Should you adjust for covariates when analyzing data from randomized controlled trials?

FDA draft guidance published this month says you should. In most cases, adjusting for covariates is not necessary. Randomization generally insurers that covariates are balanced across clinical trial arms. Randomization, however, may not always result in perfectly balanced trial arms. In these cases, the FDA notes that covariate adjustment is perfectly acceptable. There are some caveats however.

• Pre-specify covariates that matter. One concern would be “covariate hunting” whereby biased analysts could only adjust for covariates when it makes their results look better. To avoid this case, FDA wisely recommends that: “Sponsors should prospectively specify the covariates and the mathematical form of the covariate adjusted estimator in the statistical analysis plan before any unblinding of comparative data”. If a covariate is not likely to be a prognostic factor (i.e., a variable that impacts the outcome of interest), then one need not adjust for it even if there are differences across trial arms. Doing so is not problematic, but it may worse the precision of the estimator.
• Keep the number of covariates including in the adjustment reasonable. FDA’s guidance assumes that there will be a parsimonious number of covariates included in the adjustment. This doesn’t mean that including many covariates in the adjustment is not possible, but (i) a larger sample size would be needed and (ii) FDA likely will require sponsors to justify why this approach is needed.
• Use appropriate standard errors. For linear models (e.g., ordinary least squares regression, generalized linear models), FDA recommends using either Huber-White robust estimators (see (Rosenblum and van der Laan 2009) or bootstrap estimators (see Efron and Tibshirani 1993).
• Consider using interacting covariates with the treatment effect largely for exploratory analyses. This approach is reasonable if one believes that there are effect modifiers. In other words, it is possible that the treatment will work better for some patient groups than others. However, FDA is focused on the average treatment effect across the patient population of interest and generally considers interaction effects or subgroup analyses to be exploratory in nature.
• Be aware of complicating issues when using non-linear models. Using non-linear models is perfectly acceptable but they do bring with them some statistical challenges. For instance, for some parameters such as odds ratios, “even when all subgroup treatment effects are identical this subgroup-specific conditional treatment effect can differ from the unconditional treatment effect.” This issue is known as non-collapsibility. Nonlinear models are also less robust of the statistical model is mis-specified.

To address the last bullet, FDA provides a reliable approach for covariate adjustment with a binary outcome. Specifically, FDA recommends an approach known as a “standardized,” “plug-in,” or “g-computation” estimation. This approach contains the following steps:

• (1) Fit a logistic model with maximum likelihood that regresses the outcome on treatment assignments and prespecified baseline covariates. The model should include an intercept term.
• (2) For each subject, compute the model-based prediction of the probability of response under treatment in both the treatment group and control group using each subject’s specific baseline covariates.
• (3) Estimate the average response under treatment by averaging (across all subjects in the trial) the probabilities estimated in Step 2.
• (4) For each subject, compute the model-based prediction of the probability of response under control in both the treatment group and control group using each subject’s specific baseline covariates.
• (5) Estimate the average response under control by averaging (across all subjects in the trial) the probabilities estimated in Step 4.
• (6) The estimates of average responses rates in the two treatment groups from Steps 3 and 5 can be used to estimate an unconditional treatment effect, such as the risk difference, relative risk, or odds ratio

Source:

• Food and Drug Administration. Adjusting for Covariates in Randomized Clinical Trials for Drugs and Biological Products: Guidance for Industry (Draft Guidance). May 2021.

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