Methods for Improving the Variance Estimator of the Kaplan-Meier Survival Function, When There Is No, Moderate and Heavy Censoring-Applied in Oncological Datasets

In case of heavy and even moderate censoring, a common problem with the Greenwood and Peto variance estimators of the Kaplan-Meier survival function is that they can underestimate the true variance in the left and right tails of the survival distribution. Here, we introduce a variance estimator for the Kaplan-Meier survival function by assigning weight greater than zero to the censored observation. On the basis of this weight, a modification of the Kaplan-Meier survival function and its variance is proposed. An advantage of this approach is that it gives non-parametric estimates at each point whether the event occurred or not. The performance of the variance of this new method is compared with the Greenwood, Peto, regular, and adjusted hybrid variance estimators. Several combinations of these methods with the new method are examined and compared on three datasets, such as leukemia clinical trial data, thalassaemia data as well as cancer data. Thalassaemia is an inherited blood disease, very common in Pakistan, where our data are derived from.