Using discrepancy theory to improve the design of randomized controlled trials

In randomized experiments, such as a medical trials, we randomly assign the treatment, such as a drug or a placebo, that each experimental subject receives. Randomization can help us accurately estimate the difference in treatment effects with high probability. We also know that we want the two groups to be similar: ideally the two groups would be similar in every statistic we can measure beforehand. Recent advances in algorithmic discrepancy theory allow us to divide subjects into groups with similar statistics. By exploiting the Gram-Schmidt Walk algorithm of Bansal, Dadush, Garg, and Lovett, we can obtain random assignments of low discrepancy. These allow us to obtain more accurate estimates of treatment effects when the information we measure about the subjects is predictive, while also bounding the worst-case behavior when it is not. In this talk, I will formally explain the problem of estimating treatment effects in randomized controlled trials, the dangers of using fancy inference techniques instead of fancy designs, how we use the Gram-Schmidt Walk algorithm, a tight analysis of this algorithm, and how we use it to obtain confidence intervals. I hope to explain just how much we don't yet know. This is joint work with Christopher Harshaw, Fredrik Sävje, and Peng Zhang.