MLE of Multivariate Normal Parameters in the Presence of Left-censored and Missing Values

• Activity Number: 70
• Type: Contributed
• Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Heather Hoffman*+ and Robert E. Johnson
• Companies: Virginia Commonwealth University and Virginia Commonwealth University
• Keywords: limit of detection (LOD) ; maximum likelihood estimation (MLE)

Abstract

Laboratory assay data often include left-censored values reported as below the limit of detection (LOD). While simple imputation of a specific value such as LOD/2 is implemented commonly in practice, maximum likelihood methods accounting for censoring provide a more accurate way of analyzing the data. Concentration levels of contaminants in water and other types of environmental data typically are modeled with a normal or lognormal distribution. The corresponding MLE of means and variances in univariate analyses can be obtained easily from an assortment of standard software packages; however, a multivariate analysis may be more appropriate when multiple assays are measured on the same subject. For example, total nicotine intake may be represented by a linear combination of the amount of nicotine and its five metabolites present in some physiological fluid. Especially in unexposed nonsmokers, one or more of these measures may fall below the LOD. We present an algorithm that provides the maximum likelihood estimates of mean and unstructured covariance parameters corresponding to a multivariate normal (log-normal) distribution in the presence of left-censored and missing values.