 Good morning, ladies and gentlemen. I've got the amazing opportunity to tell something about our research. My name is Bogic Tjopanik. I came from the first faculty of medicine, charged within BRAC, from faculty of rheumatics and statistics, University of Economics, BRAC. Our team and me are interested in survival analysis and its applications. It's my big pleasure to say this is just joint work with Philip Mabarta and states of Kovac. Well, let's have a look at the outline of my talk. Let's start with the introduction where I'm going to introduce the local test, which is an inference test used for comparing two survival curves. And I will continue with a proposed assumption-free alternative. And after that, I will go with a simulation starting describing a bit more some properties of the meta-mural rule. Then I will put in some key findings. The situation of comparing two time events where a curve is very common in applied statistics. Although the local test is the first weapon of choice, there is a larger statistical rule used to exceed the efficiency of the local test. However, all these approaches are limited by strict statistical assumptions. The target variable in survival analysis is two-dimensional, covering both the time of the event and whether the event of the order of the sensory has occurred intuitively. Such variables are just being put in two-dimensional chart. Where usually a number of subjects are not experiencing the event of interest to a number of all subjects who split on a vertical axis at a given time point, while the horizontal axis stands for time until the event of interest or until the sensory. The local test compares the expected and observed numbers of the events of interest in both groups of subjects across all time points where there is an event. At each event time, we can construct times two times on a table and compare rates of the event between the two groups, conditional on a number at risk in the groups, which covers all individuals who have not yet had the event or been sensors. The local test checks and all hypothesis added both groups have identical hazard functions. It means that rates of the events of interest in time were shown fixed rates in the past. Under no hypothesis, the observed numbers of the events of interest is random variables for hypergeometric distribution for both groups. Truth, we can derive formulas for their expected value and variance and for the chi-square statistics which follows under no hypothesis a chi-square distribution with one degree of freedom. The local test assumes the sensory should not affect the event of interest anyhow and proportion of sensor data should be of nearly equal size in both the groups. Otherwise, the chi-squares are different if we're between the group one and two. Also, the initial total number of individuals and the number of event times should be large enough such that the chi-square test statistic fulfills its asymptotic properties. The assumption of free alternatives based on a discrete combinatorial calculation of possible states, where one will obtain data at least as extreme as the observed data. States could not be considered as monotech particle paths in a two-dimensional chart, including the non-cursing swirl curves. By estimating the numbers of the paths at least as extreme as the plotted two curves, we get a point estimate of the p-value. Here we can see two time-event swirl curves and a swirl plot marked by both lines. An example of a pair of monotonic orthogonal paths above the blue-dish line and below the red-dish line, the original swirl curves. So this pair of paths is more extreme than the original curves and is therefore contrary to the normal hypothesis. So under normal hypothesis, we assume the swirl curves are not significantly different. The p-value is a chance of obtaining data at least as extreme as the observed data. Under normal hypothesis, you can calculate the p-value as a probability of getting pairs of swirl curves such that the first curve is above the top original one and in the plot and the second curve is below the bottom original one. This is more formal than the introduced equations. The local test and the proposed assumption-free method were compared by estimulating pairs of random non-cursing curves that are not significantly different. I'll calculate the first type errors. It means when the equivalent curves are detected as different. We assumed that a more robust method should have less value of the first type error. So we generated many pairs of swirl while curves following a negative initial swirl correction as defined below. It's related to a thousand pairs of non-different curves by counting up numbers of cases where p-value was lower than or equal to zero to zero five. We could point estimates of the first type error frequencies. For the first type error rate, the organ is also about zero to zero fifty six. The first type error rate of the proposed method was lower on about zero to zero twelve. While calculating original paths in the grid of several plots, we can get a ratio of the number of all pairs or the paths that are most more distant to one to each other, which are close to one of these and the number of all non-cursing pairs of the same paths. Based on the simulation, the proposed method proved to be a higher robustness than the random test. So the assumption for the original organist seems to be a valid alternative for the comparison of two time-in-land curves. Besides, the method would be also a topic for a new R-pecgeable one, which we are going to start soon. Okay, thank you for your attention. I could try to answer your question if you would like them in the comments below.