A Comparison of Covariate Adjustment Approaches Under Model Misspecification In Individually Randomized Trials

Adjustment for baseline covariates in randomized trials has been shown to lead to gains in power and can protect against chance imbalances in covariates. For continuous covariates, there is a risk that the the form of the relationship between the covariate and outcome is misspecified when taking an adjusted approach. Using a simulation study focusing on small to medium-sized individually randomized trials, we explore whether a range of adjustment methods are robust to misspecification, either in the covariate-outcome relationship or through an omitted covariate-treatment interaction. Specifically, we aim to identify potential settings where G-computation, Inverse Probability of Treatment Weighting ( IPTW ), Augmented Inverse Probability of Treatment Weighting ( AIPTW ) and Targeted Maximum Likelihood Estimation ( TMLE ) offer improvement over the commonly used Analysis of Covariance ( ANCOVA ). Our simulations show that all adjustment methods are generally robust to model misspecification if adjusting for a few covariates, sample size is 100 or larger, and there are no covariate-treatment interactions. When there is a non-linear interaction of treatment with a skewed covariate and sample size is small, all adjustment methods can suffer from bias; however, methods that allow for interactions (such as G-computation with interaction and IPTW ) show improved results compared to ANCOVA . When there are a high number of covariates to adjust for, ANCOVA retains good properties while other methods suffer from under- or over-coverage. An outstanding issue for G-computation, IPTW and AIPTW in small samples is that standard errors are underestimated; development of small sample corrections is needed.

Weighted cumulative sum tests for random effect models with binary responses

Correlated binary responses are very commonly encountered in many disciplines like, for example, medical studies. The development of goodness-of-fit tests is essential for examining the adequacy of the fitted models. The objective of this article is to provide weighted modifications of cumulative sums or moving cumulative sums of residuals for testing goodness-of-fit of random effects logistic regression models. The proposed weights can be interpreted as the residuals of a weighted linear regression of an omitted covariate on the covariates already included in the fixed part of the model. These processes lead to supremum statistics whose null distribution is derived using simulation. Results from a simulation study suggest better performance of the weighted when compared to the unweighted supremum statistics. The proposed tests are illustrated using a real data example.