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Summary

This study evaluated bias in statistical sampling methods for log-normal, exponential, and Weibull distributions. The LOD/2 and Restricted Ordinary Smallest (ROS) methods showed minimal deviation from the mean and median across various sample sizes and censoring rates.

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Kaplan–Meier estimatorLeft-censorLimit of detectionLimit of quantificationMeasurement uncertaintyRegression on order statistics

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Area of Science:

  • Statistics
  • Biostatistics
  • Data Analysis

Background:

  • Statistical bias can significantly affect data interpretation.
  • Understanding bias in sampling is crucial for accurate analysis, especially with censored data.
  • Various methods exist for handling censored data, each with potential biases.

Purpose of the Study:

  • To determine bias degrees in specific sampling sizes and methods.
  • To evaluate deviations from median, mean, and standard deviation (SD) for different sample sizes and censoring rates.
  • To compare the performance of substitution, parametric (MLE), nonparametric (KM), and semi-parametric (ROS) methods for left-censored data.

Main Methods:

  • Generated uncensored data from log-normal, exponential, and Weibull distributions.
  • Applied left-censoring at 5%, 25%, 45%, and 65% ratios.
  • Estimated censored data using substitution (LOD and LOD/2), parametric (MLE), semi-parametric (ROS), and nonparametric (KM) methods.
  • Increased sample size from 20 to 300 in increments of 10 for evaluation.

Main Results:

  • The LOD/2 and ROS methods demonstrated superior performance in minimizing deviation from the mean across various sample sizes and censoring rates.
  • The ROS method showed better results than other methods in minimizing deviation from the median for most sample sizes and censoring rates.
  • Performance was assessed by comparing deviations from the median, mean, and SD between uncensored and censored datasets.

Conclusions:

  • The LOD/2 and ROS methods are recommended for handling left-censored data to minimize bias in statistical analyses.
  • The choice of method can impact the accuracy of statistical estimates, particularly the mean and median.
  • Further research may explore these methods with different data distributions and censoring types.