Dealing with the non-detected and non-quantified data. The example of the serum dioxin data in the French dioxin and incinerators study

Seru m analysis of dioxins, furans and PCBs were performed in 1030 adults to identify the determinants of the body-burden of these compounds in the population neighbouring waste incinerators. Despite the use of a sensitive analytical method, several concentrations were not quantified or not detected. To handle this kind of data, we used two different methods: the substitution method and the Tobit model. The results of these two methods were then compared. Results showed that when the censoring intensity is less than 30%, the method for treatment of left-censored data makes little difference. However, when the censoring intensity is larger than 30%, the resulting analysis could be sensitive to the method for handling left-censored data. 1 was carried out in 8 different areas in France around municipal solid waste incinerators to study whether serum dioxin levels were higher in people living in the vicinity of incinerators compared to referent people. In addition, some factors, such as local food consumption, were also studied to check whether it could influence their serum levels. 1030 adults (30-65 years) selected through a stratified two stage random sampling, provided blood serum samples for dioxin measurements. Exposure was assessed by concentrations of dioxins, furans and PCBs in human blood serum. In spite of low limit of quantification (LOQ) and limit of detection (LOD), several concentrations were not quantified or not detected 2 . Seve ral methods are available for handling environmental exposure data in the presence of censored values. The substitution method substitutes a single value for each censored value. Common choices for this substituted value are zero, LOD (or LOQ), LOD/2 (or LOQ/2), and LOD/√2 (or LOQ/√2). Summary statistics and regression parameters are then estimated using the data above the LOD together with these substituted values. The substitution method is commonly used but it has no theoretical basis 3 . An alternative method is to use regr ession model for censored data known as Tobit regression 4 . This method does not require substitution for valu es less than the LOD or LOQ and use maximum likelihood to estimate regression parameters. When the censoring intensity (the percentage of censored values) is low, the different methods may not lead to significantly different results. However, as the censoring intensity increases, the impact of the handling of censored data on the resulting analysis increases. The choice of the most appropriate method when dealing with an elevated number of censored data is then essential 5 . In the present work, we investigate the impact of the two different methods on the estimation of the distribution of the dioxin concentrations. We also consider the regression of the blood serum dioxin concentrations on several covariates using Tobit regression.