The flavor of research done by OR researchers in Design of Experiments is foreign to what is expected in medical statistics. A synonym of operations research might be applied decision analysis. The following paper by Nathan Kallus from Cornell is a good example:
Kallus, N. (2018). Optimal a priori balance in the design of controlled experiments. Journal of the Royal Statistical Society Series B: Statistical Methodology, 80(1), 85-112. link
We develop a unified theory of designs for controlled experiments that balance baseline covariates a priori (before treatment and before randomization) using the framework of minimax variance and a new method called kernel allocation. We show that any notion of a priori balance must go hand in hand with a notion of structure, since with no structure on the dependence of outcomes on baseline covariates complete randomization (no special covariate balance) is always minimax optimal. Restricting the structure of dependence, either parametrically or non-parametrically, gives rise to certain covariate imbalance metrics and optimal designs.
The interesting part of Kallus’s paper is the discussion of balanced designs from a mathematical point of view. The kernel allocation method as described has limitations in human subject experiments because test subjects need to all be available for assignment. In medical trials, subjects arrive sequentially, creating practical challenges.
Yet, compare that with the work on matched designs that date back to the early 1970’s with Donald Taves and Simon and Pocock. Taves has a pre-print from 2024 (Improving Clinical Trials) that compares recent matching/minimization algorithms (termed Flexible Minimization) with randomization on sample size vs selection bias metrics. Donald Taves has fortunately placed all of his academic work on minimization on Researchgate for study.
I wonder if we would still see such scientific atrocities as “non-comparative randomized trials” if knowledge of these methods was more acceptable to peer review. The late Douglas Altman discussed them in a BMJ article, and they were discussed in an old version of the CONSORT guidelines.
What I find interesting that does not seem to have been asked in the stats or OR literature: why can’t matched/minimized trials be designed so that there is actual error detection and channel redundancy (ie. 3 independent trials of 1/3 the N of an RCT), and then combined via confidence distribution meta-analysis methods, which would be especially valuable for examination of design assumptions, since individual patient data is available? We could substitute an assumption that groups are exchangeable (in expectation via randomization) with evidence that they are (partially) exchangeable in this particular case and discount the observed sample size accordingly. We might think of it as design with the physical act of cross-validation (instead of randomization).
Related Reference
Hirasawa, S (2006). An Application of Coding Theory into Experimental Design–Construction Methods for Unequal Orthogonal Arrays. (PDF)
Greenland, S. (2022). The causal foundations of applied probability and statistics. In Probabilistic and causal inference: The works of Judea Pearl (pp. 605-624) (PDF)
Greenland, S. (2023). Divergence versus decision P‐values: A distinction worth making in theory and keeping in practice: Or, how divergence P‐values measure evidence even when decision P‐values do not. Scandinavian Journal of Statistics, 50(1), 54-88. (link)
Xie, M., Singh, K., & Strawderman, W. E. (2011). Confidence distributions and a unifying framework for meta-analysis. Journal of the American Statistical Association, 106(493), 320-333. (PDF)
