On the stability of log-rank test under labeling errors

The Wilcoxon rank-sum test, also known as the Mann-Whitney U test, is a nonparametric test used to determine if there is a significant difference between the distributions of two independent samples. This test is designed specifically for two independent populations and has the following key requirements:

The Mantel-Cox log-rank test is a widely used statistical method for comparing the survival distributions of two groups. It tests whether a statistically significant difference exists in survival times between the groups without assuming a specific distribution for the survival data, making it a non-parametric test. This flexibility makes the log-rank test particularly valuable in medical research and other fields where the timing of an event, such as death or disease recurrence, is of...

The Wilcoxon signed-rank test for matched pairs evaluates the null hypothesis by combining the ranks of differences with their signs. It essentially tests whether the median of the differences in a population of matched pairs is zero. Since the test incorporates more information than the sign test, it generally yields more trustable conclusions. This test also does not require the data to follow a normal distribution, but two conditions must be met for it to be applicable: (1) the data must...

Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...

Survival trees are a non-parametric method used in survival analysis to model the relationship between a set of covariates and the time until an event of interest occurs, often referred to as the "time-to-event" or "survival time." This method is particularly useful when dealing with censored data, where the event has not occurred for some individuals by the end of the study period, or when the exact time of the event is unknown.
 Building a Survival Tree
Constructing a...

Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5%...