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Jay H. Lubin,¹ Joanne S. Colt,¹ David Camann,² Scott Davis,³ James R. Cerhan,⁴ Richard K. Severson,⁵ Leslie Bernstein,⁶ and Patricia Hartge¹

¹Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, Maryland, USA; ²Southwest Research Institute, San Antonio, Texas, USA; ³Fred Hutchinson Cancer Research Center and the University of Washington, Seattle, Washington, USA; ⁴Mayo Clinic, College of Medicine, Rochester, Minnesota, USA; ⁵Karmanos Cancer Institute and Department of Family Medicine, Wayne State University, Detroit, Michigan, USA; ⁶Department of Preventive Medicine, Norris Comprehensive Cancer Center, Keck School of Medicine, University of Southern California, Los Angeles, California, USA

Abstract
Quantitative measurements of environmental factors greatly improve the quality of epidemiologic studies but can pose challenges because of the presence of upper or lower detection limits or interfering compounds, which do not allow for precise measured values. We consider the regression of an environmental measurement (dependent variable) on several covariates (independent variables) . Various strategies are commonly employed to impute values for interval-measured data, including assignment of one-half the detection limit to nondetected values or of "fill-in" values randomly selected from an appropriate distribution. On the basis of a limited simulation study, we found that the former approach can be biased unless the percentage of measurements below detection limits is small (5-10%) . The fill-in approach generally produces unbiased parameter estimates but may produce biased variance estimates and thereby distort inference when 30% or more of the data are below detection limits. Truncated data methods (e.g., Tobit regression) and multiple imputation offer two unbiased approaches for analyzing measurement data with detection limits. If interest resides solely on regression parameters, then Tobit regression can be used. If individualized values for measurements below detection limits are needed for additional analysis, such as relative risk regression or graphical display, then multiple imputation produces unbiased estimates and nominal confidence intervals unless the proportion of missing data is extreme. We illustrate various approaches using measurements of pesticide residues in carpet dust in control subjects from a case-control study of non-Hodgkin lymphoma. Key words: dust, environmental exposure, imputation, missing data, non-Hodgkin lymphoma, pesticides. Environ Health Perspect 112:1691-1696 (2004) . doi:10.1289/ehp.7199 available via http://dx.doi.org/ [Online 13 September 2004]

Address correspondence to J. Lubin, National Cancer Institute, Biostatistics Branch, 6120 Executive Boulevard, Room 8042, Rockville, MD 20852 USA. Telephone number: (301) 496-3357. Fax: (301) 402-0081. E-mail: lubinj@mail.nih.gov

Support for this study included contracts with the National Cancer Institute: N01-PC-67010, N01-PC-67008, N02-PC-71105, N01-PC-67009, and N01-PC-65064.

The authors declare they have no competing financial interests.

Received 21 April 2004 ; accepted 13 September 2004.