This is a post hoc exploratory analysis of the COVID STEROID 2 trial7. It was conducted according to a statistical analysis plan, which was written after the pre-planned analyses of the trial were reported, but before any of the analyses reported in this manuscript were conducted (https://osf.io/2mdqn/). This manuscript was presented according to the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) checklist12, with Bayesian analyses reported according to the Reporting of Bayes Used in clinical STudies (ROBUST) guideline13.

HTE implies that some individuals respond differently, i.e., better or worse, than others who receive the same therapy due to differences between individuals. Most trials are designed to evaluate the average treatment effect, which is the summary of all individual effects in the trial sample (see supplementary appendix for additional technical details). Traditional HTE methods examine patient characteristics one at a time, looking to identify treatment effect differences according to individual variables. This approach is well known to be limited as it is underpowered (due to adjustment for multiple testing) and does not account for the fact that many characteristics under examination are correlated and may have synergistic effects. As a result, more complex relationships between variables that better define individuals, and thus may better inform understanding about the variations in treatment response, may be missed using conventional HTE approaches. Thus, identifying true and clinically meaningful HTE requires addressing these data and statistical modeling challenges. BART is inherently an attractive method for this task, as the algorithm automates the detection of nonlinear relationships and interactions hierarchically based on the strength of the relationships, thereby reducing researchers discretion when analyzing experimental data. This approach also avoids any model misspecification or bias inherent in traditional interaction test procedures. BART can also be deployed, as we do herein, within the counterfactual framework to study HTE, i.e., to estimate conditional average treatment effects given the set of covariates or potential effect modifiers11,14,15, and has shown superior performance to competing methods in extensive simulation studies16,17. These features make BART an appealing tool for trialists to explore HTE to inform future confirmatory HTE analyses in trials and hypothesis generation more broadly. Thus, this analysis used BART to evaluate the presence of multivariable HTE and estimate conditional average treatment effects among meaningful subgroups in the COVID STEROID 2 trial.

The COVID STEROID 2 trial7 was an investigator-initiated, international, parallel-group, stratified, blinded, randomized clinical trial conducted at 31 sites in 26 hospitals in Denmark, India, Sweden, and Switzerland between 27 August 2020 and 20 May 20217,18. The trial was approved by the regulatory authorities and ethics committees in all participating countries.

The trial enrolled 1000 adult patients hospitalized with COVID-19 and severe hypoxemia (10 L oxygen/min, use of non-invasive ventilation (NIV), continuous use of continuous positive airway pressure (cCPAP), or invasive mechanical ventilation (IMV)). Patients were primarily excluded due to previous use of systemic corticosteroids for COVID-19 for 5 or more days, unobtainable consent, and use of higher-dose corticosteroids for other indications than COVID-194,17. Patients were randomized 1:1 to dexamethasone 12mg/d or 6mg/d intravenously once daily for up to 10days. Additional details are provided in the primary protocol and trial report7,18.

The trial protocol was approved by the Danish Medicines Agency, the ethics committee of the Capital Region of Denmark, and institutionally at each trial site. The trial was overseen by the Collaboration for Research in Intensive Care and the George Institute for Global Health. A data and safety monitoring committee oversaw the safety of the trial participants and conducted 1 planned interim analysis. Informed consent was obtained from the patients or their legal surrogates according to national regulations.

We examined two outcomes: (1) DAWOLS at day 90 (i.e., the observed number of days without the use of IMV, circulatory support, and kidney replacement therapy without assigning dead patients the worst possible value), and (2) 90-day mortality. Binary mortality outcomes were used to match the primary trial analysis; time-to-event outcomes also generally tend to be less robust for ICU trials19. We selected DAWOLS at day 90 in lieu of the primary outcome of the trial (DAWOLS at day 28) and to align with other analyses of the trial which sought to examine outcomes in a longer term. Both outcomes were assessed in the complete intention-to-treat (ITT) population, which was 982 after the exclusion of patients without consent for the use of their data7. As the sample size is fixed, there was no formal sample size calculation for this study.

While BART is a data-driven approach that can scan for interdependent relationships among any number of factors, we only examined heterogeneity across a pre-selected set of factors deemed to be clinically relevant by the authors and members of the COVID STEROID 2 trial Management Committee. The pre-selected variables that were included in this analysis are listed below with the scale used in parentheses. Continuous covariates were standardized to have a mean of 0 and a standard deviation of 1 prior to analysis. Detailed variable definitions are available in the study protocol18.

participant age (continuous),

limitations in care (yes, no),

level of respiratory support (open system versus NIV/cCPAP versus IMV)

interleukin-6 (IL-6) receptor inhibitors (yes, no),

use of dexamethasone for up to 2days versus use for 3 to 4days prior to randomization,

participant weight (continuous),

diabetes mellitus (yes, no),

ischemic heart disease or heart failure (yes, no),

chronic obstructive pulmonary disease (yes, no), and,

immunosuppression within 3months prior to randomization (yes, no).

We evaluated HTE on the absolute scale (i.e., mean difference in days for the number of DAWOLS at day 90 and the risk difference for 90-day mortality). The analysis was separated into two stages14,20,21,22. In the first stage, conditional average treatment effects were estimated according to each participants covariates using BART models. The DAWOLS outcome was treated as a continuous variable and analyzed using standard BART, while the binary mortality outcome was analyzed using logit BART. In the second stage, a fit-the-fit approach was used, where the estimated conditional average treatment effects were used as dependent variables in models to identify covariate-defined subgroups differential treatment effects. This second stage used classification and regression trees models23, where the maximum depth was set to 3 as a post hoc decision to aid interpretability. As the fit-the-fit reflects estimates from the BART model, the resulting overall treatment effects (e.g., risk difference) vary slightly from the raw trial data.

BART models are often fit using a sum of 200 trees and specifying a base prior of 0.95 and a power prior of 2, which penalize substantial branch growth within each tree15. Although these default hyperparameters tend to work well in practice, it was possible they were not optimal for this data. Thus, the hyperparameters were evaluated using tenfold cross-validation, comparing predictive performance of the model under 27 pre-specified possibilities, namely every combination of power priors equal to 1, 2, or 3, base priors equal to 0.25, 0.5, or 0.95, and number of trees equal to 50, 200, or 400. The priors corresponding to the lowest cross-validation error were used in the final models. Each model used a Markov chain Monte Carlo procedure consisting of 4 chains that each had 100 burn-in iterations and a total length of 1100 iterations. Posterior convergence for each model was assessed using the diagnostic procedures described in Sparapani et al.24. Model diagnostics were good for all models. All parameters seemed to converge within the burn-in period and the z-scores for Gewekes convergence diagnostic25 were approximately standard normal. All BART models were fit using R statistical computing software v. 4.1.226 with the BART package v. 2.924, and all CART models were fit using the rpart package v. 4.1.1627.

The analysis was performed under the ITT paradigm; compliance issues were considered minimal. As in the primary analyses of the trial, the small amount of missing outcome data was ignored in the primary analyses. Sensitivity analyses were performed under best/worst- and worst/best-case imputation. For best/worst-case imputation, the entire estimation procedure was repeated after setting all missing mortality outcome data in the 12mg/d group to alive at 90days and all missing mortality outcome data in the 6mg/d group to dead at 90days. Then, all days with missing life support data were set to alive without life support for the 12mg/d group and the opposite for the 6mg/d group. Under worst/best-case imputation, the estimation procedure was repeated under the opposite conditions, e.g., setting all missing mortality outcome data in the 12mg/d group to dead at 90days and all missing mortality outcome data in the 6mg/d group to alive at 90days.

The resulting decision trees from each fit-the-fit analysis described above (one for the 90-day mortality outcome, and one for the 90-day DAWOLS outcome) were outputted (with continuous variables de-standardized, i.e., back-translated to the original scales). Likewise, the resulting decision trees for each outcome after best- and worst-case imputation were outputted for comparison with the complete records analyses. All statistical code is made available at https://github.com/harhay-lab/Covid-Steroid-HTE.

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