Practical Robust Fit of Enzyme Inhibition Data

This chapter describes the practical robust fit of enzyme inhibition data. The analysis of enzyme inhibition data in the context of preclinical drug screening presents unique challenges to the data analyst. Outliers are data points that are affected by gross errors caused by malfunctioning volumetric equipment, by a human error in data entry, or by countless other possible mishaps. It is shown that Huber's Minimax approach to robust statistical estimation is particularly preferable over the conventional least-squares analysis. The ordinary least square (OLS) estimate of the model parameters is sensitive to the presence of outliers, which has led to the design of various alternatives. All good data points are assigned the same weight in the iteratively reweighted series of LS estimations, exactly as they are in OLS. The practical success of Huber's method applied even to relatively small data sets, such as those arising in preclinical screening, is due to the fact that the method behaves as OLS does if the data are good, but at the same time it gives the least absolute deviation treatment to suspected outliers, while maintaining 95% asymptotic efficiency. It is found that both standardized residuals and leverages play a role in the Huber's method of robust regression analysis, implemented as iteratively re-weighted least squares.