Analysis of asymptotic time complexity of an assumption-free alternative to the log-rank test

• Autorzy: Štěpánek Lubomír , Habarta Filip , Malá Ivana , Marek Luboš

Identyfikatory

DOI

10.15439/2020F198

• Konferencja: Federated Conference on Computer Science and Information Systems (15 ; 06-09.09.2020 ; Sofia, Bulgaria)
• Języki publikacji: EN

Abstrakty

EN

Comparison of two time-event survival curves representing two groups of individuals' evolution in time is relatively usual in applied biostatistics. Although the log-rank test is the suggested tool how to face the above-mentioned problem, there is a rich statistical toolbox used to overcome some of the properties of the log-rank test. However, all of these methods are limited by relatively rigorous statistical assumptions. In this study, we introduce a new robust method for comparing two time-event survival curves. We briefly discuss selected issues of the robustness of the log-rank test and analyse a bit more some of the properties and mostly asymptotic time complexity of the proposed method. The new method models individual time-event survival curves in a discrete combinatorial way as orthogonal monotonic paths, which enables direct estimation of the p-value as it was originally defined. We also gently investigate how the surface of an area, bounded by two survival curves plotted onto a plane chart, is related to the test’s p-value. Finally, using simulated time-event data, we check the robustness of the introduced method in comparison with the log-rank test. Based on the theoretical analysis and simulations, the introduced method seems to be a promising and valid alternative to the log-rank test, particularly in case on how to compare two time-event curves regardless of any statistical assumptions.

Słowa kluczowe

EN

computational complexity; statistical distributions; statistical testing

PL

złożoność obliczeniowa; rozkłady statystyczne; testy statystyczne

• Wydawca: Polskie Towarzystwo Informatyczne
• Czasopismo: Annals of Computer Science and Information Systems
• Rocznik: 2020
• Tom: Vol. 21
• Strony: 453--460
• Opis fizyczny: Bibliogr. 21 poz., wykr., tab., wz.

Twórcy

autor

Štěpánek Lubomír

• Department of Statistics and Probability, Faculty of Informatics and Statistics, University of Economics, nám. W. Churchilla 4, 130 67 Prague, Czech Republic
• Institute of Biophysics and Informatics, First Faculty of Medicine, Charles University Salmovská 1, Prague, Czech Republic

autor

Habarta Filip

• ent of Statistics and Probability, Faculty of Informatics and Statistics, University of Economics, nám. W. Churchilla 4, 130 67 Prague, Czech Republic

autor

Malá Ivana

• ent of Statistics and Probability, Faculty of Informatics and Statistics, University of Economics, nám. W. Churchilla 4, 130 67 Prague, Czech Republic

autor

Marek Luboš

• ent of Statistics and Probability, Faculty of Informatics and Statistics, University of Economics, nám. W. Churchilla 4, 130 67 Prague, Czech Republic

Bibliografia

• 1. E. L. Kaplan and Paul Meier. “Nonparametric Estimation from Incomplete Observations”. In: Journal of the American Statistical Association 53.282 (June 1958), pp. 457–481. http://dx.doi.org/10.1080/01621459.1958.10501452.
• 2. Nathan Mantel. “Evaluation of survival data and two new rank order statistics arising in its consideration”. In: Cancer chemotherapy reports 3.50 (1966), pp. 163–170.
• 3. Huimin Li, Dong Han, Yawen Hou, et al. “Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods”. In: PLOS ONE 10.1 (Jan. 2015). Ed. by Zhongxue Chen, e0116774. http://dx.doi.org/10.1371/journal.pone.0116774.
• 4. R Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria, 2017. https://www.R-project.org/.
• 5. Therneau T. survival: A Package for Survival Analysis in R. Vienna, Austria, R package version 3.1-12. URL: https://CRAN.R-project.org/package=survival/.
• 6. F. Kong. “Robust covariate-adjusted logrank tests”. In: Biometrika 84.4 (Dec. 1997), pp. 847–862. http://dx.doi.org/10.1093/biomet/84.4.847.
• 7. Rui Song, Michael R. Kosorok, and Jianwen Cai. “Robust Covariate-Adjusted Log-Rank Statistics and Corresponding Sample Size Formula for Recurrent Events Data”. In: Biometrics 64.3 (Dec. 2007), pp. 741–750. http://dx.doi.org/10.1111/j.1541-0420.2007.00948.x.
• 8. Richard Peto and Julian Peto. “Asymptotically Efficient Rank Invariant Test Procedures”. In: Journal of the Royal Statistical Society. Series A (General) 135.2 (1972), p. 185. http://dx.doi.org/10.2307/2344317.
• 9. Song Yang and Ross Prentice. “Improved Logrank-Type Tests for Survival Data Using Adaptive Weights”. In: Biometrics 66.1 (Apr. 2009), pp. 30–38. http://dx.doi.org/10.1111/j.1541-0420.2009.01243.x.
• 10. Chenxi Li. “Doubly robust weighted log-rank tests and Renyi-type tests under non-random treatment assignment and dependent censoring”. In: Statistical Methods in Medical Research 28.9 (July 2018), pp. 2649–2664. http://dx.doi.org/10.1177/0962280218785926.
• 11. Donald G. Thomas. “Exact and asymptotic methods for the combination of 2 × 2 tables”. In: Computers and Biomedical Research 8.5 (Oct. 1975), pp. 423–446. http://dx.doi.org/10.1016/0010-4809(75)90048-8.
• 12. Cyrus R. Mehta, Nitin R. Patel, and Robert Gray. “Computing an Exact Confidence Interval for the Common Odds Ratio in Several 2 × 2 Contingency Tables”. In: Journal of the American Statistical Association 80.392 (Dec. 1985), p. 969. DOI : 10.2307/2288562.
• 13. Georg Heinze, Michael Gnant, and Michael Schemper. “Exact Log-Rank Tests for Unequal Follow-Up”. In: Biometrics 59.4 (Dec. 2003), pp. 1151–1157. http://dx.doi.org/10.1111/j.0006-341x.2003.00132.x.
• 14. Karl Mosler. Multivariate dispersion, central regions, and depth : the lift zonoid approach. New York: Springer, 2002. ISBN: 0387954120.
• 15. Tomasz Smolinski. Computational intelligence in biomedicine and bioinformatics : current trends and applications. Berlin: Springer, 2008. ISBN: 978-3-540-70776-9.
• 16. Alexander Kulikov. Combinatorial pattern matching : 25th annual symposium, CPM 2014 Moscow, Russia, June 16-18, 2014, proceedings. Cham: Springer, 2014. ISBN: 978-3-319-07565-5.
• 17. Lubomír Štěpánek, Pavel Kasal, and Jan Měšt’ák. “Evaluation of facial attractiveness for purposes of plastic surgery using machine-learning methods and image analysis”. In: 2018 IEEE 20th International Conference on e-Health Networking, Applications and Services (Healthcom). IEEE, Sept. 2018. DOI : 10.1109/healthcom.2018.8531195.
• 18. Lubomír Štěpánek, Pavel Kasal, and Jan Měšt’ák. “Machine-learning at the service of plastic surgery: a case study evaluating facial attractiveness and emotions using R language”. In: Proceedings of the 2019 Federated Conference on Computer Science and Information Systems. IEEE, Sept. 2019. http://dx.doi.org/10.15439/2019f264.
• 19. Lubomír Štěpánek, Pavel Kasal, and Jan Měšt’ák. “Evaluation of Facial Attractiveness after Undergoing Rhinoplasty Using Tree-based and Regression Methods”. In: 2019 E-Health and Bioengineering Conference (EHB). IEEE, Nov. 2019. http://dx.doi.org/10.1109/ehb47216.2019.8969932.
• 20. Lubomír Štěpánek, Pavel Kasal, and Jan Měšt’ák. “Machine-Learning and R in Plastic Surgery – Evaluation of Facial Attractiveness and Classification of Facial Emotions”. In: Advances in Intelligent Systems and Computing. Springer International Publishing, Sept. 2019, pp. 243–252. DOI : 10.1007/978-3-030-30604-5_22.
• 21. Patricia Martinková, Lubomír Štěpánek, Adéla Drabinová, et al. “Semi-real-time analyses of item characteristics for medical school admission tests”. In: Proceedings of the 2017 Federated Conference on Computer Science and Information Systems. Ed. by M. Ganzha, L. Maciaszek, and M. Paprzycki. Vol. 11. Annals of Computer Science and Information Systems. IEEE, 2017, pp. 189–194. http://dx.doi.org/10.15439/2017F380.

Uwagi

1. This research was supported by the grant no. F/45/2020 provided by Internal grant agency of University of Economics, Prague.

2. Track 2: Computer Science & Systems

3. Technical Session: 13th Workshop on Computer Aspects of Numerical Algorithms

4. Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).