Adjustment for baseline measurement error in randomized controlled trials induces bias

When estimating the treatment effect in a randomized controlled trial, it is common to have a continuous outcome which is also observed at baseline. These observations are often prone to measurement error, for example due to within-patient variability. Controversy exists in the literature about whether baseline measurement error should be adjusted for in this context. Computer simulations were used to compare the biases in the estimated treatment effect, with and without adjusting for measurement error, and for different levels of observed baseline imbalance. The impacts of sample size (30 per group and 300 per group) and reliability coefficient (0.6, 0.8 and 1) were also assessed. The results show that in randomized controlled trials, the ordinary least squares (OLS) estimator without adjusting for measurement error is unbiased. On the contrary, adjusting for measurement error leads to bias, especially when sample sizes are small and/or measurement error is large. The treatment effect adjusting for measurement error is on average overestimated when the baseline mean of the control group is larger than that of the treated group. It is underestimated when the control group has a smaller baseline mean.