Adjusting for Many Covariates in Randomized Clinical Trials with GLMs: Bias Reduction by Jackknife and Practical Guidance

Abstract

Adjusting for baseline covariates has become standard practice in analyzing randomized clinical trials. In the low-dimensional setting, it is well understood that covariate adjustment through a parametric working model can sometimes be more efficient than the unadjusted difference-in-mean estimator. However, when the number of adjusted covariates is large relative to the sample size $n$, a na\"{i}ve adjustment may introduce excessive bias, leading to invalid statistical inference. The current literature that tries to resolve this issue is either limited to linear working models or relies on sample splitting, which may raise concerns about the replicability of RCT analyses. In this paper, we devise a novel jackknife-based approach to covariate adjustment through generalized linear models (GLMs), which we term as JAckknife Score-based Adjustment (JASA), together with its calibrated version JASACal. By employing a nuanced jackknife strategy, JASA and JASACal avoid sample splitting and make full use of the data, while ensuring that the bias of JASA or JASACal is still negligible even when the number of adjusted covariates is large compared to $n$. JASA also encompasses state-of-the-art adjusted estimators through linear working models as a special case. Through extensive simulation experiments and a real data analysis, we demonstrate that JASA or JASACal can adjust for a much greater number of covariates than existing benchmarks. These empirical results also shed some new light on practical guidance for covariate adjustment with GLMs. Both JASA and JASACal have been incorporated into our R package HOIFCar available from CRAN. The package HOIFCar is developed to serve as a user-friendly option for covariate adjustment in RCTs, in particular when practitioners hope to adjust for a large number of covariates.