Proceedings of the 19th Conference on Computer Science and Intelligence Systems

DOI: http://dx.doi.org/10.15439/2024F223

Citation: Proceedings of the 19th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 39, pages 725–730 (2024)

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Abstract. 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.

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