Methods for handling missing data due to a limit of detection in longitudinal lognormal data

Abstract

In animal science, challenge model studies often produce longitudinal data. Many times the lognormal distribution is useful in modeling the data at each time point. Escherichia coli O157 (E. coli O157) studies measure and record the concentration of colonies of the bacteria. There are times when the concentration of colonies present is too low, falling below a limit of detection. In these cases a zero is recorded for the concentration. Researchers employ a method of enrichment to determine if E. coli O157 was truly not present. This enrichment process searches for bacteria colony concentrations a second time to confirm or refute the previous measurement. If enrichment comes back without evidence of any bacteria colonies present, a zero remains as the observed concentration. If enrichment comes back with presence of bacteria colonies, a minimum value is imputed for the concentration. At the conclusion of the study the data are log10-transformed. One problem with the transformation is that the log of zero is mathematically undefined, so any observed concentrations still recorded as a zero after enrichment can not be log-transformed. Current practice carries the zero value from the lognormal data to the normal data. The purpose of this report is to evaluate methods for handling missing data due to a limit of detection and to provide results for various analyses of the longitudinal data. Multiple methods of imputing a value for the missing data are compared. Each method is analyzed by fitting three different models using SAS. To determine which method is most accurately explaining the data, a simulation study was conducted.