Analysis of lognormally distributed exposure data with repeated measures and values below the limit of detection using SAS

Ann Occup Hyg. 2011 Jan;55(1):97-112. doi: 10.1093/annhyg/meq061. Epub 2010 Dec 20.


Studies of determinants of occupational exposure frequently involve left-censored lognormally distributed data, often with repeated measures. Left censoring occurs when observations are below the analytical limit of detection (LOD); repeated measures data results from taking multiple measurements on the same worker. A common method of dealing with this type of data has been to substitute a value (such as LOD/2) for the censored data followed by statistical analysis using the 'usual' methods. Recently, maximum likelihood estimation (MLE) methods have been employed to reduce bias associated with the substitution method. We compared substitution and MLE methods using simulated lognormally distributed exposure data subjected to varying amounts of censoring using two procedures available in SAS: LIFEREG and NLMIXED. In these simulations, the MLE method resulted in less bias and performed well even for censoring up to 80%, whereas the substitution method resulted in considerable bias. We illustrate the NLMIXED procedure using a dataset of chlorpyrifos air measurements collected from termiticide applicators on consecutive days over a 5-day workweek. We provide sample SAS code for several situations including one and two groups, with and without repeated measures, random slopes, and nested random effects.

Publication types

  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Computer Simulation
  • Humans
  • Likelihood Functions
  • Limit of Detection
  • Models, Statistical*
  • Occupational Exposure / analysis
  • Occupational Exposure / statistics & numerical data*