IJE Advance Access published online on August 10, 2009
International Journal of Epidemiology, doi:10.1093/ije/dyp269
Estimating the odds ratio when exposure has a limit of detection
1Department of Epidemiology and Center for AIDS Research, University of Northern California at Chapel Hill, Chapel Hill, NC, USA
2Department of Biostatistics and Lineberger Comprehensive Cancer Center, University of Northern California at Chapel Hill, Chapel Hill, NC, USA
3DB4/OB/OTS/CDER, Federal Drug Administration, Silver Spring, MD, USA
4Epidemiology Branch, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD, USA
* Corresponding author. McGavran-Greenberg Hall, Campus Box 7435, Chapel Hill, NC 27599-7435, USA. E-mail: cole{at}unc.edu
 |
Abstract |
|---|
Background In epidemiologic research, little emphasis has been placed on methods to account for left-hand censoring of ‘exposures’ due to a limit of detection (LOD).
Methods We calculate the odds of anti-HIV therapy naiveté in 45 HIV-infected men as a function of measured log10 plasma HIV RNA viral load using five approaches including ad hoc methods as well as a maximum likelihood estimate (MLE). We also generated simulations of a binary outcome with 10% incidence and a 1.5-fold increased odds per log increase in a log-normally distributed exposure with 25, 50 and 75% of exposure data below LOD. Simulated data were analysed using the same five methods, as well as the full data.
Results In the example, the estimated odds ratio (OR) varied by 1.22-fold across methods, from 1.45 to 1.77 per log10 copies of viral load and the standard error for the log OR varied by 1.52-fold across methods, from 0.31 to 0.47. In the simulations, use of full data or the MLE was unbiased with appropriate confidence interval (CI) coverage. However, as the proportion of exposure below LOD increased, substituting LOD, LOD/
2 or LOD/2 was increasingly biased with increasingly inappropriate CI coverage. Finally, exclusion of values below LOD was unbiased but imprecise.
Conclusions In this example and the settings explored by simulation, and among methods readily available to investigators (i.e. sans full data), the MLE provided an unbiased and appropriately precise estimate of the exposure–outcome OR.
Keywords Biomarkers, epidemiologic methods, limit of detection, statistical method
Accepted 6 July 2009