Analysis of censored exposure data by constrained maximization of the Shapiro-Wilk W statistic

A new method for estimating the mean and standard deviation from censored exposure data is presented. The method W(MAX) treats the censored data as variables in a constrained optimization problem. Values for the censored data are calculated by maximizing the Shapiro-Wilk W statistic subject to the constraint that the values are between 0 and the limit of detection (or other censoring limit). The methodology is illustrated here with the Microsoft Excel Solver tool using real exposure data sets subject to repeated censoring. For the data sets explored here, the W(MAX) estimates are comparable to those obtained using the restricted maximum likelihood method based on bias as the performance index.