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Rank‐based estimate of four‐parameter logistic model
Author(s) -
Crimin Kimberly S.,
McKean Joseph W.,
Vidmar Thomas J.
Publication year - 2012
Publication title -
pharmaceutical statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 38
eISSN - 1539-1612
pISSN - 1539-1604
DOI - 10.1002/pst.536
Subject(s) - outlier , wilcoxon signed rank test , parameterized complexity , rank (graph theory) , statistics , goodness of fit , non linear least squares , least squares function approximation , mathematics , estimation theory , logistic regression , robust statistics , computer science , algorithm , combinatorics , estimator , mann–whitney u test
During drug development, the calculation of inhibitory concentration that results in a response of 50% ( IC 50 ) is performed thousands of times every day. The nonlinear model most often used to perform this calculation is a four‐parameter logistic, suitably parameterized to estimate the IC 50 directly. When performing these calculations in a high‐throughput mode, each and every curve cannot be studied in detail, and outliers in the responses are a common problem. A robust estimation procedure to perform this calculation is desirable. In this paper, a rank‐based estimate of the four‐parameter logistic model that is analogous to least squares is proposed. The rank‐based estimate is based on the Wilcoxon norm. The robust procedure is illustrated with several examples from the pharmaceutical industry. When no outliers are present in the data, the robust estimate of IC 50 is comparable with the least squares estimate, and when outliers are present in the data, the robust estimate is more accurate. A robust goodness‐of‐fit test is also proposed. To investigate the impact of outliers on the traditional and robust estimates, a small simulation study was conducted. Copyright © 2012 John Wiley & Sons, Ltd.