Simultaneous modeling of detection rate and exposure concentration using semi-continuous models to identify exposure determinants when left-censored data may be a true zero.

Abstract

Background:Most methods for treating left-censored data assume the analyte is present but not quantified. Biased estimates may result if the analyte is absent such that the unobserved data represents a mixed exposure distribution with an unknown proportion clustered at zero.Objective:We used semi-continuous models to identify time and industry trends in 52,457 OSHA inspection lead sample results.Method:The first component of the semi-continuous model predicted the probability of detecting concentrations ≥0.007 mg/m3 (highest estimated detection limit, 62% of measurements). The second component predicted the median concentration of measurements ≥0.007 mg/m3. Both components included a random-effect for industry and fixed-effects for year, industry group, analytical method, and other variables. We used the two components together to predict median industry- and time-specific lead concentrations.Results:The probabilities of detectable concentrations and the median detected concentrations decreased with year; both were also lower for measurements analyzed for multiple (vs. one) metals and for those analyzed by inductively-coupled plasma (vs. atomic absorption spectroscopy). The covariance was 0.30 (standard error=0.06), confirming the two components were correlated.Significance:We identified determinants of exposure in data with over 60% left-censored, while accounting for correlated relationships and without assuming a distribution for the censored data.