A comparison of several methods for analyzing censored data.

Area of Science:

• Occupational Health
• Environmental Science
• Biostatistics

Background:

• Censored data, common in occupational exposure assessments, presents challenges for statistical analysis.
• Accurate estimation of exposure percentiles and means is crucial for risk assessment and regulatory compliance.
• Existing methods for handling data below the limit-of-detection (LOD) vary in performance.

Purpose of the Study:

• To compare the statistical performance of various methods for analyzing censored occupational exposure data.
• To evaluate methods for estimating the 95th percentile and mean of right-skewed exposure data.
• To assess method robustness under different scenarios, including varying sample sizes, LODs, and distribution types.

Main Methods:

• Evaluated maximum likelihood estimation (MLE), log-probit regression (LPR), substitution methods, non-parametric (NP) quantile methods, and Kaplan-Meier (KM) method.
• Utilized computer-generated censored datasets across diverse scenarios: varying geometric standard deviation, LOD, and sample size.
• Assessed performance using bias and root mean square error (rMSE) for estimating the 95th percentile and mean.

Main Results:

• No single method excelled in all scenarios; MLE and LPR-based methods showed consistent performance across most conditions.
• MLE methods generally yielded lower rMSE than LPR methods, particularly with small sample sizes.
• Substitution methods exhibited significant bias but sometimes low rMSE for small samples (<20).
• Non-parametric methods, including KM, performed poorly in contaminated distribution scenarios.
• Robust MLE and LPR versions showed less bias with contaminated data and multiple LODs.

Conclusions:

• Standard MLE demonstrated superior overall performance based on rMSE for both 95th percentile and mean estimation.
• Standard LPR outperformed robust LPR for mean estimation.
• Robust MLE methods are recommended when bias is the primary concern.
• The Kaplan-Meier method is not recommended for estimating the 95th percentile or mean in these scenarios.