On the consequence of substituting maximum likelihood estimates for the observations below the limit of detection

Use of maximum likelihood estimation procedures with multiple imputations to replace observations below the limit of detection (LOD) has been recommended. There is concern that the use of multiple imputations may introduce variability in the data resulting in different conclusions every time the same data are statistically analyzed. We analyzed data from National Health and Nutrition Examination Survey for 7 perfluorinated and 7 polybrominated diphenyl ethers to address these concerns. Data for each variable were subjected to 10 different iterations of statistical analysis. All observations below LOD were replaced by maximum likelihood estimation procedures with 5 imputations. The maximum variation in computing unadjusted geometric means over 10 iterations of analysis was about 2.5%. Unless the percent observations below LOD was more than 40%, maximum variation in computing adjusted geometric means was less than 1.5%. Maximum variation for computing adjusted geometric standard deviation was less than 6%. Except for border line comparisons, significance probabilities for pairwise comparisons did not vary enough to render contrasts from being statistically significant to statistically non-significant or vice versa. Similar conclusions applied to significance probabilities for regression slopes. The use of more than one multiply imputed variable in a regression model was not found to be of concern. The results show that the use of multiple imputations does not generate additional variabilities in the estimates of these statistics beyond tolerable statistical noise. However, when the percent observations in the data are relatively high, there is some possibility of obtaining disparate results.