Estimation of safe doses: critical review of the hockey stick regression method

The hockey stick regression method is a convenient method to estimate safe doses, which is a kind of regression method using segmented lines. The method seems intuitively to be useful, but needs the assumption of the existence of the positive threshold value. The validity of the assumption is considered to be difficult to be shown. The alternative methods which are not based on the assumption, are given under suitable dose-response curves by introducing a risk level. Here the method using the probit model is compared with the hockey stick regression method. Computational results suggest that the alternative method is preferable. Furthermore similar problems in the case that response is measured as a continuous value are also extended. Data exemplified are concerned with relations of SO2 to simple chronic bronchitis, relations of photochemical oxidants to eye discomfort and residual antibiotics in the lever of the chicks. These data was analyzed by the original authors under the assumption of the existence of the positive threshold values.