Statistical Methods for Composite Endpoints: Win Ratio and Beyond
Chapter 5 - Discussions
Lu Mao
Department of Biostatistics & Medical Informatics
University of Wisconsin-Madison
Aug 3, 2024
Open Problems
Covariate Adjustment
- Different from regression
- Marginal estimands for \(\mathcal H^{*(1)}\) vs \(\mathcal H^{*(0)}\), not conditioning on \(Z\)
- Gain efficiency when outcome-covariate model is true, otherwise still valid (robustness)
- Standard endpoints
- Continuous, binary, univariate survival, etc. (Tsiatis et al., 2008; Wang et al., 2021; Ye et al., 2023)
- FDA recommendation (FDA, 2023)
- Challenges with WR
- \(U\)-statistic structure
- Lack of likelihood structure
Interim Analysis
- Purpose
- Analyze interim data for evidence of efficacy/futility \(\to\) stop trial early
- Univariate survival: information accrued \(\propto\) number of events
- Challenges with WR
- Information time not event-driven
- Case study: RMST (Lu & Tian, 2021; Luo et al., 2019)
- Correlations between component events
- Dependent increments
- Information time not event-driven
Intercurrent Events
- Definition and examples
- Strategies by ICH E9 (R1)
- Hypothetical: win/loss had treatment continued \(\to\) MI/IPCW?
- Composite: death > treatment failure > lesser events?
- Principal strata: win/lose among those who would not experience treatment failure if assigned to either group
- Counterfactual pairwise comparisons (Fay et al., 2018; Mao, 2018; Wu et al., 2013)
- More work needed
Conclusion
Summary (I)
- Composite endpoints
- Death + hospitalization/progression/relapse
- Regulatory recommendation
- Traditional
- Time to first: death = nonfatal (
survival::coxph()) - Weighted total: death = \(w_D\times\) nonfatal (
Wcompo::compoML())
- Time to first: death = nonfatal (
- Hierarchical
- Win ratio, net benifit, win odds: death > nonfatal
- Estimand issue - ICH E9 (R1)
Summary (II)
- Win ratio test
- Standard: death > one nonfatal event
- Recurrent events: death > frequency > time to last/first event
WR::WRrec(ID, time, status, trt, strata)
- Sample size calculations
- Gumbel-Hougaard copula for death & nonfatal event
- Baseline parameters + component-wise HR
WR::WRSS(xi, ...)
- RMT-IF
- Net average win time on hierarchical states by \(\tau\)
rmt::rmtfit(id, time, status, trt)
- Net average win time on hierarchical states by \(\tau\)
Summary (III)
- While-alive weighted events
- Compensate for differential survival by \(\tau\)
WA::LRfit(id, time, status, trt, Dweight)
- Compensate for differential survival by \(\tau\)
- WR regression
- PW model \[
WR(t\mid Z_i, Z_j;\mathcal W)=\exp\left\{\beta^{\rm T}\left(Z_i- Z_j\right)\right\}
\]
- \(\exp(\beta)\): WRs with unit increases in covariates
WR::pwreg(ID, time, status, Z, strata)
- PW model \[
WR(t\mid Z_i, Z_j;\mathcal W)=\exp\left\{\beta^{\rm T}\left(Z_i- Z_j\right)\right\}
\]
- Generalized PO
- OR of having worse and early outcomes
Learning Objectives: A Revisit
- Have you
- Understood the statistical and scientific challenges with composite endpoints as well as regulatory guidelines/requirements
- Learned the basics of statistical methodology, e.g., testing, power analysis, nonparametric estimation, and semiparametric regression to address these challenges
- Got hands-on experience with real data using publicly available R-packages
Visit back at https://lmaowisc.github.io/ce/
Acknowledgments
Funding
- R01HL149875 (11/2019 – 7/2028)
- DMS2015526 (7/2020 – 6/2024)
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Collaborators
- KyungMann Kim, Tuo Wang, Po-Kuei Chen, Gaohong Dong, Bo Huang, Yi Li, Xinran Miao, Danyu Lin, etc.
References
Fay, M. P., Brittain, E. H., Shih, J. H., Follmann, D. A., & Gabriel, E. E. (2018). Causal estimands and confidence intervals associated with Wilcoxon-Mann-Whitney tests in randomized experiments. Statistics in Medicine, 37(20), 2923–2937. https://doi.org/10.1002/sim.7799
FDA. (2023). Guidance document: Adjusting for covariates in randomized clinical trials for drugs and biological products. US Food and Drug Adminstration. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/adjusting-covariates-randomized-clinical-trials-drugs-and-biological-products
ICH. (2020). ICH E9 (R1) addendum on estimands and sensitivity analysis in clinical trials to the guideline on statistical principles for clinical trials, step 5. London: European Medicines Evaluation Agency.
Lu, Y., & Tian, L. (2021). Statistical Considerations for Sequential Analysis of the Restricted Mean Survival Time for Randomized Clinical Trials. Statistics in Biopharmaceutical Research, 13(2), 210–218. https://doi.org/10.1080/19466315.2020.1816491
Luo, X., Huang, B., & Quan, H. (2019). Design and monitoring of survival trials based on restricted mean survival times. Clinical Trials, 16(6), 616–625. https://doi.org/10.1177/1740774519871447
Mao, L. (2018). On causal estimation using \(U\)-statistics. Biometrika, 105(1), 215–220. https://doi.org/10.1093/biomet/asx071
Tsiatis, A. A., Davidian, M., Zhang, M., & Lu, X. (2008). Covariate adjustment for two-sample treatment comparisons in randomized clinical trials: A principled yet flexible approach. Statistics in Medicine, 27(23), 4658–4677. https://doi.org/10.1002/sim.3113
Wang, B., Susukida, R., Mojtabai, R., Amin-Esmaeili, M., & Rosenblum, M. (2021). Model-Robust Inference for Clinical Trials that Improve Precision by Stratified Randomization and Covariate Adjustment. Journal of the American Statistical Association, 118(542), 1152–1163. https://doi.org/10.1080/01621459.2021.1981338
Wu, P., Han, Y., Chen, T., & Tu, X. M. (2013). Causal inference for Mann-Whitney-Wilcoxon rank sum and other nonparametric statistics. Statistics in Medicine, 33(8), 1261–1271. https://doi.org/10.1002/sim.6026
Ye, T., Shao, J., Yi, Y., & Zhao, Q. (2023). Toward Better Practice of Covariate Adjustment in Analyzing Randomized Clinical Trials. Journal of the American Statistical Association, 118(544), 2370–2382. https://doi.org/10.1080/01621459.2022.2049278