Impact of Non-Random Right Censoring on Kaplan Meier Estimates and Log-Rank Test Results: A Simulation Study

Kaplan Meier method is one of the oldest and popular method to estimate the survival function from life-time data. And Log?rank test is used to compare Kaplan Meier curves to evaluate whether or not two or more groups are statistically equivalent. In survival analysis it is assumed that censored observations are randomly distributed in data and dont have any pattern. But in real life this isnt the case always. In medical studies because of dissatisfactory/ inefficient therapy, remedication, negative news about remedy or interventions and high risk of hospital infection most of the right censoring can occur within very short time interval. In the absence of censoring randomization Kaplan Meier estimations and Log-rank test, which are the most commonly used test, results may be biased due to the unbalanced pattern of the censored observations. But there is no study to show the effect of the censored observation pattern on estimation and comparison of the survival curves. In this study we aimed to show statistical properties and performance of Kaplan Meier estimates and Log-rank test under violation of random censoring assumption. A simulation performed to show impact of non-random right censoring on Kaplan Meier estimates and Log-rank test results. Our simulations cover 3 distributions, 4 levels of censoring, and two samples size for Kaplan Meier and Log-rank test. In the all simulated data the pattern of the censored data were changed and compared to data including random censoring. As a result of our simulations, we found location pattern of right censored observation in data set has no significant effect on Kaplan Meier estimate. There were two main points which have effect on Kaplan Meier estimates were sample size and censoring rate. When comparing the curves nonrandom censoring resulted in inflation of Type I error.