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Handling Concentrations Below Quantification Limit in Population

Michel Tod

Hopital Avicenne, Bobigny, France

Three practical strategies for handling concentrations below the quantification limit (BQL) in the context of the estimation of population parameters were compared. The first method (na´ve method), consisted in discarding these values from the data. The second method (LBS method) fixed the BQL values to QL/2, while the standard deviation of the residual error model was fixed to QL/4. The third method (reference method), integrated the likelihood of the BQL values from 0 to QL. The performances of these methods were assessed with simulated data and compared to a fourth method (gold standard) which consisted in estimating the parameters assuming all the observations were available. The influences of the population size, the number of samples per subject, the proportion of BQL values and the sampling schedule were determined. In all cases, population parameters were estimated in a Bayesian framework by using WinBUGS, which relies on sampling-based techniques. Results showed that discarding BQL values leads to a poor estimation of the population parameters especially when the amount of information was low and when the proportion of BQL values was high. In contrast, the LBS method, which is very easy to implement in many softwares, worked very well. The reference method worked only slightly better and was close to the gold standard.