The stratified win statistics (win ratio, win odds, and net benefit).

The win odds and the net benefit are related directly to each other and indirectly, through ties, to the win ratio. These three win statistics test the same null hypothesis of equal win probabilities between two groups. They provide similar p-values and powers, because the Z-values of their statistical tests are approximately equal. Thus, they can complement one another to show the strength of a treatment effect. In this article, we show that the estimated variances of the win statistics are also directly related regardless of ties or indirectly related through ties. Since its introduction in 2018, the stratified win ratio has been applied in designs and analyses of clinical trials, including Phase III and Phase IV studies. This article generalizes the stratified method to the win odds and the net benefit. As a result, the relations of the three win statistics and the approximate equivalence of their statistical tests also hold for the stratified win statistics.

Use of pharmacodynamic modeling for Bayesian information borrowing in pediatric clinical trials.

The use of Bayesian methodology to design and analyze pediatric efficacy trials is one of the possible options to reduce their sample size. This reduction of the sample size results from the use of an informative prior for the parameters of interest. In most of the applications, the principle of 'information borrowing' from adults' trials is applied, which means that the informative prior is constructed using efficacy results in adult of the drug under investigation. This implicitly assumes similarity in efficacy between the selected pediatric dose and the efficacious dose in adults. The goal of this article is to propose a method to construct prior distribution for the parameter of interest, not directly constructed from the efficacy results of the efficacious dose in adult patients but using pharmacodynamic modeling of a bridging biomarker using early phase pediatric data. When combined with a model bridging the biomarker with the clinical endpoints, the prior is constructed using a variational method after simulation of the parameters of interest. A use case application illustrates how the method can be used to construct a realistic informative prior.

The win odds: statistical inference and regression.

Generalized pairwise comparisons and win statistics (i.e., win ratio, win odds and net benefit) are advantageous in analyzing and interpreting a composite of multiple outcomes in clinical trials. An important limitation of these statistics is their inability to adjust for covariates other than by stratified analysis. Because the win ratio does not account for ties, the win odds, a modification that includes ties, has attracted attention. We review and combine information on the win odds to articulate the statistical inferences for the win odds. We also show alternative variance estimators based on the exact permutation and bootstrap as well as statistical inference via the probabilistic index. Finally, we extend multiple-covariate regression probabilistic index models to the win odds with a univariate outcome. As an illustration we apply the regression models to the data in the CHARM trial.

Win statistics (win ratio, win odds, and net benefit) can complement one another to show the strength of the treatment effect on time-to-event outcomes.

Conventional analyses of a composite of multiple time-to-event outcomes use the time to the first event. However, the first event may not be the most important outcome. To address this limitation, generalized pairwise comparisons and win statistics (win ratio, win odds, and net benefit) have become popular and have been applied to clinical trial practice. However, win ratio, win odds, and net benefit have typically been used separately. In this article, we examine the use of these three win statistics jointly for time-to-event outcomes. First, we explain the relation of point estimates and variances among the three win statistics, and the relation between the net benefit and the Mann-Whitney U statistic. Then we explain that the three win statistics are based on the same win proportions, and they test the same null hypothesis of equal win probabilities in two groups. We show theoretically that the Z-values of the corresponding statistical tests are approximately equal; therefore, the three win statistics provide very similar p-values and statistical powers. Finally, using simulation studies and data from a clinical trial, we demonstrate that, when there is no (or little) censoring, the three win statistics can complement one another to show the strength of the treatment effect. However, when the amount of censoring is not small, and without adjustment for censoring, the win odds and the net benefit may have an advantage for interpreting the treatment effect; with adjustment (e.g., IPCW adjustment) for censoring, the three win statistics can complement one another to show the strength of the treatment effect. For calculations we use the R package WINS, available on the CRAN (Comprehensive R Archive Network).

Design of paediatric trials with benefit-risk endpoints using a composite score of adverse events of interest (AEI) and win-statistics.

A fundamental problem in the regulatory evaluation of a therapy is assessing whether the benefit outweighs the associated risks. This work proposes designing a trial that assesses a composite endpoint consisting of benefit and risk, hence, making the core of the design of the study, to assess benefit and risk. The proposed benefit risk measure consists of efficacy measure(s) and a risk measure that is based on a composite score obtained from pre-defined adverse events of interest (AEI). This composite score incorporates full aspects of adverse events of interest (i.e. the incidence, severity, and duration of the events). We call this newly proposed score the AEI composite score. After specifying the priorities between the components of the composite endpoint, a win-statistic (i.e. win ratio, win odds, or net benefit) is used to assess the difference between treatments in this composite endpoint. The power and sample size requirements of such a trial design are explored via simulation. Finally, using Dupixent published adult study results, we show how we can design a paediatric trial where the primary outcome is a composite of prioritized outcomes consisting of efficacy endpoints and the AEI composite score endpoint. The resulting trial design can potentially substantially reduce sample size compared to a trial designed to assess the co-primary efficacy endpoints, therefore it may address the challenge of slow enrollment and patient availability for paediatric studies.

Dynamic incorporation of real world evidence within the framework of adaptive design.

For the clinical studies in rare diseases or small patient populations, having an adequately powered randomized controlled trial is further complicated by variability. As such, sample size re-estimation can be a useful tool if at an interim look the trial sample size needs to be increased to achieve adequate power to reject the null hypothesis. Meanwhile, borrowing or extrapolating information from real-world data or real-world evidence has gained increasing use in trial design and analysis since 2014. Combining these two strategies, high-quality real-world data, if leveraged properly, has the potential to generate real-world evidence that can assist interim decision-making, lower enrollment burden, and reduce study timeline and costs. With proper borrowing from historical control, some of the challenges in these high unmet medical need studies could be resolved considerably. We examine the incorporation of real-world evidence within the framework of adaptive design strategy in pediatric type II diabetes trials where recruitment has been challenging and the completion is hardly on time. Simulations under various scenarios are conducted to assess the borrowing strategy, i.e., the matching method in combination of sample size re-estimation. Comparisons of performance metrics are presented to showcase the advantages of proposed method.

Ensuring exchangeability in data-based priors for a Bayesian analysis of clinical trials.

In many orphan diseases and pediatric indications, the randomized controlled trials may be infeasible because of their size, duration, and cost. Leveraging information on the control through a prior can potentially reduce sample size. However, unless an objective prior is used to impose complete ignorance for the parameter being estimated, it results in biased estimates and inflated type-I error. Hence, it is essential to assess both the confirmatory and supplementary knowledge available during the construction of the prior to avoid "cherry-picking" advantageous information. For this purpose, propensity score methods are employed to minimize selection bias by weighting supplemental control subjects according to their similarity in terms of pretreatment characteristics to the subjects in the current trial. The latter can be operationalized through a proposed measure of overlap in propensity-score distributions. In this paper, we consider single experimental arm in the current trial and the control arm is completely borrowed from the supplemental data. The simulation experiments show that the proposed method reduces prior and data conflict and improves the precision of the of the average treatment effect.

Real-World Evidence Utilization in Clinical Development Reflected by US Product Labeling: Statistical Review.

The US Food and Drug Administration (FDA) has shown scientific discretion in interpreting the substantial evidence requirement for the approval of new drugs with its considerations on the use of single controlled or uncontrolled trials (Federal Food, Drug, and Cosmetic Act § 505(d), 21 USC 355(d), 1962). With the passage of the 21st Centuries Cures Act (21st Century Cures-patients. House, Energy and Commerce Committee, Washington, DC, 2019 available at: https://energycommerce.house.gov/sites/republicans.energycommerce.house.gov/files/analysis/21stCenturyCures/20140516PatientsWhitePaper.pdf ), the FDA is mandated to expand the role of real-world evidence (RWE) in support of drug approval. This mandate further broadens the scope of scientific discretion to include data collected outside clinical trials. We summarize the agency's past acceptance of real-world data (RWD) sources for supporting drug approval in new indications which have been reflected in US labels. In our summary, we focus on the type of RWD and statistical methodologies presented in these labels. Furthermore, two labels were selected for in-depth assessment of the RWE presented in these labels. Through these examples, we demonstrate the issues that can be raised in data collection that could affect interpretation. In addition, a brief discussion of statistical methods that can be used to incorporate RWE to clinical development is presented.

The inverse-probability-of-censoring weighting (IPCW) adjusted win ratio statistic: an unbiased estimator in the presence of independent censoring.

The win ratio method has received much attention in methodological research, ad hoc analyses, and designs of prospective studies. As the primary analysis, it supported the approval of tafamidis for the treatment of cardiomyopathy to reduce cardiovascular mortality and cardiovascular-related hospitalization. However, its dependence on censoring is a potential shortcoming. In this article, we propose the inverse-probability-of-censoring weighting (IPCW) adjusted win ratio statistic (i.e., the IPCW-adjusted win ratio statistic) to overcome censoring issues. We consider independent censoring, common censoring across endpoints, and right censoring. We develop an asymptotic variance estimator for the logarithm of the IPCW-adjusted win ratio statistic and evaluate it via simulation. Our simulation studies show that, as the amount of censoring increases, the unadjusted win proportions may decrease greatly. Consequently, the bias of the unadjusted win ratio estimate may increase greatly, producing either an overestimate or an underestimate. We demonstrate theoretically and through simulation that the IPCW-adjusted win ratio statistic gives an unbiased estimate of treatment effect.

Pediatric Extrapolation in Type 2 Diabetes: Future Implications of a Workshop.

Extrapolation from adults to youth with type 2 diabetes (T2D) is challenged by differences in disease progression and manifestation. This manuscript presents the results of a mock-team workshop focused on examining the typical team-based decision process used to propose a pediatric development plan for T2D addressing the viability of extrapolation. The workshop was held at the American Society for Clinical Pharmacology and Therapeutics (ASCPT) in Orlando, Florida on March 21, 2018.

Incorporating Innovative Techniques Toward Extrapolation and Efficient Pediatric Drug Development.

The conduct of pediatric clinical trials is legally required, monitored, and encouraged in major geographic areas such as the United States and Europe. However, because pediatric patients are considered vulnerable populations, they should only be enrolled as research subjects in a clinical trial if enrolling adult subjects will not be able to answer the scientific question related to the health and welfare of children. Thus, there is an ethical obligation to build the foundation for the use of pediatric extrapolation and related innovative analytical strategies with appropriately designed pediatric and adult clinical trials to reduce the amount of, or general need for, additional information needed from children to reach conclusions. This manuscript discusses innovative applications of clinical trial designs, analytic strategies to more efficiently leverage prior information, and modeling approaches that impact the data required to determine efficacy of an investigational drug in pediatrics. The planning of pediatric trials and regulatory interactions related to required pediatric studies and the expectations for innovative analytics are also discussed.

Semi-parametric Bayesian regression for subgroup analysis in clinical trials.

Determining whether there are differential treatment effects in subgroups of trial participants remains an important topic in clinical trials as precision medicine becomes ever more relevant. Any assessment of differential treatment effect is predicated on being able to estimate the treatment response accurately while satisfying constraints of balancing the risk of overlooking an important subgroup with the potential to make a decision based on a false discovery. While regression models, such as marginal interaction model, have been widely used to improve accuracy of subgroup parameter estimates by leveraging the relationship between treatment and covariate, there is still a possibility that it can lead to excessively conservative or anti-conservative results. Conceivably, this can be due to the use of the normal distribution as a default prior, which forces outlying subjects to have their means over-shrunk towards the population mean, and the data from such subjects may be excessively influential in estimation of both the overall mean response and the mean response for each subgroup, or a model mis-specification. To address this issue, we investigate the use of nonparametric Bayes, particularly Dirichlet process priors, to create semi-parametric models. These models represent uncertainty in the prior distribution for the overall response while accommodating heterogeneity among individual subgroups. They also account for the effect and variation due to the unaccounted terms. As a result, the models do not force estimates to excessively shrink but still retain the attractiveness of improved precision given by the narrower credible intervals. This is illustrated in extensive simulations investigating bias, mean squared error, coverage probability and credible interval widths. We applied the method on a simulated data based closely on the results of a cystic fibrosis Phase 2 trial.

Propensity-score-based priors for Bayesian augmented control design.

Drug developers are required to demonstrate substantial evidence of effectiveness through the conduct of adequate and well-controlled (A&WC) studies to obtain marketing approval of their medicine. What constitutes A&WC is interpreted as the conduct of randomized controlled trials (RCTs). However, these trials are sometimes unfeasible because of their size, duration, and cost. One way to reduce sample size is to leverage information on the control through a prior. One consideration when forming data-driven prior is the consistency of the external and the current data. It is essential to make this process less susceptible to choosing information that only helps improve the chances toward making an effectiveness claim. For this purpose, propensity score methods are employed for two reasons: (1) it gives the probability of a patient to be in the trial, and (2) it minimizes selection bias by pairing together treatment and control within the trial and control subjects in the external data that are similar in terms of their pretreatment characteristics. Two matching schemes based on propensity scores, estimated through generalized boosted methods, are applied to a real example with the objective of using external data to perform Bayesian augmented control in a trial where the allocation is disproportionate. The simulation results show that the data augmentation process prevents prior and data conflict and improves the precision of the estimator of the average treatment effect.

Propensity score matched augmented controls in randomized clinical trials: A case study.

Existing statutes in the United States and Europe require manufacturers to demonstrate evidence of effectiveness through the conduct of adequate and well-controlled studies to obtain marketing approval of a therapeutic product. What constitutes adequate and well-controlled studies is usually interpreted as randomized controlled trials (RCTs). However, these trials are sometimes unfeasible because of their size, duration, cost, patient preference, or in some cases, ethical concerns. For example, RCTs may not be fully powered in rare diseases or in infections caused by multidrug resistant pathogens because of the low number of enrollable patients. In this case, data available from external controls (including historical controls and observational studies or data registries) can complement information provided by RCT. Propensity score matching methods can be used to select or "borrow" additional patients from the external controls, for maintaining a one-to-one randomization between the treatment arm and active control, by matching the new treatment and control units based on a set of measured covariates, ie, model-based pairing of treatment and control units that are similar in terms of their observable pretreatment characteristics. To this end, 2 matching schemes based on propensity scores are explored and applied to a real clinical data example with the objective of using historical or external observations to augment data in a trial where the randomization is disproportionate or asymmetric.

Update on dietary intake of perchlorate and iodine from U.S. food and drug administration's total diet study: 2008-2012.

The U.S. Food and Drug Administration's (FDA) Total Diet Study (TDS) monitors the US food supply for pesticide residues, industrial chemicals, radionuclides, nutrients, and toxic elements. Perchlorate and iodine intakes based on concentrations in TDS samples collected between 2008 and 2012 were estimated in order to update an earlier TDS dietary assessment. Perchlorate is used as an oxidizing agent in rocket and missile fuel, is formed naturally in the atmosphere, and occurs naturally in some soils. Because of perchlorate's presence in soil, and in irrigation, processing, and source water, it is widely found in food. Iodine was included in the study because perchlorate at high doses interferes with iodide uptake in the thyroid. Iodine (the elemental form of iodide) is essential for growth and development, and metabolism. This study uses a novel statistical method based on a clustered zero-inflated lognormal distribution model to estimate mean and 95th percentile confidence interval concentrations for perchlorate and iodine in US foods. These estimates were used to estimate mean perchlorate and iodine exposures for the total US population and for 14 age/sex groups in the US population. Estimated mean perchlorate intake for the total US population was 0.13 µg/kg bw/day, with mean intakes for the 14 age/sex groups between 0.09 and 0.43 µg/kg bw/day. The estimated mean intakes of perchlorate for all age/sex groups were below EPA's reference dose (RfD) of 0.7 µg/kg bw/day. The estimated mean iodine intake for the total US population was 216.4 µg/person/day, with mean intakes ranging from 140.9 to 296.3 µg/person/day for the 14 age/sex groups, with all age/sex groups exceeding their respective estimated average requirements (EARs).

Statistical modeling for Bayesian extrapolation of adult clinical trial information in pediatric drug evaluation.

Children represent a large underserved population of "therapeutic orphans," as an estimated 80% of children are treated off-label. However, pediatric drug development often faces substantial challenges, including economic, logistical, technical, and ethical barriers, among others. Among many efforts trying to remove these barriers, increased recent attention has been paid to extrapolation; that is, the leveraging of available data from adults or older age groups to draw conclusions for the pediatric population. The Bayesian statistical paradigm is natural in this setting, as it permits the combining (or "borrowing") of information across disparate sources, such as the adult and pediatric data. In this paper, authored by the pediatric subteam of the Drug Information Association Bayesian Scientific Working Group and Adaptive Design Working Group, we develop, illustrate, and provide suggestions on Bayesian statistical methods that could be used to design improved pediatric development programs that use all available information in the most efficient manner. A variety of relevant Bayesian approaches are described, several of which are illustrated through 2 case studies: extrapolating adult efficacy data to expand the labeling for Remicade to include pediatric ulcerative colitis and extrapolating adult exposure-response information for antiepileptic drugs to pediatrics.

Flexible shrinkage estimation of subgroup effects through Dirichlet process priors.

The paradigm shift towards precision medicine reignited interest in determining whether there are differential treatment effects in subgroups of trial participants. Intrinsic to this problem is that any assessment of a differential treatment effect is predicated on being able to estimate the treatment response accurately while satisfying constraints of balancing the risk of overlooking an important subgroup with the potential to make a decision based on a false discovery. While shrinkage models have been widely used to improve accuracy of subgroup parameter estimates by leveraging the relationship between them, there is still a possibility that it can lead to excessively conservative or anti-conservative results. This can possibly be due to the use of the normal distribution as prior, which forces outlying subjects to have their means over-shrunk towards the population mean, and the data from such subjects may be excessively influential in estimation of both the overall mean response and the mean response for each subgroup, or a model misspecification due to unaccounted variation or clustering. To address this issue, we investigate the use of nonparametric Bayes, particularly Dirichlet process priors, to create a flexible shrinkage model. This model represents uncertainty in the prior distribution for the overall response while accommodating heterogeneity among individual subgroups. We simulated data to compare estimates when there is no differential subgroup effect and when there is a differential subgroup effect. In either of these scenarios, the flexible shrinkage model does not force estimates to shrink excessively when similarity of treatment effects is not supported but still retains the attractiveness of improved precision given by the narrower credible intervals. We also applied the same method to a dataset based on trials conducted for an antimicrobial therapy on several related indications.

Non-inferiority and networks: inferring efficacy from a web of data.

In the absence of placebo-controlled trials, the efficacy of a test treatment can be alternatively examined by showing its non-inferiority to an active control; that is, the test treatment is not worse than the active control by a pre-specified margin. The margin is based on the effect of the active control over placebo in historical studies. In other words, the non-inferiority setup involves a network of direct and indirect comparisons between test treatment, active controls, and placebo. Given this framework, we consider a Bayesian network meta-analysis that models the uncertainty and heterogeneity of the historical trials into the non-inferiority trial in a data-driven manner through the use of the Dirichlet process and power priors. Depending on whether placebo was present in the historical trials, two cases of non-inferiority testing are discussed that are analogs of the synthesis and fixed-margin approach. In each of these cases, the model provides a more reliable estimate of the control given its effect in other trials in the network, and, in the case where placebo was only present in the historical trials, the model can predict the effect of the test treatment over placebo as if placebo had been present in the non-inferiority trial. It can further answer other questions of interest, such as comparative effectiveness of the test treatment among its comparators. More importantly, the model provides an opportunity for disproportionate randomization or the use of small sample sizes by allowing borrowing of information from a network of trials to draw explicit conclusions on non-inferiority.