Non-parametric comparison of survival functions with censored data: A computational analysis of greedy and Monte Carlo approaches

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

Identyfikatory

DOI

10.15439/2024F223

• Konferencja: Federated Conference on Computer Science and Information Systems (19 ; 08-11.09.2024 ; Belgrade, Serbia)
• Języki publikacji: EN

Abstrakty

EN

Comparison of two survival functions, which describe the probability of not experiencing an event of interest by a given time point in two different groups, is a typical task in survival analysis. There are several well-established methods for comparing survival functions, such as the log-rank test and its variants. However, these methods often come with rigid statistical assumptions. In this work, we introduce a non-parametric alternative for comparing survival functions that is nearly free of assumptions. Unlike the log-rank test, which requires the estimation of hazard functions derived from (or facilitating the derivation of) survival functions and assumes a minimum number of observations to ensure asymptotic properties, our method models all possible scenarios based on observed data. These scenarios include those in which the compared survival functions differ in the same way or even more significantly, thus allowing us to calculate the p-value directly. Individuals in these groups may experience an event of interest at specific time points or may be censored, i.e., they might experience the event outside the observed time points. Focusing on all scenarios where survival probabilities differ at least as much as observed usually requires computationally intensive calculations. Censoring is treated as a form of noise, increasing the range of scenarios that need to be calculated and evaluated. Therefore, to estimate the p-value, we compare a greedy approach that computes all possible scenarios in which groups' survival functions differ as observed or more, with a Monte Carlo simulation of these scenarios, alongside a traditional approach based on the log-rank test. Our proposed method reduces the first type error rate, enhancing its utility in studies where robustness against false positives is critical. We also analyze the asymptotic time complexity of both proposed approaches.

Słowa kluczowe

EN

Monte Carlo methods; error analysis; noise; estimation; focusing; probability; software; robustness; hazards; time complexity

PL

metody Monte Carlo; analiza błędów; szum; szacowanie; prawdopodobieństwo; oprogramowanie; odporność; zagrożenia; złożoność czasowa

• Wydawca: Polskie Towarzystwo Informatyczne
• Czasopismo: Annals of Computer Science and Information Systems
• Rocznik: 2024
• Tom: Vol. 39
• Strony: 725--730
• Opis fizyczny: Bibliogr. 10 poz., rys., wz.

Twórcy

autor

Štěpánek Lubomír

• Department of Statistics and Probability
• Department of Mathematics Faculty of Informatics and Statistics Prague University of Economics and Business W. Churchill’s square 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

• Department of Statistics and Probability

autor

Malá Ivana

• Department of Statistics and Probability

autor

Marek Luboš

• Department of Statistics and Probability

Bibliografia

• 1. Nathan Mantel. “Evaluation of survival data and two new rank order statistics arising in its consideration”. In: Cancer Chemotherapy Reports 50.3 (1966), pp. 163–170.
• 2. 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.
• 3. 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.
• 4. 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.
• 5. 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.
• 6. 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. DOI: 10.1177/0962280218785926.
• 7. Štěpánek, F. Habarta, I. Malá, and L. Marek, “Analysis of asymptotic time complexity of an assumption-free alternative to the log-rank test,” in Proceedings of the 2020 Federated Conference on Computer Science and Information Systems, ser. FedCSIS 2020. IEEE, Sep. 2020, p. 453–460.
• 8. Štěpánek, F. Habarta, I. Malá, and L. Marek, Reducing the First-Type Error Rate of the Log-Rank Test: Asymptotic Time Complexity Analysis of An Optimized Test’s Alternative. Springer International Publishing, Dec. 2021, p. 281–302.
• 9. Donald E Knuth. “Big omicron and big omega and big theta”. In: ACM Sigact News 8.2 (1976), pp. 18–24.
• 10. R Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria, 2023. URL: https://www.R-project.org/.

Uwagi

1. This research is supported by grant F4/50/2023 from the Internal Grant Agency of the Prague University of Economics and Business.

2. Thematic Sessions: Short Papers