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

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').

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.

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.

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.