Methods for Improving the Variance Estimator of the Kaplan–Meier Survival Function, When There Is No, Moderate and Heavy Censoring-Applied in Oncological Datasets - Khan, Habib Nawaz; Zaman, Qamruz; Azmi, Fatima; Shahzada, Gulap; Jakovljevic, Mihajlo (Frontiers in Public Health, 2022)
In the case of heavy and even moderate censoring, a common problem with the Greenwood and Peto variance estimators of the Kaplan-Meier ( KM) 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. Based on this weight, a modification of the Kaplan-Meier survival function and its variance is proposed. An advantage of this approach is that it gives nonparametric 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 data sets including leukaemia clinical trial data, thalassaemia data as well as cancer data. Thalassaemia is an inherited blood disease, very common in Pakistan, where our data is derived from.