ABSTRACT
Durations of any event, such as duration of hospitalization, is usually found to have a highly skewed distribution and incomplete values due to dropouts and limited follow-up. The usual methods of statistical analysis are, therefore, not applicable. The method of survival analysis is a nonparametric method and is designed to overcome these problems. Survival is a generic term and is used for any time-toevent data. The entire survival pattern at different points in time is studied by the Kaplan-Meier method under certain conditions. Logrank method is used to compare survival pattern in two or more groups. Hazard is the rate of occurrence of an event per unit of time and studied by Cox method. The concept of survival and all these methods of survival analysis are briefly discussed in this short note in a non-mathematical format for medical audience.
ABSTRACT
The purpose of this article was to introduce the likelihood ratio test， six nonparametric tests， and the SAS implementation of the survival data. Based on the assumption that the survival data had the exponential distribution， the likelihood ratio test method was derived， the main difference between six nonparametric test methods was that they had different weight functions. Under the conditions of non-stratification and stratification， the seven survival data hypothesis testing methods mentioned above could be used， and their common point was that their test statistics all followed the χ2 distribution. Through two examples and by means of the SAS software， the article realized the various hypothesis tests for two or more groups of survival data， outputed and explained SAS calculation results， and made statistical and professional conclusions.
ABSTRACT
The purpose of this article was to introduce the log-rank test and the SAS implementation. There were many different expression forms for the test statistics of the log-rank tests. Among them， there were two most common expression forms： the first was similar to "Pearson΄s goodness-of-fit χ2 test statistic"； the second was similar to "the test statistic of the odds ratio of high-dimensional table data， that was， the Breslow-Day΄s χ2 test statistic". The log-rank test statistic had two distribution types， one was the χ2 distribution， the other was the standard normal distribution. In the process of constructing log-rank test statistics， there were four contents that needed to be paid attention to： ① the sequential multiple four-fold tables formed by stratification or partition after sorting according to the individual "survival time"； ② it was necessary to distinguish whether the "survival time of each individual" was the complete data or the censored data； ③ only the calculation of the "theoretical or expected frequency" on a specific grid ［for example， （1，1） grid］ in each four-fold table data； ④ the method of calculating the theoretical frequency was different from the one in the independent test of the data of the four-fold table. Based on two examples with the different data structures， the paper realized the log-rank tests with the help of the SAS software.
ABSTRACT
Length of time is a variable often encountered during data analysis. Survival analysis provides simple, intuitive results concerning time-to-event for events of interest, which are not confined to death. This review introduces methods of analyzing time-to-event. The Kaplan-Meier survival analysis, log-rank test, and Cox proportional hazards regression modeling method are described with examples of hypothetical data.