Limitations of maximum likelihood estimation procedures when a majority of the observations are below the limit of detection.

We evaluated the performance of maximum likelihood estimation procedures to estimate the population mean and standard deviation (SD) of log-transformed data sets containing serum or urinary analytical measurements with 50-80% of observations below the limit of detection (LOD). We found that maximum likelihood procedures are limited in their ability to accurately estimate the population mean and SD when the percent of censored data was large and sample size was small. The means were more likely to be underestimated and the SDs were more likely to be overestimated using these procedures. When the sample size, N, was <or=100 and the percent of observations below the LOD, P, was >or=70%, the procedure without imputations performed better than those with imputations. However, the procedure with multiple imputations performed better than or was comparable to other procedures when N was at least 100. This finding was consistent with the improved estimates of the mean and SD in a data set ( N = 113) of polychlorinated biphenyl (PCB) concentrations using multiple imputations. We recommend the use of maximum likelihood procedures with multiple imputation when N >or= 100 and P < 70%. A maximum likelihood procedure without imputation should be preferred when N < 100 and P >or= 70%. However, it should be the expected that biases for both mean and SD in these circumstances may be unacceptably high.