Treatment allocation adaptive randomization methods in clinical trials with few individuals may influence model parameter estimation
Yevgen Ryeznik (1, 2), Oleksandr Sverdlov (3), Andrew C. Hooker (2)
(1) Department of Mathematics, Uppsala University, (2) Department of Pharmaceutical Biosciences, Uppsala University, (3) Early Development Biostatistics – Translational Medicine, Novartis Pharmaceuticals Corporation
Objectives:
In dose-response studies with censored time-to-event outcomes, D-optimal designs depend on the true model parameters and the amount of censoring in the model. In practice, such designs can be implemented adaptively, by performing dose assignments according to updated knowledge of the dose-response curve at interim analyses [1]. 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 [2]. In addition, since D-optimal designs target a decrease in uncertainty of estimated model parameters based on an optimal allocation of patients, then a randomization procedure which accurately achieves these targets (optimal proportions) is required. The choice of the randomization method becomes crucial when the sample size of a study is small, since some randomization procedures may have large shifts from the desired allocations. 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. In addition to standard comparisons of balance and randomness, we compare the procedures in terms of the quality of model parameter estimation. In addition, the effect of patient selection bias on parameter estimation is investigated. The results of this work should help clinical investigators to select an appropriate randomization procedure for their dose-response study.
Methods:
We consider a quadratic dose-response model for log-transformed Weibull event times that are subject to right censoring. For implementing the D-optimal designs, randomization procedures with possibly unequal target allocation are used. There exist many different randomization procedures which may target (un)equal allocation and keep a good balance across treatment arms. We compare several randomization procedures in terms of balance and randomness as well as estimation efficiency and impact on bias and uncertainty of parameter estimates. We consider single-stage, two-stage, and multi-stage adaptive designs. In order to investigate the effect of patient selection bias on model parameter estimation, we use the approach described in [3], but modified for a three-arm randomization setting.
Results:
A simple (and commonly implemented) completely randomized design is most variable and it is likely to deviate from the targeted D-optimal design for small sample sizes. This results in larger uncertainty in dose-response estimation and loss of design efficiency, especially for small sample sizes. Other randomization schemes achieve a tighter allocation balance, leading to higher efficiency, on average, and more accurate estimation of the dose-response relationship. For a multi-stage design with early stopping rules, there are randomization procedures that may require smaller sample size compared to completely random allocation. The presence of selection bias has a negative impact on quality of estimation. The commonly used uniform (non-optimal) design has the worst performance in this scenario.
Conclusions:
The choice of a randomization procedure to implement optimal designs is important for model parameter estimation (quality of dose-response estimation), especially for small sample sizes. To our knowledge, this is the first investigation of the impact of randomization on model parameter estimation. For best performance, an adaptive multi-stage design with small cohort sizes should be implemented with a randomization procedure that ensures a “well-balanced” allocation according to the targeted optimal design at each stage.
References:
[1] Ryeznik Y, Sverdlov O, Hooker AC "Adaptive Optimal Designs for Dose-Finding Studies with Time-to-Event Outcomes", AAPS J. 2017 20(1):24.
[2] Rosenberger WF, Lachin JM "Randomization in Clinical Trials", 2nd ed., 2016, Wiley Series in Probability and Statistics.
[3] Rückbeil MV, Hilgers RD, Heussen N "Assessing the impact of selection bias on test decisions in trials with a time-to-event outcome", 2017, Statistics in Medicine Vol. 36, p. 2656-2668
