Incorporating baseline covariates in the analysis of an individually randomized trial or CRT can improve the precision of treatment effect estimates and enhance the statistical power of the trial (Morris et al 2022; Hemming et al 2025; US Food and Drug Administration 2023). The magnitude of improvement in precision and power is driven by the degree to which the selected baseline covariates are prognostic for the outcome. Adjustment for baseline covariates that are not prognostic for the outcome can result in a loss of precision and power, though this loss is often negligible in adjustments for a small number of nonprognostic covariates (Hemming et al 2025; Colantuoni and Rosenblum 2015).

For trials that use stratified randomization based on baseline covariates, the research team should account for the stratification variables in the estimation of the treatment effect to realize the gains in precision (Colantuoni and Rosenblum 2015). Moreover, in CRTs that consent and enroll participants to the clusters after treatment assignment, adjustment for covariates that contribute to differential selection of participants can help mitigate potential bias in treatment effect estimates (Hemming et al 2025; Li et al 2022). Therefore, the decision to use an adjusted analysis should be driven by the specific context of the trial, including the feasibility of collecting baseline covariates, scientific knowledge about the correlation between the baseline covariates and the trial outcomes, the use of a stratified randomization strategy, and the possibility of selection bias in identification of trial participants.

Upon deciding to use baseline covariate adjustment, trialists must decide which covariates to include and how to perform the adjustment, such as what specific statistical analysis approach will be used. The answers to these questions should align with the definition of the treatment effect of interest—that is, the “estimand” (Kahan et al 2023). In CRTs, the target for estimation may be the participant-average treatment effect or the cluster-average treatment effect, since 2 different populations (participants and clusters) are important to recognize in CRTs.

Selection of Baseline Covariates

It is generally recommended to include a limited number of prespecified baseline covariates. The covariates can include those believed to be prognostic for the outcome, those related to participant selection (if applicable), or those related to outcome missingness (if applicable).

As mentioned above, adjustment for covariates that are not related to the outcome can reduce the precision of the estimated treatment effect. Moreover, when estimating a cluster-average treatment effect, the number of clusters should be considered when selecting the cluster-level covariates for adjustment, since the number of such covariates should be much less than the number of clusters. When estimating the participant-average treatment effect, covariates may be measured at the participant level or the cluster level, and cluster-level summaries of participant-level variables (such as average age) may be included. When estimating the cluster-average treatment effect, covariates may be measured at the cluster level or represent a cluster summary of participant-level covariates.

Selection of Analytic Approach

The most common estimand in CRTs is the participant-average treatment effect, which can be estimated using direct adjustment or marginal standardization (the g-computation). The most recognized direct adjustment approach in individually randomized trials is the analysis of covariance (ANCOVA) procedure, in which a linear regression model is fit with main terms for treatment arm and baseline covariates. In a linear model, the estimated coefficient for the main term for treatment arm is the estimated participant-average treatment effect, provided that any interactions with treatment use mean-centered variables (Colantuoni and Rosenblum 2015; Yang and Tsiatis 2001).

The generalized linear mixed model (GLMM) and the GEE are natural extensions of the ANCOVA approach to CRTs that incorporate the correlation between outcomes from participants in the same cluster. (See the Intraclass Correlation section of this chapter.) Care must be taken with direct adjustment for a treatment effect represented as an odds ratio or any other noncollapsible treatment effect definition. For example, the coefficient for the treatment arm in a covariate-adjusted GEE logistic model represents a covariate-dependent treatment effect. However, marginal standardization is a natural approach to generating meaningful summaries, even for nonlinear models like logistic regression.

Marginal standardization requires specification of an outcome regression model, typically a GEE with main terms for treatment arm and baseline covariates. Using the fit of the model, the predicted outcomes under both treatment arms are obtained for all participants, then the appropriate summary of these treatment arm–predicted outcomes are calculated (for example, mean difference or risk difference). Recent developments in weighted g-computation and efficient influence functions, including targeted maximum likelihood estimation, have allowed for extensions of the marginal standardization approach with improved robustness properties (for example, unbiased treatment effects even when the outcome regression model is misspecified, such as missing key interactions or not correctly modeling the functional form for continuous covariates) and asymptotic guarantees that the variance of the adjusted estimator will be less than or equal to that of an unadjusted estimator (Wang 2024; Benitez et al 2023). Researchers are exploring the behavior of these extensions of the marginal standardization approach when the parametric outcome regression model is replaced with flexible machine learning models (Wang 2024; Benitez et al 2023).

There are also several approaches for estimating the cluster-average treatment effect. The simplest is to apply the ANCOVA approach to the cluster-average outcome with adjustment for cluster-level baseline covariates, which may include cluster-average summaries of participant-level covariates. Both the direct adjustment and the marginal standardization approaches can be modified to allow for estimation of the cluster-average outcome. For example, to obtain the cluster-average treatment effect in the marginal standardization approach, the predicted outcomes are first summarized within each cluster and then the cluster-average is obtained.

Summary

Incorporating prognostic baseline covariates and stratification variables into treatment effect estimation can improve precision and power. A limited number of prespecified baseline variables should be included in the analysis. The analysis approach should be consistent with the treatment effect definition (that is, whether the target is the participant-average treatment effect or the cluster-average treatment effect).

Not included is this discussion is the impact of informative cluster sizes on estimating treatment effects in CRTs. Regardless of whether baseline covariates are included, the statistical analysis approaches described in this section could produce biased estimates of treatment effects if the cluster size is informative. See Li et al (2022), Kahan et al (2023), Wang et al (2024), and Kahan et al (2023) for discussions of appropriate adjustments to the models.