Evaluation of maximum likelihood procedures to estimate left censored observations

The optimal procedure for estimating chemical levels below the limit of detection (LOD) remains a topic of interest when working with ultratrace analysis of environmental or clinical specimens. Unique to this investigation, we evaluated the performance of three maximum likeli-hood estimation (MLE) procedures to estimate the population mean and standard deviation from chemical data with 10-40% observations below the LOD. Randomly drawn observations from the normal distributions with these parameter estimates were used to replace censored observations. Final estimates of the mean and standard deviation (SD) were obtained from these full samples and compared to actual population mean mu and SD sigma. The study demonstrated that the average percent relative bias for both the mean and SD increased as the sample size decreased and the percent observations below the LOD increased. The MLE procedure with multiple imputations almost always had acceptable coverage rates for both the mean and the SD. These findings support earlier observations, and they suggest that MLE with multiple imputations is the preferred method to estimate mean and SD when the frequency of left censored observations in the population is <= 40%.