How to Balance Prognostic Factors in Controlled Phase II Trials: Stratified Permuted Block Randomization or Minimization? An Analysis of Clinical Trials in Digestive Oncology

Abstract

In controlled phase II trials, major prognostic factors need to be well balanced between arms. The main procedures used are SPBR (Stratified Permuted Block Randomization) and minimization. First, we provide a systematic review of the treatment allocation procedure used in gastrointestinal oncology controlled phase II trials published in 2019. Second, we performed simulations using data from six phase II studies to measure the impacts of imbalances and bias on the efficacy estimations. From the 40 articles analyzed, all mentioned randomization in both the title and abstract, the median number of patients included was 109, and 77.5% were multicenter. Of the 27 studies that reported at least one stratification variable, 10 included the center as a stratification variable, 10 used minimization, 9 used SBR, and 8 were unspecified. In real data studies, the imbalance increased with the number of centers. The total and marginal imbalances were higher with SBR than with minimization, and the difference increased with the number of centers. The efficiency estimates per arm were close to the original trial estimate in both procedures. Minimization is often used in cases of numerous centers and guarantees better similarity between arms for stratification variables for total and marginal imbalances in phase II trials.

Keywords: minimization; phase II trials; randomization.

Figure 1

Decision regarding the arm allocation of the 8th patient () depending on the 2 procedures: Stratified Permuted Block Randomization (left side) and minimization (right side). The characteristics of the 7 patients who were already randomized in the study are shown at the top left of the diagram. The study’s stratification variables are represented using colors and pictograms (see top right of diagram).

Figure 2

Literature review flowchart: PRISMA flow diagram of our systematic analysis of controlled phase II trials in digestive oncology published in 2019.

Figure 3

Simulation of re-randomized real databases. The impact on imbalance depending on the selected method. For each trial, the distribution of the imbalances (total, marginal, and within-stratum) calculated in the 1000 simulated data sets for the 2 allocation arm methods (minimization and SPBR) is presented: boxes correspond to the interquartile range imbalance (25th–75th percentiles), the central segment corresponds to the median imbalance, and the whiskers are the lines that extend from the top or the bottom of the box extending to 1.5 times the interquartile range, bullets correspond to outliers.