On optimal designs for clinical trials: An updated review

Optimization of clinical trial designs can help investigators achieve higher qualityresults for the given resource constraints. The present paper gives an overviewof optimal designs for various important problems that arise in different stages ofclinical drug development, including phase I dose–toxicity studies; phase I/II studiesthat consider early efficacy and toxicity outcomes simultaneously; phase IIdose–response studies driven by multiple comparisons (MCP), modeling techniques(Mod), or their combination (MCP–Mod); phase III randomized controlled multiarmmulti-objective clinical trials to test difference among several treatment groups;and population pharmacokinetics–pharmacodynamics experiments. We find thatmodern literature is very rich with optimal design methodologies that can be utilizedby clinical researchers to improve efficiency of drug development

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

Ordinary Least Squares: the Adequacy of Linear Regression Solutions under Multicollinearity and without it

The article deals with the problem of economic adequacy of solving a linear regression problem by the OLS method. The study uses the following definition of adequacy: a linear regression solution is considered adequate if it not only has correct signs but also correctly reflects the relationship between coefficients of regression in the population. If in this case the coefficient of determination is greater than 0.8, the solution is considered economically adequate. As an indicator of adequacy of a linear regression problem solution it is proposed to use a 10 % level of the coefficient of variability (CV) of the regression coefficients. It is shown that OLS solutions may be not adequate to the solution in the population, although they may be physically correct (with correct signs) and statistically significant. The mentioned result is obtained by using the artificial data population (ADP) algorithm. The ADP allows generating data of any size with known regression coefficients in the whole population, which can be calculated with the aid of the OLS solution for a very large sample. The ADP algorithm makes it possible to change the regular component of the influence of the regressors on the response. Besides, the random changes of regressors in the ADP are divided into two parts. The first part is coherent to the response changes, but the second part is completely random (incoherent). This one allows changing the near-collinearity level of the data by changing the variance of the incoherent noise in regressors. Studies using ADP have shown that with a high probability the OLS solutions are physically incorrect if the sample sizes (n) are less than 23; physically correct but not adequate for 23 400. Furthermore, it is noted that if the elimination of strongly correlated regressors is not economically justified but is rather a measure of lowering the value of the VIF-factor, the results may be far from the reality. In this regard, it is stated that the use of the MOLS eliminates the need to exclude strongly correlated regressors at all, since the accuracy of the MOLS solution increases with an increase in the VIF

Optimal adaptive designs and adaptive randomization techniques for clinical trials

In this Ph.D. thesis, we investigate how to optimize the design of clinical trials by constructing optimal adaptive designs, and how to implement the design by adaptive randomization. The results of the thesis are summarized by four research papers preceded by three chapters: an introduction, a short summary of the results obtained, and possible topics for future work. In Paper I, we investigate the structure of a D-optimal design for dose-finding studies with censored time-to-event outcomes. We show that the D-optimal design can be much more efficient than uniform allocation design for the parameter estimation. The D-optimal design obtained depends on true parameters of the dose-response model, so it is a locally D-optimal design. We construct two-stage and multi-stage adaptive designs as approximations of  the D-optimal design when prior information about model parameters is not available. Adaptive designs provide very good approximations to the locally D-optimal design, and can potentially reduce total sample size in a study with a pre-specified stopping criterion. In Paper II, we investigate statistical properties of several restricted randomization procedures which target unequal allocation proportions in a multi-arm trial. We compare procedures in terms of their operational characteristics such as balance, randomness, type I error/power, and allocation ratio preserving (ARP) property. We conclude that there is no single “best” randomization procedure for all the target allocation proportions, but the choice of randomization can be done through computer-intensive simulations for a particular target allocation. In Paper III, we combine the results from the papers I and II to implement optimal designs in practice when the sample size is small. The simulation study done in the paper shows that the choice of randomization procedure has an impact on the quality of dose-response estimation. An adaptive design with a small cohort size should be implemented with a procedure that ensures a “well-balanced” allocation according to the D-optimal design at each stage. In Paper IV, we obtain an optimal design for a comparative study with unequal treatment costs and investigate its properties. We demonstrate that unequal allocation may decrease the total study cost while having the same power as traditional equal allocation. However, a larger sample size may be required. We suggest a strategy on how to choose a suitable randomization procedure which provides a good trade-off between balance and randomness to implement optimal allocation. If there is a strong linear trend in observations, then the ARP property is important to maintain the type I error and power at a certain level. Otherwise, a randomization-based inference can be a good alternative for non-ARP procedures

Optimal adaptive designs and adaptive randomization techniques for clinical trials

In this Ph.D. thesis, we investigate how to optimize the design of clinical trials by constructing optimal adaptive designs, and how to implement the design by adaptive randomization. The results of the thesis are summarized by four research papers preceded by three chapters: an introduction, a short summary of the results obtained, and possible topics for future work. In Paper I, we investigate the structure of a D-optimal design for dose-finding studies with censored time-to-event outcomes. We show that the D-optimal design can be much more efficient than uniform allocation design for the parameter estimation. The D-optimal design obtained depends on true parameters of the dose-response model, so it is a locally D-optimal design. We construct two-stage and multi-stage adaptive designs as approximations of  the D-optimal design when prior information about model parameters is not available. Adaptive designs provide very good approximations to the locally D-optimal design, and can potentially reduce total sample size in a study with a pre-specified stopping criterion. In Paper II, we investigate statistical properties of several restricted randomization procedures which target unequal allocation proportions in a multi-arm trial. We compare procedures in terms of their operational characteristics such as balance, randomness, type I error/power, and allocation ratio preserving (ARP) property. We conclude that there is no single “best” randomization procedure for all the target allocation proportions, but the choice of randomization can be done through computer-intensive simulations for a particular target allocation. In Paper III, we combine the results from the papers I and II to implement optimal designs in practice when the sample size is small. The simulation study done in the paper shows that the choice of randomization procedure has an impact on the quality of dose-response estimation. An adaptive design with a small cohort size should be implemented with a procedure that ensures a “well-balanced” allocation according to the D-optimal design at each stage. In Paper IV, we obtain an optimal design for a comparative study with unequal treatment costs and investigate its properties. We demonstrate that unequal allocation may decrease the total study cost while having the same power as traditional equal allocation. However, a larger sample size may be required. We suggest a strategy on how to choose a suitable randomization procedure which provides a good trade-off between balance and randomness to implement optimal allocation. If there is a strong linear trend in observations, then the ARP property is important to maintain the type I error and power at a certain level. Otherwise, a randomization-based inference can be a good alternative for non-ARP procedures

Balancing the Objectives of Statistical Efficiency and Allocation Randomness in Randomized Controlled Trials

Various restricted randomization procedures are available to achieve equal (1:1) allocation in a randomized clinical trial. However, for some procedures, there is a nonnegligible probability of imbalance in the final numbers which may result in an underpowered study. It is important to assess such probability at the study planning stage and make adjustments in the design if needed. In this paper, we perform a quantitative assessment of the tradeoff between randomness, balance, and power of restricted randomization designs targeting equal allocation. First, we study the small-sample performance of biased coin designs with known asymptotic properties and identify a design with an excellent balance–randomness tradeoff. Second, we investigate the issue of randomization-induced treatment imbalance and the corresponding risk of an underpowered study. We propose two risk mitigation strategies: increasing the total sample size or fine-tuning the biased coin parameter to obtain the least restrictive randomization procedure that attains the target power with a high, user-defined probability for the given sample size. Our approach is simple and yet generalizable to more complex settings, including trials with stratified randomization and multi-arm trials with possibly unequal randomization ratios

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

Balancing the Objectives of Statistical Efficiency and Allocation Randomness in Randomized Controlled Trials

Various restricted randomization procedures are available to achieve equal (1:1) allocation in a randomized clinical trial. However, for some procedures, there is a nonnegligible probability of imbalance in the final numbers which may result in an underpowered study. It is important to assess such probability at the study planning stage and make adjustments in the design if needed. In this paper, we perform a quantitative assessment of the tradeoff between randomness, balance, and power of restricted randomization designs targeting equal allocation. First, we study the small-sample performance of biased coin designs with known asymptotic properties and identify a design with an excellent balance–randomness tradeoff. Second, we investigate the issue of randomization-induced treatment imbalance and the corresponding risk of an underpowered study. We propose two risk mitigation strategies: increasing the total sample size or fine-tuning the biased coin parameter to obtain the least restrictive randomization procedure that attains the target power with a high, user-defined probability for the given sample size. Additionally, we investigate an approach for finding the most balanced design that satisfies a constraint on the chosen measure of randomness. Our proposed methodology is simple and yet generalizable to more complex settings, such as trials with stratified randomization and multi-arm trials with possibly unequal randomization ratios.</p

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