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The randomized controlled trial is the gold standard for evaluating the effects of an intervention or treatment, whether in a clinical, laboratory, or other setting. A key requirement is to assign experimental subjects to treatment and control groups in a way that maximizes the statistical power of the study while minimizing bias. The most popular method of group assignment is randomization, including variants such as stratified, permuted block, and biased-coin randomization. The latter are designed to get better statistical balance between groups, especially for small trials. An alternative approach with some strong advocates is minimization, which may be partly random or fully deterministic depending on how it is implemented. But might there be a useful third alternative applicable to some types of trials?

 

The above thought was inspired by the following problem that an Accelrys field scientist presented to me: Given 50 animal subjects with varying body mass, how can they be divided into 5 equal-sized groups such that the body mass mean and variance are roughly the same for each group? In other words, we want the distribution of body mass within each group to be nearly the same. To both of us, this looked like a Pareto problem in which the variance of the within-group mean (variance-of-mean) and the variance of the within-group variance (variance-of-variance) across groups should be simultaneously minimized.

 

I implemented a simple genetic algorithm in a Pipeline Pilot protocol to do a Pareto optimization for this problem. Here's what the typical results look like in a tradeoff plot showing the Pareto results after 500 iterations, compared to results for randomization and minimization (both constrained to result in equal group sizes):

 

 

Variance-of-variance vs. variance-of-mean for alternative methods of assigning subjects to groups

 

 

Each color/symbol represents a different approach, with results from Pareto optimization shown as blue circles; results from multiple random partitionings shown as black stars; and results from minimizations with the subjects processed in different random orders shown as red triangles. Observe that for this very simple problem, the Pareto approach gives the lowest variance-of-mean and variance-of-variance values.

 

Might Pareto optimization be an alternative to traditional randomization and minimization for trial design? I don't know. Given the constraints of the approach, it may be more applicable to lab studies than to clinical trials. But these exploratory results look intriguing. I provide the protocol along with some more thoughts in an Accelrys Community forum posting.

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