A test for treatment effects in randomized controlled trials, harnessing the power of ultrahigh dimensional big data

Background: The randomized controlled trial (RCT) is the gold-standard research design in biomedicine. However, practical concerns often limit the sample size, n, the number of patients in a RCT. We aim to show that the power of a RCT can be increased by increasing p, the number of baseline covariates (sex, age, socio-demographic, genomic, and clinical profiles et al, of the patients) collected in the RCT (referred to as the 'dimension'). Methods: The conventional test for treatment effects is based on testing the 'crude null' that the outcomes of the subjects are of no difference between the two arms of a RCT. We propose a 'high-dimensional test' which is based on testing the 'sharp null' that the experimental intervention has no treatment effect whatsoever, for patients of any covariate profile. Results: Using computer simulations, we show that the high-dimensional test can become very powerful in detecting treatment effects for very large p, but not so for small or moderate p. Using a real dataset, we demonstrate that the P value of the high-dimensional test decreases as the number of baseline covariates increases, though it is still not significant. Conclusion: In this big-data era, pushing p of a RCT to the millions, billions, or even trillions may someday become feasible. And the high-dimensional test proposed in this study can become very powerful in detecting treatment effects.