Comparison of Pocock and Simon's covariate-adaptive randomization procedures in clinical trials.

When multiple influential covariates need to be balanced during a clinical trial, stratified blocked randomization and covariate-adaptive randomization procedures are frequently used in trials to prevent bias and enhance the validity of data analysis results. The latter approach is increasingly used in practice for a study with multiple covariates and limited sample sizes. Among a group of these approaches, the covariate-adaptive procedures proposed by Pocock and Simon are straightforward to be utilized in practice. We aim to investigate the optimal design parameters for the patient treatment assignment probability of their developed three methods. In addition, we seek to answer the question related to the randomization performance when additional covariates are added to the existing randomization procedure. We conducted extensive simulation studies to address these practically important questions.

Mathematical programming tools for randomization purposes in small two-arm clinical trials: A case study with real data.

Modern randomization methods in clinical trials are invariably adaptive, meaning that the assignment of the next subject to a treatment group uses the accumulated information in the trial. Some of the recent adaptive randomization methods use mathematical programming to construct attractive clinical trials that balance the group features, such as their sizes and covariate distributions of their subjects. We review some of these methods and compare their performance with common covariate-adaptive randomization methods for small clinical trials. We introduce an energy distance measure that compares the discrepancy between the two groups using the joint distribution of the subjects' covariates. This metric is more appealing than evaluating the discrepancy between the groups using their marginal covariate distributions. Using numerical experiments, we demonstrate the advantages of the mathematical programming methods under the new measure. In the supplementary material, we provide R codes to reproduce our study results and facilitate comparisons of different randomization procedures.

Regression-based multiple treatment effect estimation under covariate-adaptive randomization.

Covariate-adaptive randomization methods are widely used in clinical trials to balance baseline covariates. Recent studies have shown the validity of using regression-based estimators for treatment effects without imposing functional form requirements on the true data generation model. These studies have had limitations in certain scenarios; for example, in the case of multiple treatment groups, these studies did not consider additional covariates or assumed that the allocation ratios were the same across strata. To address these limitations, we develop a stratum-common estimator and a stratum-specific estimator under multiple treatments. We derive the asymptotic behaviors of these estimators and propose consistent nonparametric estimators for asymptotic variances. To determine their efficiency, we compare the estimators with the stratified difference-in-means estimator as the benchmark. We find that the stratum-specific estimator guarantees efficiency gains, regardless of whether the allocation ratios across strata are the same or different. Our conclusions were also validated by simulation studies and a real clinical trial example.

Bayesian adaptive design for covariate-adaptive historical control information borrowing.

Interest in incorporating historical data in the clinical trial has increased with the rising cost of conducting clinical trials. The intervention arm for the current trial often requires prospective data to assess a novel treatment, and thus borrowing historical control data commensurate in distribution to current control data is motivated in order to increase the allocation ratio to the current intervention arm. Existing historical control borrowing adaptive designs adjust allocation ratios based on the commensurability assessed through study-level summary statistics of the response agnostic of the distributions of the trial subject characteristics in the current and historical trials. This can lead to distributional imbalance of the current trial subject characteristics across the treatment arms as well as between current control data and borrowed historical control data. Such covariate imbalance may threaten the internal validity of the current trial by introducing confounding factors that affect study endpoints. In this article, we propose a Bayesian design which borrows and updates the treatment allocation ratios both covariate-adaptively and commensurate to covariate dependently assessed similarity between the current and historical control data. We employ covariate-dependent discrepancy parameters which are allowed to grow with the sample size and propose a regularized local regression procedure for the estimation of the parameters. The proposed design also permits the current and the historical controls to be similar to varying degree, depending on the subject level characteristics. We evaluate the proposed design extensively under the settings derived from two placebo-controlled randomized trials on vertebral fracture risk in post-menopausal women.

Handling misclassified stratification variables in the analysis of randomised trials with continuous outcomes.

Many trials use stratified randomisation, where participants are randomised within strata defined by one or more baseline covariates. While it is important to adjust for stratification variables in the analysis, the appropriate method of adjustment is unclear when stratification variables are affected by misclassification and hence some participants are randomised in the incorrect stratum. We conducted a simulation study to compare methods of adjusting for stratification variables affected by misclassification in the analysis of continuous outcomes when all or only some stratification errors are discovered, and when the treatment effect or treatment-by-covariate interaction effect is of interest. The data were analysed using linear regression with no adjustment, adjustment for the strata used to perform the randomisation (randomisation strata), adjustment for the strata if all errors are corrected (true strata), and adjustment for the strata after some errors are discovered and corrected (updated strata). The unadjusted model performed poorly in all settings. Adjusting for the true strata was optimal, while the relative performance of adjusting for the randomisation strata or the updated strata varied depending on the setting. As the true strata are unlikely to be known with certainty in practice, we recommend using the updated strata for adjustment and performing subgroup analyses, provided the discovery of errors is unlikely to depend on treatment group, as expected in blinded trials. Greater transparency is needed in the reporting of stratification errors and how they were addressed in the analysis.

Simulated annealing for balancing covariates.

Covariate balance is one of the fundamental issues in designing experiments for treatment comparisons, especially in randomized clinical trials. In this article, we introduce a new class of covariate-adaptive procedures based on the Simulated Annealing algorithm aimed at balancing the allocations of two competing treatments across a set of pre-specified covariates. Due to the nature of the simulated annealing, these designs are intrinsically randomized, thus completely unpredictable, and very flexible: they can manage both quantitative and qualitative factors and be implemented in a static version as well as sequentially. The properties of the suggested proposal are described, showing a significant improvement in terms of covariate balance and inferential accuracy with respect to all the other procedures proposed in the literature. An illustrative example based on real data is also discussed.

Regression analysis for covariate-adaptive randomization: A robust and efficient inference perspective.

Linear regression is arguably the most fundamental statistical model; however, the validity of its use in randomized clinical trials, despite being common practice, has never been crystal clear, particularly when stratified or covariate-adaptive randomization is used. In this article, we investigate several of the most intuitive and commonly used regression models for estimating and inferring the treatment effect in randomized clinical trials. By allowing the regression model to be arbitrarily misspecified, we demonstrate that all these regression-based estimators robustly estimate the treatment effect, albeit with possibly different efficiency. We also propose consistent non-parametric variance estimators and compare their performances to those of the model-based variance estimators that are readily available in standard statistical software. Based on the results and taking into account both theoretical efficiency and practical feasibility, we make recommendations for the effective use of regression under various scenarios. For equal allocation, it suffices to use the regression adjustment for the stratum covariates and additional baseline covariates, if available, with the usual ordinary-least-squares variance estimator. For unequal allocation, regression with treatment-by-covariate interactions should be used, together with our proposed variance estimators. These recommendations apply to simple and stratified randomization, and minimization, among others. We hope this work helps to clarify and promote the usage of regression in randomized clinical trials.

The precision interventions for severe and/or exacerbation-prone asthma (PrecISE) adaptive platform trial: statistical considerations.

The Precision Interventions for Severe and/or Exacerbation-prone Asthma (PrecISE) study is an adaptive platform trial designed to investigate novel interventions to severe asthma. The study is conducted under a master protocol and utilizes a crossover design with each participant receiving up to five interventions and at least one placebo. Treatment assignments are based on the patients' biomarker profiles and precision health methods are incorporated into the interim and final analyses. We describe key elements of the PrecISE study including the multistage adaptive enrichment strategy, early stopping of an intervention for futility, power calculations, and the primary analysis strategy.

Re-randomization tests in clinical trials.

As randomization methods use more information in more complex ways to assign patients to treatments, analysis of the resulting data becomes challenging. The treatment assignment vector and outcome vector become correlated whenever randomization probabilities depend on data correlated with outcomes. One straightforward analysis method is a re-randomization test that fixes outcome data and creates a reference distribution for the test statistic by repeatedly re-randomizing according to the same randomization method used in the trial. This article reviews re-randomization tests, especially in nonstandard settings like covariate-adaptive and response-adaptive randomization. We show that re-randomization tests provide valid inference in a wide range of settings. Nonetheless, there are simple examples demonstrating limitations.

The Shiny Balancer - software and imbalance criteria for optimally balanced treatment allocation in small RCTs and cRCTs.

BACKGROUND: In randomised controlled trials with only few randomisation units, treatment allocation may be challenging if balanced distributions of many covariates or baseline outcome measures are desired across all treatment groups. Both traditional approaches, stratified randomisation and allocation by minimisation, have their own limitations. A third method for achieving balance consists of randomly choosing from a preselected list of sufficiently balanced allocations. As with minimisation, this method requires that heterogeneity between treatment groups is measured by specified imbalance metrics. Although certain imbalance measures are more commonly used than others, to the author's knowledge there is no generally accepted "gold standard", neither for categorical and even less so for continuous variables. METHODS: An intuitive and easily accessible web-based software tool was developed which allows for balancing multiple variables of different types and using various imbalance metrics. Different metrics were compared in a simulation study. RESULTS: Using simulated data, it could be shown that for categorical variables, χ2-based imbalance measures seem to be viable alternatives to the established "quadratic imbalance" metric. For continuous variables, using the area between the empirical cumulative distribution functions or the largest difference in the three pairs of quartiles is recommended to measure imbalance. Another imbalance metric suggested in the literature for continuous variables, the (symmetrised) Kullback-Leibler divergence, should be used with caution. CONCLUSION: The Shiny Balancer offers the possibility to visually explore the balancing properties of several well established or newly suggested imbalance metrics, and its use is particularly advocated in clinical studies with few randomisation units, as it is typically the case in cluster randomised trials.

Validity and power considerations on hypothesis testing under minimization.

Minimization, a dynamic allocation method, is gaining popularity especially in cancer clinical trials. Aiming to achieve balance on all important prognostic factors simultaneously, this procedure can lead to a substantial reduction in covariate imbalance compared with conventional randomization in small clinical trials. While minimization has generated enthusiasm, some controversy exists over the proper analysis of such a trial. Critics argue that standard testing methods that do not account for the dynamic allocation algorithm can lead to invalid statistical inference. Acknowledging this limitation, the International Conference on Harmonization E9 guideline suggests that 'the complexity of the logistics and potential impact on analyses be carefully evaluated when considering dynamic allocation'. In this article, we investigate the proper analysis approaches to inference in a minimization design for both continuous and time-to-event endpoints and evaluate the validity and power of these approaches under a variety of scenarios both theoretically and empirically. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.

Optimal design for inference on the threshold of a biomarker.

Enrichment designs with a continuous biomarker require the estimation of a threshold to determine the subpopulation benefitting from the treatment. This article provides the optimal allocation for inference in a two-stage enrichment design for treatment comparisons when a continuous biomarker is suspected to affect patient response. Several design criteria, associated with different trial objectives, are optimized under balanced or Neyman allocation and under equality of the first two empirical biomarker's moments. Moreover, we propose a new covariate-adaptive randomization procedure that converges to the optimum with the fastest available rate. Theoretical and simulation results show that this strategy improves the efficiency of a two-stage enrichment clinical trial, especially with smaller sample sizes and under heterogeneous responses.

Outpatient follow-up of tumour diseases through video-based value-oriented behavioural activation (ViVA): study protocol for a randomised controlled trial.

BACKGROUND: In Germany, approximately half a million people are diagnosed with cancer annually; this can be traumatic and lead to depression, anxiety, and adjustment disorders necessitating psycho-oncological intervention. Value-oriented behavioural activation, adopted from depression psychotherapy, aims to provide structured support to help patients adjust their personal values, goals, and activities within the context of their changed life situation. This trial aims to evaluate the effectiveness of video-based value-oriented behavioural activation against German S3-Guideline-compliant aftercare for cancer patients dealing with psychological distress. METHODS: This trial will use covariate-adaptive randomisation according to gender and type of tumour disease to assign participants to one of two study arms (value-oriented behavioural activation consisting of 12 manualised follow-up sessions delivered via video consultation vs. S3-Guideline-compliant aftercare comprising three supportive talks). Psychological strain, psychosocial distress, quality of life, work-related outcomes, fear of cancer recurrence, goal adjustment, satisfaction with the consultant-participant relationship, and rumination will be measured at baseline, twice during treatment, posttreatment, and at the 6-month follow-up. The target sample of 146 tumour patients experiencing high psychosocial distress will be recruited at the Rehazentrum Oberharz, Germany. DISCUSSION: This trial aims to test the effectiveness of value-oriented behavioural activation in aftercare for tumour patients, focusing on its capacity to reduce distress and the potential for long-term effects evaluated through a 6-month follow-up. The study's possible challenges include enrolling a sufficient sample and ensuring adherence to treatment, mitigated through in-person recruitment and rigorous training of staff. If successful, the results will be of high public health relevance, especially for psychotherapeutic care in rural areas and among patients with limited mobility considering the video-based approach of the trial. TRIAL REGISTRATION: This study was registered at the German Clinical Trials Register: DRKS00031900 on Sep 19, 2023.

Validity of tests under covariate-adaptive biased coin randomization and generalized linear models.

Some covariate-adaptive randomization methods have been used in clinical trials for a long time, but little theoretical work has been done about testing hypotheses under covariate-adaptive randomization until Shao et al. (2010) who provided a theory with detailed discussion for responses under linear models. In this article, we establish some asymptotic results for covariate-adaptive biased coin randomization under generalized linear models with possibly unknown link functions. We show that the simple t-test without using any covariate is conservative under covariate-adaptive biased coin randomization in terms of its Type I error rate, and that a valid test using the bootstrap can be constructed. This bootstrap test, utilizing covariates in the randomization scheme, is shown to be asymptotically as efficient as Wald's test correctly using covariates in the analysis. Thus, the efficiency loss due to not using covariates in the analysis can be recovered by utilizing covariates in covariate-adaptive biased coin randomization. Our theory is illustrated with two most popular types of discrete outcomes, binary responses and event counts under the Poisson model, and exponentially distributed continuous responses. We also show that an alternative simple test without using any covariate under the Poisson model has an inflated Type I error rate under simple randomization, but is valid under covariate-adaptive biased coin randomization. Effects on the validity of tests due to model misspecification is also discussed. Simulation studies about the Type I errors and powers of several tests are presented for both discrete and continuous responses.

Weighted re-randomization tests for minimization with unbalanced allocation.

Re-randomization test has been considered as a robust alternative to the traditional population model-based methods for analyzing randomized clinical trials. This is especially so when the clinical trials are randomized according to minimization, which is a popular covariate-adaptive randomization method for ensuring balance among prognostic factors. Among various re-randomization tests, fixed-entry-order re-randomization is advocated as an effective strategy when a temporal trend is suspected. Yet when the minimization is applied to trials with unequal allocation, fixed-entry-order re-randomization test is biased and thus compromised in power. We find that the bias is due to non-uniform re-allocation probabilities incurred by the re-randomization in this case. We therefore propose a weighted fixed-entry-order re-randomization test to overcome the bias. The performance of the new test was investigated in simulation studies that mimic the settings of a real clinical trial. The weighted re-randomization test was found to work well in the scenarios investigated including the presence of a strong temporal trend.

Estimation of hurst exponent for sequential monitoring of clinical trials with covariate adaptive randomization.

BACKGROUND: Classical Brownian motion (BM) has been commonly used in monitoring clinical trials including those with covariate adaptive randomization (CAR). Independent increment property is commonly assumed in the sequential monitoring process of the clinical trials with CAR designs. However, in reality, correlation may exist in the error terms of the underlying model, resulting in dependent increment in the sequential monitoring process. METHODS: We conducted simulations for estimating the Hurst exponent to evaluate the stochastic property in the covariate adaptive randomized clinical trials under two scenarios: 1. CAR designs with independent and identically distributed error terms. 2. CAR designs with correlated error terms. The theoretical properties of covariate adaptive randomized clinical trials with correlated error structure were investigated. A test statistic including the covariance pattern of the error terms was proposed. CONCLUSION: In our study, the sequential test statistics under CAR procedure is shown to be asymptotically Brownian motion when the error structure is correctly specified. Further, Brownian motion is a special case of fractional Brownian motion when Hurst exponent equals to 0.5. Our simulations are consistent with the theoretical asymptotic results.

Testing for treatment effect in covariate-adaptive randomized trials with generalized linear models and omitted covariates.

Concerns have been expressed over the validity of statistical inference under covariate-adaptive randomization despite the extensive use in clinical trials. In the literature, the inferential properties under covariate-adaptive randomization have been mainly studied for continuous responses; in particular, it is well known that the usual two-sample t-test for treatment effect is typically conservative. This phenomenon of invalid tests has also been found for generalized linear models without adjusting for the covariates and are sometimes more worrisome due to inflated Type I error. The purpose of this study is to examine the unadjusted test for treatment effect under generalized linear models and covariate-adaptive randomization. For a large class of covariate-adaptive randomization methods, we obtain the asymptotic distribution of the test statistic under the null hypothesis and derive the conditions under which the test is conservative, valid, or anti-conservative. Several commonly used generalized linear models, such as logistic regression and Poisson regression, are discussed in detail. An adjustment method is also proposed to achieve a valid size based on the asymptotic results. Numerical studies confirm the theoretical findings and demonstrate the effectiveness of the proposed adjustment method.

Inference under covariate-adaptive randomization: A simulation study.

In clinical trials, several covariate-adaptive designs have been proposed to balance treatment arms with respect to key covariates. Although some argue that conventional asymptotic tests are still appropriate when covariate-adaptive randomization is used, others think that re-randomization tests should be used. In this manuscript, we compare by simulation the performance of asymptotic and re-randomization tests under covariate-adaptive randomization. Our simulation study confirms results expected by the existing theory (e.g. asymptotic tests do not control type I error when the model is miss-specified). Furthermore, it shows that (i) re-randomization tests are as powerful as the asymptotic tests if the model is correct; (ii) re-randomization tests are more powerful when adjusting for covariates; (iii) minimization and permuted blocks provide similar results.

A randomized and comparative study to assess safety and efficacy of supplemental treatment of a herbal formulation - Aayudh Advance comprising essential oils in patients with corona virus 2019 (COVID-19).

OBJECTIVE: The purpose of this study was to examine the effect of herbal formulation - Aayudh Advance on viral load as well as recovery duration in mild symptomatic patients diagnosed with Corona Virus Disease 2019 (COVID-19). It also aimed to study the effect of Herbal formulation - Aayudh Advance in terms of clinical improvement of various sign and symptoms in mild symptomatic COVID-19 patients. METHOD: Once the patient suffice the requirement of inclusion, exclusion criteria of the study than as per the method of 'Covariate Adaptive Randomization' technique, patient was assigned in either Aayudh Advance arm (Test arm) or Control Arm. Here standard of Care treatment was given to all patients of both the arms. Treatment was given for the period of 14 days or till patient turned COVID-19 negative, which ever was earlier. Clinical signs and symptoms viz. body temperature, SpO 2, Scoring of Cough & Scoring of Shortness of breath were recorded on all 5 Clinical visits along with biochemical testing like RT-PCR (with CT value of E gene and RDRP gene), serum ferritin, CRP and NLR observed on weekly Visit. RESULT: Total 74 patients were enrolled in the present study. Out of which 60 patients (30 patients in each group) have completed study as per the protocol, whereas 14 patients have voluntarily withdrawn from the study due to getting early discharge from the hospital. All patients in Aayudh Advance treatment group recovered (100%) after 14 days. This observed recovery was 15.38% more as compared to Standard of Care treatment alone. Further, there was statistically significant reduction (p < 0.05) in viral load as indicated by significant increase in CT value of E-gene and RDRP gene. Further, no patients reported any Adverse Reaction as well as no drug to drug interaction was observed with supplemental treatment with Aayudh Advance. CONCLUSION: The Aayudh Advance was found safe as well as more effective in terms of reduction of viral load. % recovery was more in Treatment arm as compared to Control arm in mild symptomatic COVID-19 patients.

Testing hypotheses under adaptive randomization with continuous covariates in clinical trials.

Covariate-adaptive designs are widely used to balance covariates and maintain randomization in clinical trials. Adaptive designs for discrete covariates and their asymptotic properties have been well studied in the literature. However, important continuous covariates are often involved in clinical studies. Simply discretizing or categorizing continuous covariates can result in loss of information. The current understanding of adaptive designs with continuous covariates lacks a theoretical foundation as the existing works are entirely based on simulations. Consequently, conventional hypothesis testing in clinical trials using continuous covariates is still not well understood. In this paper, we establish a theoretical framework for hypothesis testing on adaptive designs with continuous covariates based on linear models. For testing treatment effects and significance of covariates, we obtain the asymptotic distributions of the test statistic under null and alternative hypotheses. Simulation studies are conducted under a class of covariate-adaptive designs, including the p-value-based method, the Su's percentile method, the empirical cumulative-distribution method, the Kullback-Leibler divergence method, and the kernel-density method. Key findings about adaptive designs with independent covariates based on linear models are (1) hypothesis testing that compares treatment effects are conservative in terms of smaller type I error, (2) hypothesis testing using adaptive designs outperforms complete randomization method in terms of power, and (3) testing on significance of covariates is still valid.