Rank-based estimate of four-parameter logistic model

During drug development, the calculation of inhibitory concentration that results in a response of 50% (IC50) 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 IC50 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 IC50 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.