@Manual{hce,
    title = {{hce}: Design and Analysis of Hierarchical Composite Endpoints},
    author = {Gasparyan, Samvel B},
    year = {2026},
    journal = {CRAN: The Comprehensive R Archive Network, R package, version 0.9.0},
    url = {https://doi.org/10.32614/CRAN.package.hce},
  }

@article{gasparyan2021power,
  title={Power and sample size calculation for the win odds test: application to an ordinal endpoint in COVID-19 trials},
  author={Gasparyan, Samvel B and Kowalewski, Elaine K and Folkvaljon, Folke and Bengtsson, Olof and Buenconsejo, Joan and Adler, John and Koch, Gary G},
  journal={Journal of Biopharmaceutical Statistics},
  volume={31},
  number={6},
  pages={765--787},
  year={2021},
  publisher={Taylor \& Francis},
  url = {https://doi.org/10.1080/10543406.2021.1968893}
}

@article{gasparyan2022design,
  title={Design and analysis of studies based on hierarchical composite endpoints: Insights from the DARE-19 Trial},
  author={Gasparyan, Samvel B and Buenconsejo, Joan and Kowalewski, Elaine K and Oscarsson, Jan and Bengtsson, Olof F and Esterline, Russell and Koch, Gary G and Berwanger, Otavio and Kosiborod, Mikhail N},
  journal={Therapeutic Innovation \& Regulatory Science},
  volume={56},
  number={5},
  pages={785--794},
  year={2022},
  publisher={Springer},
  url = {https://doi.org/10.1007/s43441-022-00420-1}
}

@article{gasparyan2022comments,
  title={Comments on “Sample size formula for a win ratio endpoint” by RX Yu and J. Ganju},
  author={Gasparyan, Samvel B and Kowalewski, Elaine K and Koch, Gary G},
  journal={Statistics in Medicine},
  volume={41},
  number={14},
  pages={2688--2690},
  year={2022},
  publisher={Wiley Online Library},
  url = {https://doi.org/10.1002/sim.9379}
}

@article{gasparyan2021adjusted,
  title={Adjusted win ratio with stratification: calculation methods and interpretation},
  author={Gasparyan, Samvel B and Folkvaljon, Folke and Bengtsson, Olof and Buenconsejo, Joan and Koch, Gary G},
  journal={Statistical Methods in Medical Research},
  volume={30},
  number={2},
  pages={580--611},
  year={2021},
  publisher={SAGE Publications Sage UK: London, England},
  url = {https://doi.org/10.1177/0962280220942558}
}

@incollection{gasparyanhierarchical,
  title={Hierarchical Composite Endpoints in COVID-19: The DARE-19 Trial},
  author={Gasparyan, Samvel B and Kowalewski, Elaine K and Buenconsejo, Joan and Koch, Gary G},
  booktitle={Case Studies in Innovative Clinical Trials},
  pages={95--148},
  year={2023},
  publisher={Chapman and Hall/CRC},
  url = {https://doi.org/10.1201/9781003288640-7}
}

@article{beigel2020remdesivir,
  title={Remdesivir for the treatment of Covid-19},
  author={Beigel, John H and Tomashek, Kay M and Dodd, Lori E and Mehta, Aneesh K and Zingman, Barry S and Kalil, Andre C and Hohmann, Elizabeth and Chu, Helen Y and Luetkemeyer, Annie and Kline, Susan and others},
  journal={New England Journal of Medicine},
  volume={383},
  number={19},
  pages={1813--1826},
  year={2020},
  publisher={Mass Medical Soc},
  url = {https://doi.org/10.1056/NEJMoa2007764}
}



@Article{buyse2010generalized,
  title={Generalized pairwise comparisons of prioritized outcomes in the two-sample problem},
  author={Buyse, Marc},
  journal={Statistics in medicine},
  volume={29},
  number={30},
  pages={3245--3257},
  year={2010},
  publisher={Wiley Online Library},
  url = {https://doi.org/10.1002/sim.3923}
}

@Article{rauch2014opportunities,
  title={Opportunities and challenges of combined effect measures based on prioritized outcomes},
  author={Rauch, Geraldine and Jahn-Eimermacher, Antje and Brannath, Werner and Kieser, Meinhard},
  journal={Statistics in Medicine},
  volume={33},
  number={7},
  pages={1104--1120},
  year={2014},
  publisher={Wiley Online Library},
  url = {https://doi.org/10.1002/sim.3923}
}


@Article{poc2012,
  author = {SJ Pocock and CA Ariti and TJ Collier and D Wang},
  title = {The win ratio: a new approach to the analysis of composite endpoints in clinical trials based on clinical priorities},
  year = {2012},
  journal = {European Heart Journal},
  volume = {33},
  number = {2},
  pages = {176--182},
  url = {https://doi.org/10.1093/eurheartj/ehr352}
}

@Article{verbeeck2020unbiasedness,
  title={Unbiasedness and efficiency of non-parametric and UMVUE estimators of the probabilistic index and related statistics},
  author={Verbeeck, Johan and Deltuvaite-Thomas, Vaiva and Berckmoes, Ben and Burzykowski, Tomasz and Aerts, Marc and Thas, Olivier and Buyse, Marc and Molenberghs, Geert},
  journal={Statistical Methods in Medical Research},
  volume = {30},
  number = {3},
  pages={747--768},
  year={2021},
  publisher={SAGE Publications Sage UK: London, England}, 
  url = {https://doi.org/10.1177/0962280220966629}
}


@article{peng2020use,
  title={The use of the win odds in the design of non-inferiority clinical trials},
  author={Peng, Lei},
  journal={Journal of Biopharmaceutical Statistics},
  volume={30},
  number={5},
  pages={941--946},
  year={2020},
  publisher={Taylor \& Francis},
  url = {https://doi.org/10.1080/10543406.2020.1757690}
}


@article{brunner2021win,
  title={Win odds: An adaptation of the win ratio to include ties},
  author={Brunner, Edgar and Vandemeulebroecke, Marc and M{\"u}tze, Tobias},
  journal={Statistics in Medicine},
  year={2021},
  publisher={Wiley Online Library},
  url = {https://doi.org/10.1002/sim.8967}
}

@article{dong2022winwinnet,
  title={Win statistics (win ratio, win odds, and net benefit) can complement one another to show the strength of the treatment effect on time-to-event outcomes},
  author={Dong, Gaohong and Huang, Bo and Verbeeck, Johan and Cui, Ying and Song, James and Gamalo-Siebers, Margaret and Wang, Duolao and Hoaglin, David C and Seifu, Yodit and M{\"u}tze, Tobias and others},
  journal={Pharmaceutical Statistics},
  year={2022},
  publisher={Wiley Online Library},
  url = {https://doi.org/10.1002/pst.2251}
}


@Article{dong2020,
  author = {G Dong and DC Hoaglin and J Qiu and RA Matsouaka YW Chang and J Wang and M Vandemeulebroecke},
  title = {The win ratio: on interpretation and handling of ties},
  year = {2020},
  journal = {Statistics in Biopharmaceutical Research},
  volume = {12},
  number = {1},
  pages = {99--106},
  url = {https://doi.org/10.1080/19466315.2019.1575279}
}


@Manual{obrien2006,
  title = {Exploiting the Link Between the Wilcoxon–Mann–Whitney Test and a Simple Odds Statistic},
  author = {RG O’Brien and JM Castelloe},
  organization = {\textsf{SAS} Institute Inc.},
  address = {Cary, NC},
  year = {2006},
  url = {https://support.sas.com/resources/papers/proceedings/proceedings/sugi31/209-31.pdf}
}
@article{yu2022sample,
  title={Sample size formula for a win ratio endpoint},
  author={Yu, Ron Xiaolong and Ganju, Jitendra},
  journal={Statistics in medicine},
  volume={41},
  number={6},
  pages={950--963},
  year={2022},
  publisher={Wiley Online Library},
  url = {https://doi.org/10.1002/sim.9297}
}


@book{agresti2013categorical,
  title={Categorical data analysis},
  author={Agresti, Alan},
  year={2013},
  publisher={John Wiley \& Sons},
  url={https://www.wiley.com/en-gb/Categorical+Data+Analysis%2C+3rd+Edition-p-9780470463635}
}


@article{kruskal1954measures,
  title={Measures of association for cross classifications},
  author={Kruskal, William H and Goodman, Leo},
  journal={Journal of the American Statistical Association},
  volume={49},
  number={268},
  pages={732--764},
  year={1954},
  url = {https://doi.org/10.2307/2281536}
}


@article{somers1962new,
  title={A new asymmetric measure of association for ordinal variables},
  author={Somers, Robert H},
  journal={American sociological review},
  pages={799--811},
  year={1962},
  publisher={JSTOR},
  url = {https://doi.org/10.2307/2090408}
}

@article{mann1947test,
  title={On a test of whether one of two random variables is stochastically larger than the other},
  author={Mann, Henry B and Whitney, Donald R},
  journal={The Annals of Mathematical Statistics},
  pages={50--60},
  year={1947}
}

@Article{Hoeff,
  author = {W Hoeffding},
  title = {A Class of Statistics with Asymptotically Normal Distribution},
  year = {1948},
  journal = {The Annals of Mathematical Statistics},
  volume = {19},
  number = {3},
  pages = {293--325},
  url={https://doi.org/10.1214/aoms/1177730196}
}


@article{khce1,
  title={Validity and utility of a hierarchical composite endpoint for clinical trials of kidney disease progression: A review},
  author={Little, Dustin J and Gasparyan, Samvel B and Schloemer, Patrick and Jongs, Niels and Brinker, Meike and Karpefors, Martin and Taso, Christoph and Rethemeier, Nicole and Frison, Lars and Nkulikiyinka, Richard and Rossert, Jerome and Heerspink, Hiddo L},
  year={2023},
  journal = {Journal of the American Society of Nephrology},
  volume = {34},
  number = {12},
  pages = {1928--1935},
  url = {https://doi.org/10.1681/ASN.0000000000000244}
}

@article{khce2,
  title={Development and validation of a new HCE for clinical trials of kidney disease progression},
  author={Heerspink, Hiddo L and Jongs, Niels and Schloemer, Patrick and Little, Dustin J and Brinker, Meike and Taso, Christoph and Karpefors, Martin and Wheeler, David C and Bakris, George and Perkovich, Vlado and Nkulikiyinka, Richard and  Rossert Jerome and Gasparyan, Samvel B},
  year={2023},
  volume = {34},
  number = {12},
  pages = {2025--2038},
  journal = {Journal of the American Society of Nephrology},
  url = {https://doi.org/10.1681/ASN.0000000000000243}
}

@article{khce3,
  title={A hierarchical kidney outcome using win statistics in patients with heart failure from the DAPA-HF and DELIVER trials},
  author={Kondo, Toru and Jhund, Pardeep S and Gasparyan, Samvel B and Yang, Mingming and Claggett, Brian L and McCausland, Finnian R and Tolomeo, Paolo and Vadagunathan, Muthiah and Heerspink, Hiddo JL and Solomon, Scott D and others},
  journal={Nature Medicine},
  volume = {30},
  number = {5},
  pages={1432--1439},
  year={2024},
  publisher={Nature Publishing Group US New York},
  url = {https://doi.org/10.1038/s41591-024-02941-8}
}

@article{kosiborod2021dapagliflozin,
  title={Dapagliflozin in patients with cardiometabolic risk factors hospitalised with COVID-19 (DARE-19): a randomised, double-blind, placebo-controlled, phase 3 trial},
  author={Kosiborod, Mikhail N and Esterline, Russell and Furtado, Remo HM and Oscarsson, Jan and Gasparyan, Samvel B and Koch, Gary G and Martinez, Felipe and Mukhtar, Omar and Verma, Subodh and Chopra, Vijay and others},
  journal={The lancet Diabetes \& endocrinology},
  volume={9},
  number={9},
  pages={586--594},
  year={2021},
  publisher={Elsevier},
  url ={https://doi.org/10.1016/S2213-8587(21)00180-7}
}

@article{kosiborod2021effects,
  title={Effects of dapagliflozin on prevention of major clinical events and recovery in patients with respiratory failure because of COVID-19: Design and rationale for the DARE-19 study},
  author={Kosiborod, Mikhail and Berwanger, Otavio and Koch, Gary G and Martinez, Felipe and Mukhtar, Omar and Verma, Subodh and Chopra, Vijay and Javaheri, Ali and Ambery, Philip and Gasparyan, Samvel B and others},
  journal={Diabetes, Obesity and Metabolism},
  volume={23},
  number={4},
  pages={886--896},
  year={2021},
  publisher={Wiley Online Library},
  url = {https://doi.org/10.1111/dom.14296}
}

@article{kondo2023use,
  title={Use of Win Statistics to Analyze Outcomes in the DAPA-HF and DELIVER Trials},
  author={Kondo, Toru and Gasparyan, Samvel B and Jhund, Pardeep S and Bengtsson, Olof and Claggett, Brian L and de Boer, Rudolf A and Hernandez, Adrian F and Inzucchi, Silvio E and Kosiborod, Mikhail N and K{\o}ber, Lars and others},
  journal={NEJM Evidence},
  volume={2},
  number={11},
  pages={EVIDoa2300042},
  year={2023},
  publisher={Massachusetts Medical Society},
  url = {https://doi.org/10.1056/EVIDoa2300042}
}

@article{karpefors2023maraca,
  title={The maraca plot: A novel visualization of hierarchical composite endpoints},
  author={Karpefors, Martin and Lindholm, Daniel and Gasparyan, Samvel B},
  journal={Clinical Trials},
  volume={20},
  number={1},
  pages={84--88},
  year={2023},
  publisher={SAGE Publications Sage UK: London, England},
  url = {https://doi.org/10.1177/17407745221134949}
}

  @Manual{maraca,
    title = {maraca: The Maraca Plot: Visualization of Hierarchical Composite
Endpoints in Clinical Trials},
    author = {{Martin Karpefors} and {Samvel B. Gasparyan} and {Monika Huhn}},
    year = {2024},
    note = {R package version 0.7},
    url = {https://CRAN.R-project.org/package=maraca}
  }
  
  @article{noether1987sample,
  title={Sample size determination for some common nonparametric tests},
  author={Noether, Gottfried E},
  journal={Journal of the American Statistical Association},
  volume={82},
  number={398},
  pages={645--647},
  year={1987},
  publisher={Taylor \& Francis},
  url = {https://doi.org/10.1080/01621459.1987.10478478}
}

@article{gasp2024bds,
  title={Basic Data Structure for Hierarchical Composite Endpoints: An Application to Kidney Disease Trials},
  author={Gasparyan, Samvel B and Major, Nicole and B{\"a}ckberg, Christoffer and Ravikiran, Srivathsa and Wani, Parag and Karpefors, Martin and Gasparyan, Samvel B},
  journal={Journal of the Society for Clinical Data Management},
  volume={4},
  number={1},
  year={2024},
  publisher={Society for Clinical Data Management},
  url ={https://doi.org/10.47912/jscdm.265}
}

@article{brunner2000nonparametric,
  title={The nonparametric Behrens-Fisher problem: asymptotic theory and a small-sample approximation},
  author={Brunner, Edgar and Munzel, Ullrich},
  journal={Biometrical Journal: Journal of Mathematical Methods in Biosciences},
  volume={42},
  number={1},
  pages={17--25},
  year={2000},
  publisher={Wiley Online Library},
  url={https://doi.org/10.1002/(SICI)1521-4036(200001)42:1%3C17::AID-BIMJ17%3E3.0.CO;2-U}
}

@misc{CDISC, 
  title={ADaM}, 
  url={https://www.cdisc.org/standards/foundational/adam}, 
  year={2009},  
  author={CDISC, Clinical Data Interchange Standards Consortium}
} 


@article{bamber1975area,
  title={The area above the ordinal dominance graph and the area below the receiver operating characteristic graph},
  author={Bamber, Donald},
  journal={Journal of mathematical psychology},
  volume={12},
  number={4},
  pages={387--415},
  year={1975},
  publisher={Elsevier},
  url={https://doi.org/10.1016/0022-2496(75)90001-2}
}

@article{dong2023win,
  title={Win statistics (win ratio, win odds, and net benefit) can complement one another to show the strength of the treatment effect on time-to-event outcomes},
  author={Dong, Gaohong and Huang, Bo and Verbeeck, Johan and Cui, Ying and Song, James and Gamalo-Siebers, Margaret and Wang, Duolao and Hoaglin, David C and Seifu, Yodit and M{\"u}tze, Tobias and others},
  journal={Pharmaceutical Statistics},
  volume={22},
  number={1},
  pages={20--33},
  year={2023},
  publisher={Wiley Online Library},
  url={https://doi.org/10.1002/pst.2251}
}

@article{delong1988comparing,
  title={Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach},
  author={DeLong, Elizabeth R and DeLong, David M and Clarke-Pearson, Daniel L},
  journal={Biometrics},
  volume={44},
  number={3},
  pages={837--845},
  year={1988},
  publisher={JSTOR},
  url={https://doi.org/10.2307/2531595}
}

@article{koch1998issues,
  title={Issues for covariance analysis of dichotomous and ordered categorical data from randomized clinical trials and non-parametric strategies for addressing them},
  author={Koch, Gary G and Tangen, Catherine M and Jung, Jin-Whan and Amara, Ingrid A},
  journal={Statistics in medicine},
  volume={17},
  number={15-16},
  pages={1863--1892},
  year={1998},
  publisher={Wiley Online Library},
  url={https://doi.org/10.1002/(sici)1097-0258(19980815/30)17:15/16%3C1863::aid-sim989%3E3.0.co;2-m}
}

@article{kalil2021baricitinib,
  title={Baricitinib plus remdesivir for hospitalized adults with Covid-19},
  author={Kalil, Andre C and Patterson, Thomas F and Mehta, Aneesh K and Tomashek, Kay M and Wolfe, Cameron R and Ghazaryan, Varduhi and Marconi, Vincent C and Ruiz-Palacios, Guillermo M and Hsieh, Lanny and Kline, Susan and others},
  journal={New England Journal of Medicine},
  volume={384},
  number={9},
  pages={795--807},
  year={2021},
  publisher={Mass Medical Soc},
  url={https://doi.org/10.1056/NEJMoa2031994}
}

@article{brunner2025unbiased,
  title={An unbiased rank-based estimator of the Mann--Whitney variance including the case of ties},
  author={Brunner, Edgar and Konietschke, Frank},
  journal={Statistical Papers},
  volume={66},
  number={1},
  pages={20},
  year={2025},
  publisher={Springer},
  url={http://doi.org/10.1007/s00362-024-01635-0}
}

@book{brunner2018rank,
  title={Rank and pseudo-rank procedures for independent observations in factorial designs},
  author={Brunner, Edgar and Bathke, Arne C and Konietschke, Frank},
  year={2018},
  publisher={Springer},
  url={http://doi.org/10.1007/978-3-030-02914-2}
}

@inproceedings{sklar1959fonctions,
  title={Fonctions de r{\'e}partition {\`a} n dimensions et leurs marges},
  author={Sklar, M},
  booktitle={Annales de l'ISUP},
  volume={8},
  number={3},
  pages={229--231},
  year={1959}
}

@book{nelsen2006introduction,
  title={An introduction to copulas},
  author={Nelsen, Roger B},
  year={2006},
  publisher={Springer}
}

@article{marshall1988families,
  title={Families of multivariate distributions},
  author={Marshall, Albert W and Olkin, Ingram},
  journal={Journal of the American statistical association},
  volume={83},
  number={403},
  pages={834--841},
  year={1988},
  publisher={Taylor \& Francis}
}

@article{nolan2020univariate,
  title={Univariate stable distributions},
  author={Nolan, John P},
  journal={Springer Series in Operations Research and Financial Engineering},
  volume={10},
  pages={978--3},
  year={2020},
  publisher={Springer}
}

@article{hofert2011nested,
  title={Nested Archimedean copulas meet R: The nacopula package},
  author={Hofert, Marius and M{\"a}chler, Martin},
  journal={Journal of Statistical Software},
  volume={39},
  pages={1--20},
  year={2011}
}

@article{chambers1976method,
  title={A method for simulating stable random variables},
  author={Chambers, John M and Mallows, Colin L and Stuck, BW},
  journal={Journal of the american statistical association},
  volume={71},
  number={354},
  pages={340--344},
  year={1976},
  publisher={Taylor \& Francis}
}

@article{hofert2025copula,
  title={copula: Multivariate Dependence with Copulas},
  author={Hofert, Marius and Kojadinovic, Ivan and Maechler, Martin and Yan, Jun},
  journal={R package version 1.1-5},
  url={https://CRAN.R-project.org/package=copula},
  year={2025}
}

@article{schuurhuis2025new,
  title={A New Approach to the Nonparametric Behrens--Fisher Problem With Compatible Confidence Intervals},
  author={Sch{\"u}{\"u}rhuis, Stephen and Konietschke, Frank and Brunner, Edgar},
  journal={Biometrical Journal},
  volume={67},
  number={6},
  pages={e70096},
  year={2025},
  publisher={Wiley Online Library}
}
