A mixture model for occupational exposure mean testing with a limit of detection

Information from detectable exposure measurements randomly sampled from a left-truncated log-normal distribution may be used to evaluate the distribution of nondetectable values that fall below an analytic limit of detection. If the proportion of nondetects is larger than expected under log normality, alternative models to account for these unobserved data should be considered. We discuss one such model that incorporates a mixture of true zero exposures and a log-normal distribution with possible left censoring, previously considered in a different context by Moulton and Halsey (1995, Biometrics 51, 1570-1578). A particular relationship is demonstrated between maximum likelihood parameter estimates based on this mixture model and those assuming either left-truncated or left-censored data. These results emphasize the need for caution when choosing a model to fit data involving nondetectable values. A one-sided likelihood ratio test for comparing mean exposure under the mixture model to an occupational exposure limit is then developed and evaluated via simulations. An example demonstrates the potential impact of specifying an incorrect model for the nondetectable values.