Estimation of Variance Functions in Assays with Possibly Unequal Replication and Nonnormal Data

Estimation of parametric variance functions for assays relies on transformation of standard deviations based on replication at each concentration. The quality of such estimates has been shown to have direct impact on the quality of inference based on the fitted calibration curve. The theory of Davidian and Carroll (1987) is used to demonstrate that ignoring unequal replication can lead to bias and inefficiency in estimation and that weighting the common log-linear estimator to account for it can improve efficiency. A comparison of efficiency of estimation for different transformations for nonnormal distributions is given. An alternate method to account for such bias is investigated that may be useful for assays with large numbers of replicates and several outliers, and leads to a comparison of Gini's mean difference to sample standard deviation. A method for computing all of these estimators using standard software is described.