# Robustness of ANCOVA in randomised trials with unequal randomisation

## TL;DR

This paper investigates the robustness of ANCOVA in randomized trials with unequal randomization, showing that the sandwich standard error is preferable over the model-based one when randomization probabilities differ from 1/2.

## Contribution

It extends previous results by analyzing ANCOVA's standard error properties under unequal randomization, recommending the sandwich estimator for valid inference.

## Key findings

- Model-based standard error is inconsistent with unequal randomization.
- Sandwich standard error provides valid inference under misspecification.
- Results guide best practices for analyzing randomized trials with unequal allocation.

## Abstract

Randomised trials with continuous outcomes are often analysed using ANCOVA, with adjustment for prognostic baseline covariates. In an article published recently, Wang \etal proved that in this setting the model based standard error estimator for the treamtent effect is consistent under outcome model misspecification, provided the probability of randomisation to each treatment is 1/2. In this article, we extend their results allowing for unequal randomisation. These demonstrate that the model based standard error is in general inconsistent when the randomisation probability differs from 1/2. In contrast, the sandwich standard error can provide asymptotically valid inferences under misspecification when randomisation probabilities are not equal, and is therefore recommended when randomisation is unequal.