Evaluating Left-Censored Data Through Substitution, Parametric, Semi-parametric, and Nonparametric Methods: A Simulation Study

Abstract

In this study, an attempt was made to determine the degrees of bias in particular sampling sizes and methods. The aim of the study was to determine deviations from the median, the mean, and the standard deviation (SD) in different sample sizes and at different censoring rates for log-normal, exponential, and Weibull distributions in the case of full and censored data sampling. Thus, the concept of “censoring” and censoring types was handled in the first place. Then substitution, parametric (MLE), nonparametric (KM), and semi-parametric (ROS) methods were introduced for the evaluation of left-censored observations. Within the scope of the present study, the data were produced uncensored based on the different parameters of each distribution. Then the datasets were left-censored at the ratios of 5, 25, 45, and 65 %. The censored data were estimated through substitution (LOD and LOD/$\sqrt{2}$), parametric (MLE), semi-parametric (ROS), and nonparametric (KM) methods. In addition, evaluation was made by increasing the sample size from 20 to 300 by tens. Performance comparison was made between the uncensored dataset and the censored dataset on the basis of deviations from the median, the mean, and the SD. The results of simulation studies show that LOD/$\sqrt{2}$ and ROS methods give better results than other methods in deviation from the mean in different sample sizes and at different censoring rates, while ROS gives better results than other methods in deviation from the median in almost all sample sizes and at almost all censoring rates.