Applications of segmented regression models for biomedical studies

Abstract

In many biological models, a relationship between variables may be modeled as a linear or polynomial function that changes abruptly when an independent variable obtains a threshold level. Usually, the transition point is unknown, and a major objective of the analysis is its estimation. This type of model is known as a segmented regression model. We present two methods, Gallant and Fuller's (J Am. Stat. Assoc. 68: 144-147, 1973) method and Tishler and Zang's (J. Am. Stat. Assoc. 76: 980-987, 1981) method, using nonlinear least-squares techniques for estimating the transition point. We give the following three examples: a hypoglycemia study, a testosterone study, and an estimate of age-cortisol relationship. Simulation techniques are used to compare the two methods. We conclude that these models provide useful information and that the two methods studied produce essentially equivalent results. We recommend that both methods be used to analyze a data set if possible to avoid problems due to local minima and that if the results do not agree, then evaluation of the likelihood function in the range of the estimates be used to determine the best estimate.