Co-occurrence and correlation of arsenic, cadmium, and lead in processed foods intended for infants and young children: evaluation of two statistical approaches adapted to censored data and their implications for risk management.

We evaluated the co-occurrence of arsenic (As), cadmium (Cd), and lead (Pb) in 10 categories of processed foods intended for infants and young children (<2 years old) and adapted methodology to characterise and evaluate the impact of correlations on toxic element (TE) concentrations in these foods. Co-occurrence was assessed by calculating the frequency of samples having concentrations above the limit of detection (LOD) among TE sets (i.e. As-Cd, As-Pb, Cd-Pb, and As-Cd-Pb). Pairwise correlations were evaluated using two statistical approaches adapted to censored data: (i) non-parametric Kendall's tau and (ii) parametric Bayesian modelling. Nonparametric and parametric correlation analyses showed similar results. We found positive correlations among one or more pairs of the TEs (As, Pb, and Cd) in 9 of the 10 categories of foods intended for infants and young children and a negative correlation for one TE pair for a single food category. Where positive correlations are observed, removing samples with high concentrations of a given TE reduces the mean of the other TEs in that food. We also explored the impact of correlations among TEs on the fraction of the supply below maximum levels. Positive correlations among TEs have the potential to reduce the impact on the supply when setting multiple maximum levels.