APPLICATIONS OF SEGMENTED REGRESSION-MODELS FOR BIOMEDICAL STUDIES

In many biological models, a relationship between variables may be mod eled as a linear or polynomial function that changes abruptly when an independent variable obtains a threshold level. Usually, the transitio n point is unknown, and a major objective of the analysis is its estim ation. This type of model is known as a segmented regression model. We present two methods, Gallant and Fuller's (J. Am. Stat. Assoc. 68: 14 4-147, 1973) method and Tishler and Zang's (J. Am. Stat. Assoc. 76: 98 0-987, 1981) method, using nonlinear least-squares techniques for esti mating the transition point. We give the following three examples: a h ypoglycemia study, a testosterone study, and an estimate of age-cortis ol relationship. Simulation techniques are used to compare the two met hods. We conclude that these models provide useful information and tha t the two methods studied produce essentially equivalent results. We r ecommend that both methods be used to analyze a data set if possible t o avoid problems due to local minima and that if the results do not ag ree, then evaluation of the likelihood function in the range of the es timates be used to determine the best estimate.