Adjusting for 
Covariates in 
Randomized Clinical 
Trials for Drugs and 
Biological Products 
Guidance for Industry 
 
 
 
 
 
 
 
 
 
 
 
 
 
U.S. Department of Health and Human Services 
Food and Drug Administration 
Center for Drug Evaluation and Research (CDER) 
Center for Biologics Evaluation and Research (CBER) 
Oncology Center of Excellence (OCE) 
 
 
May 2023 
Biostatistics 
 
    
Adjusting for 
Covariates in 
Randomized Clinical 
Trials for Drugs and 
Biological Products 
Guidance for Industry 
 
Additional copies are available from: 
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Center for Drug Evaluation and Research 
Food and Drug Administration 
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and/or 
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 Food and Drug Administration 
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Email: ocod@fda.hhs.gov 
https://www.fda.gov/vaccines-blood-biologics/guidance-compliance-regulatory-information-biologics/biologics-guidances   
 
U.S. Department of Health and Human Services 
Food and Drug Administration 
Center for Drug Evaluation and Research (CDER) 
Center for Biologics Evaluation and Research (CBER) 
Oncology Center of Excellence (OCE) 
May 2023 
Biostatistics 
  Contains Nonbinding Recommendations 
 
TABLE OF CONTENTS 
 
 
 
I.  INTRODUCTION............................................................................................................. 1 
II.  BACKGROUND ............................................................................................................... 2 
III.  RECOMMENDATIONS FOR COVARIATE ADJUSTMENT IN CLINICAL 
TRIALS .............................................................................................................................. 3 
A.  General Considerations ................................................................................................................. 3 
B.  Linear Models ................................................................................................................................ 4 
C.  Nonlinear Models ........................................................................................................................... 5 
IV.   REFERENCES .................................................................................................................. 8 
i  Contains Nonbinding Recommendations 
 
Adjusting for Covariates in Randomized Clinical Trials for Drugs 
and Biological Products 
Guidance for Industry1 
 
 
This guidance represents the current thinking of the Food and Drug Administration (FDA or Agency) on 
this topic. It does not establish any rights for any person and is not binding on FDA or the public. You can 
use an alternative approach if it satisfies the requirements of the applicable statutes and regulations. To 
discuss an alternative approach, contact the FDA office responsible for this guidance as listed on the title 
page.  
 
 
 
 
I.  INTRODUCTION  
 
This guidance describes FDAs current recommendations regarding adjusting for covariates in 
the statistical analysis of randomized clinical trials in drug2 development programs. This 
guidance provides recommendations for the use of covariates in the analysis of randomized, 
parallel group clinical trials that are applicable to both superiority trials and noninferiority trials. 
The main focus of the guidance is on the use of prognostic baseline covariates3 to improve 
statistical efficiency for estimating and testing treatment effects. This guidance does not address 
use of covariates to control for confounding variables in non-randomized trials, the use of 
covariates in models to account for missing outcome data (National Research Council 2010), the 
use of covariate adjustment for analyzing longitudinal repeated measures data, the use of 
Bayesian methods for covariate adjustment, or the use of machine learning methods for covariate 
adjustment.  
 
In general, FDAs guidance documents do not establish legally enforceable responsibilities. 
Instead, guidances describe the Agencys current thinking on a topic and should be viewed only 
as recommendations, unless specific regulatory or statutory requirements are cited. The use of 
the word should in Agency guidances means that something is suggested or recommended, but 
not required.  
 
 
 
1 This guidance has been prepared by the Office of Biostatistics in the Center for Drug Evaluation and Research in 
cooperation with the Center for Biologics Evaluation and Research at the Food and Drug Administration. 
 
2 The term drug used in this guidance refers to both human drugs and biological products. 
 
3 The term prognostic baseline covariates used in this guidance refers to baseline covariates that are likely to be 
associated with the primary endpoint. Use of predictive baseline covariates to identify groups more likely to benefit 
from treatment is beyond the scope of this guidance. 
 
  1  Contains Nonbinding Recommendations 
 
II.  BACKGROUND 
 
Baseline covariates in this guidance refer to demographic factors, disease characteristics, or other 
information collected from participants before the time of randomization. Covariate adjustment 
refers to the use of baseline covariate measurements for estimating and testing population-level 
treatment effects between randomized groups.  
 
In many randomized controlled trials, the primary analysis used to estimate treatment effects of a 
new drug might not adjust for baseline covariates (through what is termed an unadjusted 
analysis). However, incorporating prognostic baseline covariates in the design and analysis of 
clinical trial data can result in a more efficient use of data to demonstrate and quantify the effects 
of treatment. Moreover, this can be done with minimal impact on bias or the Type I error rate.  
 
The ICH guidance for industry E9 Statistical Principles for Clinical Trials (September 1998)4 
addresses these issues briefly. The ICH E9 guidance encourages the identification of covariates 
and factors expected to have an important influence on the primary variable(s). The ICH E9 
guidance strongly advises prespecification of the principal features of the eventual statistical 
analysis, including how to account for [covariates] in the analysis to improve precision and to 
compensate for any lack of balance between treatment groups. The ICH E9 guidance also 
cautions against adjusting for covariates measured after randomization because they could be 
affected by the treatments.  
 
This guidance is consistent with the ICH guidance for industry E9(R1) Statistical Principles for 
Clinical Trials: Addendum: Estimands and Sensitivity Analysis in Clinical Trials. After 
specifying the treatment condition of interest, target population, and endpoint variable  the 
treatment effect estimated by covariate adjustment is a population summary measure defining an 
estimand.  
 
This guidance provides general considerations and additional recommendations for covariate 
adjustment using linear and nonlinear models.5 In linear models, adjustment for prognostic 
baseline covariates often leads to improved precision by reducing residual variance. When 
adjusting for covariates based on fitting nonlinear regression models, such as logistic regression 
models in studies with binary outcomes, there are additional considerations that arise because 
inclusion of baseline covariates in a regression model can change the treatment effect that is 
being estimated. As explained below, after suitably addressing the treatment effect definition, 
covariate adjustment using linear or nonlinear models can be used to improve statistical 
efficiency.  
 
 
 
 
 
4 We update guidances periodically. To make sure you have the most recent version of a guidance, check the FDA 
guidance web page at https://www.fda.gov/regulatory-information/search-fda-guidance-documents. 
5 For this guidance, nonlinear models can include generalized linear models with nonlinear link functions. 
  2  Contains Nonbinding Recommendations 
 
III.  RECOMMENDATIONS FOR COVARIATE ADJUSTMENT IN CLINICAL 
TRIALS   
 
A.  General Considerations 
 
  An unadjusted analysis is acceptable for the primary analysis of an efficacy endpoint. 
 
  Sponsors can adjust for baseline covariates in the analyses of efficacy endpoints in 
randomized clinical trials. Doing so will generally reduce the variability of estimation of 
treatment effects and thus lead to narrower confidence intervals and more powerful 
hypothesis testing. 
 
  Sponsors should prospectively specify the detailed procedures for executing covariate-
adjusted analysis before any unblinding of comparative data. FDA review will emphasize the 
prespecified primary analysis rather than post-hoc analyses using different models or 
covariates.  
 
  Covariate adjustment leads to efficiency gains when the covariates are prognostic for the 
outcome of interest in the trial. Therefore, FDA recommends that sponsors adjust for 
covariates that are anticipated to be most strongly associated with the outcome of interest. In 
some circumstances these covariates may be known from the scientific literature. In other 
cases, it may be useful to use previous studies (e.g., a Phase 2 trial) to select prognostic 
covariates or form prognostic indices.  
 
  Covariate adjustment can still be performed with covariates that are not prognostic, but there 
may not be any gain in precision (or may be a loss in precision) compared with an unadjusted 
analysis. 
 
  Covariate adjustment is acceptable even if baseline covariates are strongly associated with 
each other (e.g., body weight and body mass index). However, adjusting for less correlated 
baseline covariates generally provides greater efficiency gains. 
 
  Randomization is often stratified by baseline covariates. A covariate adjustment model 
should generally include strata variables and can also include covariates not used for 
stratifying randomization. In some cases, incorrect stratification may occur and result in 
actual and as-randomized baseline strata variables. A covariate adjustment model can use 
either strata variable definition as long as this is prespecified.  
 
  Sponsors can conduct randomization/permutation tests with covariate adjustment 
(Rosenbaum 2002). 
 
  In a trial that uses covariate adjustment, the sample size and power calculations can be based 
on adjusted or unadjusted methods. The latter will often lead to a more conservative sample 
size. 
 
  3  Contains Nonbinding Recommendations 
 
  Clinical trials often record a baseline measurement of a defined characteristic and record a 
later measurement of the characteristic to be used as an outcome. Adjusting for the baseline 
value rather than (or in addition to) defining the primary endpoint as a change from baseline 
is generally acceptable. Sponsors proposing to define the outcome as a percentage change 
rather than an absolute change from baseline should discuss the outcome definition and use 
of covariate adjustment with the relevant review division. Sponsors proposing to perform 
noninferiority testing on ratios of treatment group means rather than differences of treatment 
group means should also discuss change from baseline outcome definitions and use of 
covariate adjustment with the relevant review division. 
 
  Sponsors should discuss proposals for complex covariate-adaptive randomization, data-
adaptive covariate selection, or use of covariate adjustment in an adaptive design with the 
relevant review division.  
 
  The statistical properties of covariate adjustment are best understood when the number of 
covariates adjusted for in the study is small relative to the sample size (Tsiatis et al. 2008). 
Therefore, sponsors should discuss their proposal with the relevant review division if the 
number of covariates is large relative to the sample size or if proposing to adjust for a 
covariate with many levels (e.g., study site in a trial with many sites). 
 
B.  Linear Models 
 
  Covariate adjustment through a linear model is an acceptable method for estimating the 
average treatment effect, which is the difference in expected outcomes between subjects 
assigned to treatment and control groups. Generally, the outcome is regressed on an intercept, 
treatment assignment indicator, and baseline covariates, and the model is estimated using 
ordinary least squares. The resulting estimated regression coefficient for the treatment 
indicator is the estimate of the average treatment effect. 
 
  The average treatment effect is an example of an unconditional treatment effect, which 
quantifies the effect at the population level of moving a target population from untreated to 
treated. 
 
  Even when the linear regression model is misspecified and does not accurately capture the 
relationships between the outcome, covariates, and treatment, covariate adjustment through a 
linear model is a valid method for estimating and performing inference for the average 
treatment effect (Lin, 2013). However, the power of hypothesis tests and precision of 
estimates generally improves if the model more closely approximates the true relationships 
among the outcome, covariates, and treatment. 
  
  Nominal standard errors are often the default method in most statistical software packages. 
Even if the model is incorrectly specified, they are acceptable in two arm trials with 1:1 
randomization. However, in other settings, these standard errors can be inaccurate when the 
model is misspecified. Therefore, the Agency recommends that sponsors consider use of a 
robust standard error method such as the Huber-White sandwich standard error when the 
model does not include treatment by covariate interactions (Rosenblum and van der Laan 
  4  Contains Nonbinding Recommendations 
 
2009; Lin 2013). Other robust standard error methods proposed in the literature can also 
cover cases with interactions (Ye et al. 2022). An appropriate nonparametric bootstrap 
procedure can also be used (Efron and Tibshirani 1993). 
 
  An analysis ignoring stratified randomization is likely to overestimate standard errors and 
can be unduly conservative when performing inference for the average treatment effect. The 
Agency recommends that the standard error computation account for stratified 
randomization. There are several methods for computing standard errors when combining 
stratification with covariate adjustment and possible model misspecification (Bugni et al. 
2018; Ye et al. 2021). The statistical properties of such methods are best understood when 
the number of strata is small relative to the sample size. Sponsors can propose methods to 
account for stratified randomization in computing standard errors, confidence intervals, and 
hypothesis testing. 
 
  The linear model may include treatment by covariate interaction terms. However, when using 
this approach, the primary analysis can still be based on an estimate from the model of the 
average treatment effect (Tsiatis et al. 2008; Ye et al. 2021). As noted in the ICH E9 
guidance, interaction effects may be important to assess in supportive analysis or exploratory 
analysis. This is because differences in treatment effects across subgroups defined by 
baseline covariates could be relevant to prescribers, patients, and other stakeholders and can 
imply that the average treatment effect gives an incomplete summary of efficacy.  
 
C.  Nonlinear Models 
 
  Covariate adjustment with nonlinear models is often used in the analysis of clinical trial data 
when the primary outcome of interest is not measured on a continuous scale or is right 
censored (e.g., binary outcome, ordinal outcome, count outcome, or time-to-event outcome). 
Adjustment using nonlinear models is a potentially acceptable method for analyzing these 
data from a clinical trial. However, there are additional issues described below that should be 
considered before using nonlinear models. 
 
  In general, treatment effects may differ across subgroups. However, with 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 (i.e., 
the effect at the population level from moving the target population from untreated to treated) 
(Gail et al. 1984). This is termed non-collapsibility (Agresti 2002), which is distinct from 
confounding and can occur despite randomization and large sample sizes. An example of 
non-collapsibility of the odds ratio for a hypothetical clinical trial is illustrated in Table 1 
below. The unconditional odds ratio in the hypothetical target population is 4.8, which is 
lower than the conditional odds ratio of 8.0 in each of the biomarker-positive and biomarker-
negative subgroups. In trials with time-to-event outcomes, the hazard ratio can also be non-
collapsible. Unlike the odds ratio or hazard ratio, the risk difference and relative risk are 
collapsible.  
 
 
 
  5  Contains Nonbinding Recommendations 
 
Table 1: Non-collapsibility of the Odds Ratio in a Hypothetical Target Population  
Percentage of  Success rate 
  target  Odds ratio 
New drug  Placebo 
population 
Biomarker-
50%  80.0%  33.3%  8.0 
positive 
Biomarker-
50%  25.0%  4.0%  8.0 
negative 
Combined  100%  52.5%  18.7%  4.8 
 
  As part of the prespecification of the estimand of interest, sponsors should specify whether 
the treatment effect of interest in an analysis is a conditional or unconditional treatment 
effect.  
 
  Cochran-Mantel-Haenszel methods (Mantel and Haenszel 1959) are acceptable for the 
analysis of clinical trial data with binary endpoints if there is interest in estimating a 
conditional treatment effect, which is assumed to be constant across subgroups defined by a 
covariate taking a discrete number of levels (e.g., the value 8.0 in Table 1).  
 
  Fitting a nonlinear regression of the outcome on treatment and baseline covariates similarly 
attempts to estimate a conditional treatment effect. Nonlinear models extend Cochran-
Mantel-Haenszel methods by allowing adjustment for continuous covariates, such as age. In 
nonlinear regression models (without treatment by covariate interactions), the treatment 
effect is assumed to be approximately constant across subgroups defined by baseline 
covariates in the model and can provide more individualized information than the 
unconditional treatment effect if the assumption holds (and not otherwise). Nonlinear models 
such as logistic regression or proportional hazards regression (which can include 
stratification of the baseline hazard) are commonly used in many clinical settings.  
 
  Sponsors should discuss with the relevant review divisions specific proposals in a protocol or 
statistical analysis plan containing nonlinear regression to estimate conditional treatment 
effects for the primary analysis. When estimating a conditional treatment effect through 
nonlinear regression, the model assumptions will generally not be exactly correct, and results 
can be difficult to interpret if the model is misspecified and treatment effects substantially 
differ across subgroups. Interpretability increases with the quality of model specification. 
Sponsors should discuss any planned assessments of model assumptions and implications for 
analyses with the relevant review division. 
 
  Sponsors can perform covariate-adjusted estimation and inference for an unconditional 
treatment effect (e.g., the odds ratio of 4.8 in Table 1) in the primary analysis of data from a 
randomized trial. The method used should provide valid inference under approximately the 
same minimal statistical assumptions that would be needed for unadjusted estimation in a 
randomized trial. With nonlinear models using a covariate-adjusted estimator for an 
unconditional treatment effect, sponsors can use an appropriate bootstrap method or standard 
error formulas justified in the statistical literature for confidence interval construction. A 
  6  Contains Nonbinding Recommendations 
 
variety of statistically reliable methods have been proposed in the literature for covariate 
adjustment with unconditional treatment effects (Colantuoni and Rosenblum 2015). 
 
  Covariate-adjusted estimators of unconditional treatment effects that are robust to 
misspecification of regression models have been proposed for randomized clinical trials with 
binary outcomes (e.g., Steingrimsson et al. 2017), ordinal outcomes (e.g., Diaz et al. 2016), 
count outcomes (e.g., Rosenblum and van der Laan 2010), and time-to-event outcomes (e.g., 
Tangen and Koch 1999; Lu and Tsiatis 2008). If a novel method is proposed and statistical 
properties are unclear, the specific proposal should be discussed with the review division.  
 
  As an example, the following are steps for one reliable method for covariate adjustment for 
unconditional treatment effects with binary outcomes that produces a resulting estimator 
(Steingrimsson et al. 2017; Freedman 2008) termed the standardized, plug-in, or g-
computation estimator: 
 
(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, regardless of treatment group assignment, compute the model-based 
prediction of the probability of response under treatment using the subjects 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, regardless of treatment group assignment, compute the model-based 
prediction of the probability of response under control using the subjects 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. 
 
  Inverse probability of treatment weighting is another reliable method of covariate adjustment 
for unconditional treatment effects in randomized trials (Williamson et al. 2013). 
 
  An analysis ignoring stratified randomization is likely to overestimate standard errors and 
can be unduly conservative when performing inferences for an unconditional treatment 
effect. The Agency recommends that the standard error computation account for stratified 
randomization. There are several methods for computing standard errors when combining 
stratification with covariate adjustment and possible model misspecification (e.g., Wang et 
al. 2021). The statistical properties of such methods are best understood when the number of 
  7  Contains Nonbinding Recommendations 
 
strata is small relative to the sample size. Sponsors can propose methods to account for 
stratified randomization in computing standard errors, confidence intervals, and hypothesis 
testing.  
 
 
IV.   REFERENCES 
 
Agresti, A, 2002, Categorical Data Analysis, Second Edition, New York (NY): John Wiley & 
Sons, Inc. 
 
Bugni, F, IA Canay, and AM Shaikh, 2018, Inference Under Covariate-Adaptive Randomization, 
Journal of the American Statistical Association, 113(524):1784-1796. 
 
Colantuoni, E and M Rosenblum, 2015, Leveraging Prognostic Baseline Variables to Gain 
Precision in Randomized Trials, Statistics in Medicine, 34(18): 26022617.. 
 
Diaz, I, E Colantuoni, and M Rosenblum, 2016, Enhanced Precision in the Analysis of 
Randomized Trials with Ordinal Outcomes, Biometrics, 72(2):422-431. 
 
Efron, B and RJ Tibshirani, 1993, An Introduction to the Bootstrap, Boca Raton (FL): Chapman 
& Hall. 
 
Freedman DA, 2008, Randomization Does Not Justify Logistic Regression, Statistical Science, 
23(2):237-249. 
 
Gail, MH, S Wieand, and S Piantadosi, 1984, Biased Estimates of Treatment Effect in 
Randomized Experiments with Nonlinear Regressions and Omitted Covariates, Biometrika, 
71(3):431-444. 
 
Lin W, 2013, Agnostic Notes on Regression Adjustments to Experimental Data: Reexamining 
Freedmans Critique, Annals of Applied Statistics, 7(1):295-318. 
 
Lu, X and AA Tsiatis, 2008, Improving the Efficiency of the Log-Rank Test Using Auxiliary 
Covariates, Biometrika, 95(3):679-694. 
 
Mantel, N and W Haenszel, 1959, Statistical Aspects of the Analysis of Data from Retrospective 
Studies of Disease, Journal of the National Cancer Institute, 22(4):719-748. 
 
National Research Council, 2010, The Prevention and Treatment of Missing Data in 
Clinical Trials, Washington (DC): The National Academies Press. 
 
Rosenbaum PR, 2002, Covariance Adjustment in Randomized Experiments and Observational 
Studies. Statistical Science, 17(3):286-327.  
 
  8  Contains Nonbinding Recommendations 
 
Rosenblum, M and MJ van der Laan, 2009, Using Regression Models to Analyze Randomized 
Trials: Asymptotically Valid Hypothesis Tests Despite Incorrectly Specified Models, Biometrics, 
65(3):937-945. 
 
Rosenblum, M and MJ van der Laan, 2010, Simple, Efficient Estimators of Treatment Effects in 
Randomized Trials Using Generalized Linear Models to Leverage Baseline Variables, 
International Journal of Biostatisitcs, 6(1):13. 
 
Steingrimsson, JA, DF Hanley, and M Rosenblum, 2017, Improving precision by adjusting for 
prognostic baseline variables in randomized trials with binary outcomes, without regression 
model assumptions, Contemporary Clinical Trials, 54:18-24. 
 
Tangen, CM and GG Koch, 1999, Nonparametric Analysis of Covariance for Hypothesis Testing 
with Logrank and Wilcoxon Scores and Survival-Rate Estimation in a Randomized Clinical 
Trial, Journal of Biopharmaceutical Statistics, 9(2):307-338. 
 
Tsiatis, AA, M Davidian, M Zhang, and X Lu, 2008, Covariate Adjustment for Two-Sample 
Treatment Comparisons in Randomized Trials: A Principled Yet Flexible Approach, Statistics in 
Medicine, 27(23):4658-4677. 
 
Wang, B, R Susukida, R Mojtabai, M Amin-Esmaeili, and M Rosemblum, 2021. Model-Robust 
Inference for Clinical Trials that Improve Precision by Stratified Randomization and Covariate 
Adjustment, Journal of the American Statistical Association, doi: 
10.1080/01621459.2021.1981338.  
 
Williamson, EJ, A Forbes, and IR White, 2013, Variance Reduction in Randomised Trials by 
Inverse Probability of Treatment Weighting Using the Propensity Score, Statistics in Medicine, 
33(5):721-737.  
 
Ye, T, Y Yi, and J Shao, 2021, Inference on The Average Treatment Effect Under Minimization 
and Other Covariate-Adaptive Randomization Methods, Biometrika, 109(1)33-47. 
 
Ye, T, J Shao, Y Yi, and Q Zhao, 2022, Toward better practice Of Covariate Adjustment In 
Analyzing Randomized Clinical Trials, Journal of the American Statistical Association, doi: 
10.1080/01621459.2022.2049278. 
  9