The Application of Robust Calibration to Radioimmunoassay

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Abstract
The minute concentrations of many biochemically and clinically important substances are currently estimated by radioimmunoassay (RIA). Traditionally, the most popular approaches to statistical analysis of RIA data have been to linearize the data through transformation and fit the calibration curve using least squares or to directly fit a nonlinear calibration curve using least squares. Estimates of the hormone concentration in patients are then obtained using this curve. The transformation is frequently unsuccessful in linearizing the data, and the least squares fit can lead to erroneous results in both approaches since the many sources of error which exist in the RIA process often result in outlier observations. An approach to the analysis of RIA data which incorporates robust estimation methods was described. An algorithm was presented for obtaining M-estimates of nonlinear calibration curves. Curves to be fitted were modified hyperbolae based on 12-16 observations. A procedure based on the application of the Bonferroni Inequality was presented for obtaining tolerance-like interval estimates of the concentration of the hormone of interest in the patients. Results of simulations were cited to support the method of construction of confidence bands for the fitted calibration curve. Data obtained from the Veteran''s Hospital, Buffalo, New York [USA] were used to illustrate the application of the algorithm which was presented.

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