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

Abstract

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.

Keywords: Additional covariates; Allocation predictability; Covariate adaptive randomization; Imbalance score; Pocock and Simon; Statistical power.

Fig. 1

Imbalance score, allocation predictability, and weighted score of the PS procedure based on three treatment assignment probability methods: PS_p, PS_q, and PS_t. These methods are compared with CR, and SBR with the block size of 6 for a study with 3 treatments and two influential factors

Fig. 2

Imbalance score and allocation predictability of the SBR and SBSD methods with the block sizes of 6, 12, and 18. SBR: stratified block randomization; SBSD: stratified big stick design

Fig. 3

For a 3-arm study with the total sample size of 60, imbalance score, allocation predictability, and weighted score are plotted as a function of the parameters in the three PS methods, when the number of study sites is increased from 2 to 20

Fig. 4

Imbalance score and allocation predictability of the three PS methods: the PS_p=0.5 method (rows 1 and 2), the PS_q=0.5 method (rows 3 and 4), and the PS_t=0.8 method (rows 5 and 6), as a function of the total sample size and the number factors in the CAR for a study with 3 treatments. The range approach (left) and the SD approach (right) are used in the covariate imbalance score calculation

Fig. 5

Imbalance score and allocation predictability of the PS_t method and the HDBR method as a function of the total sample size and the number factors in the CAR for a study with 3 treatments. HDBR: hierarchical dynamic balancing randomization

Fig. 6

Statistical power of a two-arm CAR design as a function of ${\rho }_3$, given ${\rho }_4$ from 0.1 to 0.7. In the CAR design, the treatment assignment probability was set as 60%. The first and the second row has the correlation ${\rho }_2=0.2$ and 0.1. When the number of factor is zero, it is a CR design

Fig. 7

Statistical power of a two-arm CAR design as a function of ${\rho }_3$, given ${\rho }_1=0.3$, ${\rho }_2=0.2$, and ${\rho }_4=0.4$. Five different p values (0.55 to 0.8) in the PS_p method and five t values (0.6 to 0.95) in the PS_t method were studied, for two, three, and four factors (row 1, row 2, and row 3)