In this paper we present two new algorithms for the layout optimization problem: this concerns the placement of circular, weighted objects inside a circular container, the two objectives being to minimize imbalance of mass and to minimize the radius of the container.
Our algorithm highlights allocations that minimize imbalance between treatment groups across multiple baseline covariates.
It is intended these algorithms are an easy to use and convenient tool to be used by researchers who wish to minimize imbalance between treatment arms across multiple baseline stratification variables ensuring that ICH guidance is adhered to.
To minimize imbalance over several strata with a number of clusters no divisible by five, the SAS macro was programmed to start the cyclic assignment by assigning one of the colors at random (with probability 1/5).
The algorithm generates an ordered list of the possible permutations of randomization within each block – at the top of the list are the permutations which minimize imbalance the best.
To minimize imbalance over several strata with odd numbers of clusters, these strata were paired, and clusters were alternately allocated to either training or control, the first cluster being allocated to either training or control depending on the flip of a coin.
The goal of adaptive randomization may be to minimize imbalance in baseline covariates among treatment groups (covariate-adaptive randomization) or to increase the proportion of patients assigned to the seemingly more effective treatment while reducing overall trial enrollment (response-adaptive randomization).
Randomization will be conducted using a dynamic allocation [ 26] algorithm minimizing imbalances across multiple assigned stratification factors.
For this purpose, a new terminology referred to as the quantitative imbalance and operation modification factor were defined and the operating conditions of furnace required to minimize the imbalances were investigated with computational fluid dynamics (CFD).
