re-estimation of the R and P treatment means at interim analysis, which have not been done previously. Our proposed method guarantees control of Type 1 error rate analytically. It helps to reduce the average sample size when the original fixed design is overpowered and increases the sample size and power when the original study and group sequential design are under-powered. Our proposed adaptive design can help generic drug sponsors cut cost and improve success rate, making clinical study endpoint BE studies more affordable and more generic drugs accessible to the public.

Quality improvement in health service programmes often involves introducing small, low-risk programmatic changes, such as modifying workflows, to incrementally improve outcomes, which accumulate over time to have significant overall gains in quality and efficiency. Although these changes are common in health services, they are rarely evaluated using statistically rigorous designs, partly because conventional randomised trials are perceived as inefficient for detecting modest effects. This study was motivated by a vision screening and referral programme and focuses on evaluating the modest but important impacts of low-risk QI interventions. To advance data-driven approaches for achieving quality improvement, we used a simulation study to explore the use of Bayesian adaptive trial designs to compare two variants of programmatic changes that yield small improvements in outcomes. The study examined key adaptive design features, including interim analysis frequency, prior specification, and early stopping rules for efficacy and equivalence. Changes in error rates, sample size, and bias were assessed across scenarios with small effect sizes ranging from 0% to 5%. The findings were used to configure an ideal trial design that prioritises rapid identification of the more effective programmatic change while minimizing the risk of adopting an inferior one. The recommended trial design incorporates a sceptical prior, a stringent stopping rule for efficacy, and a relaxed criteria to stop for equivalence. Under this design, a marginal improvement as small as 1% could be detected with high probability using considerably fewer participants than would be required under conventional, fixed-size randomised controlled trials. Bayesian adaptive trial designs offer a feasible approach for evaluating low-risk, incremental QI interventions in high-throughput service settings. Their use may support more efficient, data-driven decision-making when modest improvements are expected and the consequences of incorrect adoption are limited.

BackgroundCardiovascular and oncology trials increasingly require large sample sizes and long follow-up periods. Several approaches have been developed to optimize sample size including sample size re-estimation based on the promising zone approach. With time-to-event endpoints, methods traditionally used to test for treatment effects are based on proportional hazards assumptions, which may not always hold. We propose an adaptive design wherein using interim data, Bayesian computation of Predictive Power (PP) guides the increase in sample size and/or the minimum follow-up duration.MethodsPROTECT IV is designed to evaluate mechanical circulatory support device vs. standard of care during high-risk percutaneous coronary intervention with the initial enrolment of 1252 patients and initial minimum follow-up of 12 months. The primary endpoint is the composite rate of all-cause death, stroke, durable left ventricular assist device implant or heart transplant, myocardial infarction or hospitalization for cardiovascular causes. The study will employ an adaptive increase in sample size and/or minimum follow-up at the Interim analysis. The adaptations utilize simulations to choose a new sample size up to 2500 and new minimal follow-up time up to 36 months that provides PP of at least 90%.ResultsVia extensive simulations, we have examined the utility of the proposed design for situations like delayed treatment effect, early benefit only and in general crossing of survival curves. Separate Piece-wise Constant Hazard Models with non-influential (weakly-informative) Gamma-priors are fitted to the interim data for the two treatment arms, free from the proportional hazards assumptions, thus yielding more robust interim decision making. The Bayesian modeling facilitates sampling of future observations from the posterior predictive distributions with the predictive probability of trial success is computed via Monte-Carlo simulations. Simulation results show that the fitting Bayesian Piecewise Exponential models to the interim data along with the use of the posterior predictive distributions lead to more “specific” adaptation rules compared to the frequentist Conditional Power while the overall operating characteristics, type-I error and power, are similar.ConclusionFor clinical trials with time-to-event endpoints and where crossing of survival curves might be anticipated at the planning stage, flexible modeling along with wholesome use of patient-level data such as the calculation of predictive power as proposed here, may be more robust and efficient in making interim decisions such as sample size increase than the traditional use of the conditional power based on summary statistics and proportional hazards assumption.Supplementary InformationThe online version contains supplementary material available at 10.1007/s43441-025-00861-4.

34 Background: Phase II clinical trials aim to identify promising experimental regimens for further testing in phase III trials. Testing targeted therapies with predictive biomarkers mandates efficient trial designs. Current biomarker-based trial designs, including the enrichment, all-comers, and adaptive designs, randomize patients to receive treatment or not throughout the entire duration of the trial. Recognizing the need for randomization yet acknowledging the possibility of promising but nonconclusive results after a preplanned interim analysis (IA), we propose a two-stage phase II design that allows for the possibility of direct assignment (i.e., stop randomization and assign all patients to the experimental arm in stage II) based on IA results. Methods: Using simulations, we compared properties of the direct assignment option design to a 1:1 randomized phase II design and assessed the impact of the timing of IA (after 33%, 50%, or 67% of accrual) and number of IA (one versus two with option for direct assignment at the first and second) over a range of response rate ratios (between 1.0 and 3.0). Results: Between 12% and 30% of the trials (out of 6,000 simulated trials) adopt direct assignment in stage II, with direct adoption depending on the treatment effect size and specified type I error rate (TIER). The direct assignment option design has minimal loss in power (<1.8%) and minimal increase in T1ER (<2.1%) compared to a 1:1 randomized design. The maximum loss in power across possible timings of IA was <1.2%. For the direct assignment option design, there was a 20%-50% increase in the number of patients treated on the experimental (vs. control) arm for the 1 IA case, and 40%-100% increase for the 2 IA case. Conclusions: Testing predictive biomarkers in clinical trials requires new design strategies. In the spectrum of phase II designs from adaptive to balanced randomized all-comers or enrichment designs, the direct assignment design provides a middle ground with desirable statistical properties that may appeal to both clinicians and patients.

Many late-phase clinical trials recruit subjects at multiple study sites. This introduces a hierarchical structure into the data that can result in a power-loss compared to a more homogeneous single-center trial. Building on a recently proposed approach to sample size determination, we suggest a sample size recalculation procedure for multicenter trials with continuous endpoints. The procedure estimates nuisance parameters at interim from noncomparative data and recalculates the sample size required based on these estimates. In contrast to other sample size calculation methods for multicenter trials, our approach assumes a mixed effects model and does not rely on balanced data within centers. It is therefore advantageous, especially for sample size recalculation at interim. We illustrate the proposed methodology by a study evaluating a diabetes management system. Monte Carlo simulations are carried out to evaluate operation characteristics of the sample size recalculation procedure using comparative as well as noncomparative data, assessing their dependence on parameters such as between-center heterogeneity, residual variance of observations, treatment effect size and number of centers. We compare two different estimators for between-center heterogeneity, an unadjusted and a bias-adjusted estimator, both based on quadratic forms. The type 1 error probability as well as statistical power are close to their nominal levels for all parameter combinations considered in our simulation study for the proposed unadjusted estimator, whereas the adjusted estimator exhibits some type 1 error rate inflation. Overall, the sample size recalculation procedure can be recommended to mitigate risks arising from misspecified nuisance parameters at the planningstage.

In this study, how the application changes with the size of the scale, type I error rate and power of test values were examined in different sample sizes. The material of this study is the random numbers generated according to different sample sizes and different group means of standard deviation out of populations that hold multinomial distribution. In the study, permutation test, F-test and Kruskal-Wallis (KW) test were examined using combinations with different sample sizes (n = 5, 10, 20, 30, 50) and different p values (probability of occurrence of events which are 0.25, 0.50, 0.75) first interms of Type I error rate and then power of the test using different group averages (Δ =1.0, 1.5, 2.0). As a result of the simulations, it is seen that with small sample sizes, Kruskal-Wallis test was unable to maintain Type I error rate at 0.05 level. In the evaluation of such Likert-type data, it can be stated that, permutation test, one of the distribution free tests, is more practical than other tests in terms of maintaining the Type I error rate at 0.05 level and high power of test values. The permutation test is satisfactory in terms of both the type I error rate and the power of the test. Also, permutation test is a distribution-free test. Therefore, can be used without prerequisites. In almost every combination (π, Δ, k, n), permutation test had similar or superior type 1 error and power values than the F and KW tests. It was observed that compared to the 5 visual analogue scale, when the data is measured in 10 and 20 visual analogue scale, the power of test values decreased. In other words, if more than 5 visual analogue scale are made on the visual analogue scale data, the results would negatively be affected.