Understanding an impact of patient enrollment pattern on predictability of central (unstratified) randomization in a multi-center clinical trial.

In a multi-center randomized controlled trial (RCT) with competitive recruitment, eligible patients are enrolled sequentially by different study centers and are randomized to treatment groups using the chosen randomization method. Given the stochastic nature of the recruitment process, some centers may enroll more patients than others, and in some instances, a center may enroll multiple patients in a row, for example, on a given day. If the study is open-label, the investigators might be able to make intelligent guesses on upcoming treatment assignments in the randomization sequence, even if the trial is centrally randomized and not stratified by center. In this paper, we use enrollment data inspired by a real multi-center RCT to quantify the susceptibility of two restricted randomization procedures, the permuted block design and the big stick design, to selection bias under the convergence strategy of Blackwell and Hodges (1957) applied at the center level. We provide simulation evidence that the expected proportion of correct guesses may be greater than 50% (i.e., an increased risk of selection bias) and depends on the chosen randomization method and the number of study patients recruited by a given center that takes consecutive positions on the central allocation schedule. We propose some strategies for ensuring stronger encryption of the randomization sequence to mitigate the risk of selection bias.

Selecting a randomization method for a multi-center clinical trial with stochastic recruitment considerations.

BACKGROUND: The design of a multi-center randomized controlled trial (RCT) involves multiple considerations, such as the choice of the sample size, the number of centers and their geographic location, the strategy for recruitment of study participants, amongst others. There are plenty of methods to sequentially randomize patients in a multi-center RCT, with or without considering stratification factors. The goal of this paper is to perform a systematic assessment of such randomization methods for a multi-center 1:1 RCT assuming a competitive policy for the patient recruitment process. METHODS: We considered a Poisson-gamma model for the patient recruitment process with a uniform distribution of center activation times. We investigated 16 randomization methods (4 unstratified, 4 region-stratified, 4 center-stratified, 3 dynamic balancing randomization (DBR), and a complete randomization design) to sequentially randomize n = 500 patients. Statistical properties of the recruitment process and the randomization procedures were assessed using Monte Carlo simulations. The operating characteristics included time to complete recruitment, number of centers that recruited a given number of patients, several measures of treatment imbalance and estimation efficiency under a linear model for the response, the expected proportions of correct guesses under two different guessing strategies, and the expected proportion of deterministic assignments in the allocation sequence. RESULTS: Maximum tolerated imbalance (MTI) randomization methods such as big stick design, Ehrenfest urn design, and block urn design result in a better balance-randomness tradeoff than the conventional permuted block design (PBD) with or without stratification. Unstratified randomization, region-stratified randomization, and center-stratified randomization provide control of imbalance at a chosen level (trial, region, or center) but may fail to achieve balance at the other two levels. By contrast, DBR does a very good job controlling imbalance at all 3 levels while maintaining the randomized nature of treatment allocation. Adding more centers into the study helps accelerate the recruitment process but at the expense of increasing the number of centers that recruit very few (or no) patients-which may increase center-level imbalances for center-stratified and DBR procedures. Increasing the block size or the MTI threshold(s) may help obtain designs with improved randomness-balance tradeoff. CONCLUSIONS: The choice of a randomization method is an important component of planning a multi-center RCT. Dynamic balancing randomization with carefully chosen MTI thresholds could be a very good strategy for trials with the competitive policy for patient recruitment.

Steady-state statistical properties and implementation of randomization designs with maximum tolerated imbalance restriction for two-arm equal allocation clinical trials.

In recent decades, several randomization designs have been proposed in the literature as better alternatives to the traditional permuted block design (PBD), providing higher allocation randomness under the same restriction of the maximum tolerated imbalance (MTI). However, PBD remains the most frequently used method for randomizing subjects in clinical trials. This status quo may reflect an inadequate awareness and appreciation of the statistical properties of these randomization designs, and a lack of simple methods for their implementation. This manuscript presents the analytic results of statistical properties for five randomization designs with MTI restriction based on their steady-state probabilities of the treatment imbalance Markov chain and compares them to those of the PBD. A unified framework for randomization sequence generation and real-time on-demand treatment assignment is proposed for the straightforward implementation of randomization algorithms with explicit formulas of conditional allocation probabilities. Topics associated with the evaluation, selection, and implementation of randomization designs are discussed. It is concluded that for two-arm equal allocation trials, several randomization designs offer stronger protection against selection bias than the PBD does, and their implementation is not necessarily more difficult than the implementation of the PBD.

A roadmap to using randomization in clinical trials.

BACKGROUND: Randomization is the foundation of any clinical trial involving treatment comparison. It helps mitigate selection bias, promotes similarity of treatment groups with respect to important known and unknown confounders, and contributes to the validity of statistical tests. Various restricted randomization procedures with different probabilistic structures and different statistical properties are available. The goal of this paper is to present a systematic roadmap for the choice and application of a restricted randomization procedure in a clinical trial. METHODS: We survey available restricted randomization procedures for sequential allocation of subjects in a randomized, comparative, parallel group clinical trial with equal (1:1) allocation. We explore statistical properties of these procedures, including balance/randomness tradeoff, type I error rate and power. We perform head-to-head comparisons of different procedures through simulation under various experimental scenarios, including cases when common model assumptions are violated. We also provide some real-life clinical trial examples to illustrate the thinking process for selecting a randomization procedure for implementation in practice. RESULTS: Restricted randomization procedures targeting 1:1 allocation vary in the degree of balance/randomness they induce, and more importantly, they vary in terms of validity and efficiency of statistical inference when common model assumptions are violated (e.g. when outcomes are affected by a linear time trend; measurement error distribution is misspecified; or selection bias is introduced in the experiment). Some procedures are more robust than others. Covariate-adjusted analysis may be essential to ensure validity of the results. Special considerations are required when selecting a randomization procedure for a clinical trial with very small sample size. CONCLUSIONS: The choice of randomization design, data analytic technique (parametric or nonparametric), and analysis strategy (randomization-based or population model-based) are all very important considerations. Randomization-based tests are robust and valid alternatives to likelihood-based tests and should be considered more frequently by clinical investigators.

Pharmacometrics meets statistics-A synergy for modern drug development.

Modern drug development problems are very complex and require integration of various scientific fields. Traditionally, statistical methods have been the primary tool for design and analysis of clinical trials. Increasingly, pharmacometric approaches using physiology-based drug and disease models are applied in this context. In this paper, we show that statistics and pharmacometrics have more in common than what keeps them apart, and collectively, the synergy from these two quantitative disciplines can provide greater advances in clinical research and development, resulting in novel and more effective medicines to patients with medical need.

Opportunity for efficiency in clinical development: An overview of adaptive clinical trial designs and innovative machine learning tools, with examples from the cardiovascular field.

Modern data analysis tools and statistical modeling techniques are increasingly used in clinical research to improve diagnosis, estimate disease progression and predict treatment outcomes. What seems less emphasized is the importance of the study design, which can have a serious impact on the study cost, time and statistical efficiency. This paper provides an overview of different types of adaptive designs in clinical trials and their applications to cardiovascular trials. We highlight recent proliferation of work on adaptive designs over the past two decades, including some recent regulatory guidelines on complex trial designs and master protocols. We also describe the increasing role of machine learning and use of metaheuristics to construct increasingly complex adaptive designs or to identify interesting features for improved predictions and classifications.

Implementing unequal randomization in clinical trials with heterogeneous treatment costs.

Equal randomization has been a popular choice in clinical trial practice. However, in trials with heterogeneous variances and/or variable treatment costs, as well as in settings where maximization of every trial participant's benefit is an important design consideration, optimal allocation proportions may be unequal across study treatment arms. In this paper, we investigate optimal allocation designs minimizing study cost under statistical efficiency constraints for parallel group clinical trials comparing several investigational treatments against the control. We show theoretically that equal allocation designs may be suboptimal, and unequal allocation designs can provide higher statistical power for the same budget or result in a smaller cost for the same level of power. We also show how optimal allocation can be implemented in practice by means of restricted randomization procedures and how to perform statistical inference following these procedures, using invoked population-based or randomization-based approaches. Our results provide further support to some previous findings in the literature that unequal randomization designs can be cost efficient and can be successfully implemented in practice. We conclude that the choice of the target allocation, the randomization procedure, and the statistical methodology for data analysis is an essential component in ensuring valid, powerful, and robust clinical trial results.

Implementing Optimal Designs for Dose-Response Studies Through Adaptive Randomization for a Small Population Group.

In dose-response studies with censored time-to-event outcomes, D-optimal designs depend on the true model and the amount of censored data. In practice, such designs can be implemented adaptively, by performing dose assignments according to updated knowledge of the dose-response curve at interim analysis. It is also essential that treatment allocation involves randomization-to mitigate various experimental biases and enable valid statistical inference at the end of the trial. In this work, we perform a comparison of several adaptive randomization procedures that can be used for implementing D-optimal designs for dose-response studies with time-to-event outcomes with small to moderate sample sizes. We consider single-stage, two-stage, and multi-stage adaptive designs. We also explore robustness of the designs to experimental (chronological and selection) biases. Simulation studies provide evidence that both the choice of an allocation design and a randomization procedure to implement the target allocation impact the quality of dose-response estimation, especially for small samples. For best performance, a multi-stage adaptive design with small cohort sizes should be implemented using a randomization procedure that closely attains the targeted D-optimal design at each stage. The results of the current work should help clinical investigators select an appropriate randomization procedure for their dose-response study.

A comparative study of restricted randomization procedures for multiarm trials with equal or unequal treatment allocation ratios.

Randomization designs for multiarm clinical trials are increasingly used in practice, especially in phase II dose-ranging studies. Many new methods have been proposed in the literature; however, there is lack of systematic, head-to-head comparison of the competing designs. In this paper, we systematically investigate statistical properties of various restricted randomization procedures for multiarm trials with fixed and possibly unequal allocation ratios. The design operating characteristics include measures of allocation balance, randomness of treatment assignments, variations in the allocation ratio, and statistical characteristics such as type I error rate and power. The results from the current paper should help clinical investigators select an appropriate randomization procedure for their clinical trial. We also provide a web-based R shiny application that can be used to reproduce all results in this paper and run simulations under additional user-defined experimental scenarios.

Adaptive Optimal Designs for Dose-Finding Studies with Time-to-Event Outcomes.

We consider optimal design problems for dose-finding studies with censored Weibull time-to-event outcomes. Locally D-optimal designs are investigated for a quadratic dose-response model for log-transformed data subject to right censoring. Two-stage adaptive D-optimal designs using maximum likelihood estimation (MLE) model updating are explored through simulation for a range of different dose-response scenarios and different amounts of censoring in the model. The adaptive optimal designs are found to be nearly as efficient as the locally D-optimal designs. A popular equal allocation design can be highly inefficient when the amount of censored data is high and when the Weibull model hazard is increasing. The issues of sample size planning/early stopping for an adaptive trial are investigated as well. The adaptive D-optimal design with early stopping can potentially reduce study size while achieving similar estimation precision as the fixed allocation design.

RARtool: A MATLAB Software Package for Designing Response-Adaptive Randomized Clinical Trials with Time-to-Event Outcomes.

Response-adaptive randomization designs are becoming increasingly popular in clinical trial practice. In this paper, we present RARtool, a user interface software developed in MATLAB for designing response-adaptive randomized comparative clinical trials with censored time-to-event outcomes. The RARtool software can compute different types of optimal treatment allocation designs, and it can simulate response-adaptive randomization procedures targeting selected optimal allocations. Through simulations, an investigator can assess design characteristics under a variety of experimental scenarios and select the best procedure for practical implementation. We illustrate the utility of our RARtool software by redesigning a survival trial from the literature.

Exact Bayesian Inference Comparing Binomial Proportions, With Application to Proof-of-Concept Clinical Trials.

The authors revisit the problem of exact Bayesian inference comparing two independent binomial proportions. Numerical integration in R is used to compute exact posterior distribution functions, probability densities, and quantiles of the risk difference, relative risk, and odds ratio. An application of the methodology is given in the context of randomized comparative proof-of-concept clinical trials that are driven by evaluation of quantitative criteria combining statistical significance and clinical relevance. A two-stage adaptive design based on predictive probability of success is proposed and its operating characteristics are studied via Monte Carlo simulation. The authors conclude that exact Bayesian methods provide an elegant and efficient way to facilitate design and analysis of proof-of-concept studies.

Efficient and ethical response-adaptive randomization designs for multi-arm clinical trials with Weibull time-to-event outcomes.

We consider a design problem for a clinical trial with multiple treatment arms and time-to-event primary outcomes that are modeled using the Weibull family of distributions. The D-optimal design for the most precise estimation of model parameters is derived, along with compound optimal allocation designs that provide targeted efficiencies for various estimation problems and ethical considerations. The proposed optimal allocation designs are studied theoretically and are implemented using response-adaptive randomization for a clinical trial with censored Weibull outcomes. We compare the merits of our multiple-objective response-adaptive designs with traditional randomization designs and show that our designs are more flexible, realistic, generally more ethical, and frequently provide higher efficiencies for estimating different sets of parameters.