Practical help for specifying the target difference in sample size calculations for RCTs: the DELTA2 five-stage study, including a workshop

BACKGROUND: The randomised controlled trial is widely considered to be the gold standard study for comparing the effectiveness of health interventions. Central to its design is a calculation of the number of participants needed (the sample size) for the trial. The sample size is typically calculated by specifying the magnitude of the difference in the primary outcome between the intervention effects for the population of interest. This difference is called the 'target difference' and should be appropriate for the principal estimand of interest and determined by the primary aim of the study. The target difference between treatments should be considered realistic and/or important by one or more key stakeholder groups. OBJECTIVE: The objective of the report is to provide practical help on the choice of target difference used in the sample size calculation for a randomised controlled trial for researchers and funder representatives. METHODS: The Difference ELicitation in TriAls2 (DELTA2) recommendations and advice were developed through a five-stage process, which included two literature reviews of existing funder guidance and recent methodological literature; a Delphi process to engage with a wider group of stakeholders; a 2-day workshop; and finalising the core document. RESULTS: Advice is provided for definitive trials (Phase III/IV studies). Methods for choosing the target difference are reviewed. To aid those new to the topic, and to encourage better practice, 10 recommendations are made regarding choosing the target difference and undertaking a sample size calculation. Recommended reporting items for trial proposal, protocols and results papers under the conventional approach are also provided. Case studies reflecting different trial designs and covering different conditions are provided. Alternative trial designs and methods for choosing the sample size are also briefly considered. CONCLUSIONS: Choosing an appropriate sample size is crucial if a study is to inform clinical practice. The number of patients recruited into the trial needs to be sufficient to answer the objectives; however, the number should not be higher than necessary to avoid unnecessary burden on patients and wasting precious resources. The choice of the target difference is a key part of this process under the conventional approach to sample size calculations. This document provides advice and recommendations to improve practice and reporting regarding this aspect of trial design. Future work could extend the work to address other less common approaches to the sample size calculations, particularly in terms of appropriate reporting items. FUNDING: Funded by the Medical Research Council (MRC) UK and the National Institute for Health Research as part of the MRC-National Institute for Health Research Methodology Research programme

Extrapolation of efficacy and other data to support the development of new medicines for children:a systematic review of methods

Objective When developing new medicines for children, the potential to extrapolate from adult data to reduce the experimental burden in children is well recognised. However, significant assumptions about the similarity of adults and children are needed for extrapolations to be biologically plausible. We reviewed the literature to identify statistical methods that could be used to optimise extrapolations in paediatric drug development programmes. Methods Web of Science was used to identify papers proposing methods relevant for using data from a ‘source population’ to support inferences for a ‘target population’. Four key areas of methods development were targeted: paediatric clinical trials, trials extrapolating efficacy across ethnic groups or geographic regions, the use of historical data in contemporary clinical trials and using short-term endpoints to support inferences about long-term outcomes. Results Searches identified 626 papers of which 52 met our inclusion criteria. From these we identified 102 methods comprising 58 Bayesian and 44 frequentist approaches. Most Bayesian methods (n = 54) sought to use existing data in the source population to create an informative prior distribution for a future clinical trial. Of these, 46 allowed the source data to be down-weighted to account for potential differences between populations. Bayesian and frequentist versions of methods were found for assessing whether key parameters of source and target populations are commensurate (n = 34). Fourteen frequentist methods synthesised data from different populations using a joint model or a weighted test statistic. Conclusions Several methods were identified as potentially applicable to paediatric drug development. Methods which can accommodate a heterogeneous target population and which allow data from a source population to be down-weighted are preferred. Methods assessing the commensurability of parameters may be used to determine whether it is appropriate to pool data across age groups to estimate treatment effects

Can we disregard the whole model? Omnibus non-inferiority testing for R2R^{2} in multivariable linear regression and η^2\hat{\eta}^{2} in ANOVA

Determining a lack of association between an outcome variable and a number of different explanatory variables is frequently necessary in order to disregard a proposed model (i.e., to confirm the lack of an association between an outcome and predictors). Despite this, the literature rarely offers information about, or technical recommendations concerning, the appropriate statistical methodology to be used to accomplish this task. This paper introduces non-inferiority tests for ANOVA and linear regression analyses, that correspond to the standard widely used $F$-test for $\hat{\eta}^2$ and $R^{2}$, respectively. A simulation study is conducted to examine the type I error rates and statistical power of the tests, and a comparison is made with an alternative Bayesian testing approach. The results indicate that the proposed non-inferiority test is a potentially useful tool for 'testing the null.'Comment: 30 pages, 6 figure

Unified Approaches for Frequentist and Bayesian Methods in Two-Sample Clinical Trials with Binary Endpoints

Two opposing paradigms, analyses via frequentist or Bayesian methods, dominate the statistical literature. Most commonly, frequentist approaches have been used to design and analyze clinical trials, though Bayesian techniques are becoming increasingly popular. However, these two paradigms can generate divergent results even in analyses of the same trial data, which may harm the scientific interpretability of the trial. Therefore, it is crucial to harmonize analyses under each approach. In this dissertation, novel unified approaches for one-sided frequentist and Bayesian hypothesis testing problems comparing two proportions in fixed-sample and group-sequential clinical trials are proposed. When a frequentist design with desired type I and II error rates are given, the unification is achieved by deriving specific Bayesian decision thresholds and sample sizes. Similarly, when a Bayesian design is given, the unification is achieved by deriving corresponding frequentist characteristics. In addition, theoretical methods to determine the Bayesian decision threshold, sample size and power are provided. Numerical results show that the unified approach can yield the same type I and II error rates for frequentist and Bayesian hypothesis tests through a numerical study. Further, detailed evaluations suggest that Bayesian priors specifications, allocation ratios, number of analyses can affect the resulting Bayesian sample sizes and decision thresholds. Overall, the unified approach can be adopted into the current clinical trial setting and is helpful to make trial results translatable between frequentist and Bayesian methods

Statistical considerations of noninferiority, bioequivalence and equivalence testing in biosimilars studies

In recent years, the development of follow-on biological products (biosimilars) has received increasing attention. The dissertation covers statistical methods related to three topics of Non-inferiority (NI), Bioequivalence (BE) and Equivalence in demonstrating biosimilarity. For NI, one of the key requirements is constancy assumption, that is, the effect of reference treatment is the same in current NI trials as in historical superiority trials. However if a covariate interacts with the treatment arms, then changes in distribution of this covariate will result in violation of constancy assumption. We propose a modified covariate-adjustment fixed margin method, and recommend it based on its performance characteristics in comparison with other methods. Topic two is related to BE inference for log-normal distributed data. Two drugs are bioequivalent if the difference of a pharmacokinetics (PK) parameter of two products falls within prespecified margins. In the presence of unspecified variances, existing methods like two one-sided tests and Bayesian analysis in BE setting limit our knowledge on the extent that inference of BE is affected by the variability of the PK parameter. We propose a likelihood approach that retains the unspecified variances in the model and partitions the entire likelihood function into two components: F-statistic function for variances and t-statistic function for difference of PK parameter. The advantage of the proposed method over existing methods is it helps identify range of variances where BE is more likely to be achieved. In the third topic, we extend the proposed likelihood method for Equivalence inference, where data is often normal distributed. In this part, we demonstrate an additional advantage of the proposed method over current analysis methods such as likelihood ratio test and Bayesian analysis in Equivalence setting. The proposed likelihood method produces results that are same or comparable to current analysis methods in general case when model parameters are independent. However it yields better results in special cases when model parameters are dependent, for example the ratio of variances is directly proportional to the ratio of means. Our research results suggest the proposed likelihood method serves a better alternative than the current analysis methods to address BE/Equivalence inference

Improving the efficiency of clinical trial designs by using historical control data or adding a treatment arm to an ongoing trial

The most common type of confirmatory trial is a randomised trial comparing the experimental treatment of interest to a control treatment. Confirmatory trials are expensive and take a lot of time in the planning, set up and recruitment of patients. Efficient methodology in clinical trial design is critical to save both time and money and allow treatments to become available to patients quickly. Often there are data available on the control treatment from a previous trial. These historical data are often used to design new trials, forming the basis of sample size calculations, but are not used in the analysis of the new trial. Incorporating historical control data into the design and analysis could potentially lead to more efficient trials. When the historical and current control data agree, incorporating historical control data could reduce the number of control patients required in the current trial and therefore the duration of the trial, or increase the precision of parameter estimates. However, when the historical and current data are inconsistent, there is a potential for biased treatment effect estimates, inflated type I error and reduced power. We propose two novel weights to assess agreement between the current and historical control data: a probability weight based on tail area probabilities; and a weight based on the equivalence of the historical and current control data parameters. For binary outcome data, agreement is assessed using the posterior distributions of the response probability in the historical and current control data. For normally distributed outcome data, agreement is assessed using the marginal posterior distributions of the difference in means and the ratio of the variances of the current and historical control data. We consider an adaptive design with an interim analysis. At the interim, the agreement between the historical and current control data is assessed using the probability or equivalence probability weight approach. The allocation ratio is adapted to randomise fewer patients to control when there is agreement and revert back to a standard trial design when there is disagreement. The final analysis is Bayesian utilising the analysis approach of the power prior with a fixed weight. The operating characteristics of the proposed design are explored and we show how the equivalence bounds can be chosen at the design stage of the current study to control the maximum inflation in type I error. We then consider a design where a treatment arm is added to an ongoing clinical trial. For many disease areas, there are often treatments in different stages of the development process. We consider the design of a two-arm parallel group trial where it is planned to add a new treatment arm during the trial. This could potentially save money, patients, time and resources. The addition of a treatment arm creates a multiple comparison problem. Dunnett (1955) proposed a design that controls the family-wise error rate when comparing multiple experimental treatments to control and determined the optimal allocation ratio. We have calculated the correlation between test statistics for the method proposed by Dunnett when a treatment arm is added during the trial and only concurrent controls are used for each treatment comparison. We propose an adaptive design where the sample size of all treatment arms are increased to control the family-wise error rate. We explore adapting the allocation ratio once the new treatment arm is added to maximise the overall power of the trial