Battered data--some clinical effects of the abuse of multiple regression methods: the NSD
The NSD equation, D . 1850 x T0.11 x N0.24, is a celebrated transmogrification of Cohen's two well-known collations of data on response to clinical irradiations (3 degrees erythema and 0.90 ablation of skin cancer) in which the relation of D and T is fixed by the data selected by Cohen and the additional constraint that N correspond to a schedule of five treatments per week is imposed subsequently by Ellis. The present paper shows that the equation, if correct, would have little clinical significance because the proportion, P, in which the dose, D, elicits the 3 degree erythema is unspecified: D . D(P) . D(.). The paper shows that the NSD equation is also incorrect because the ad hoc method by which Ellis estimates the exponents is inconsistent with the constraints imposed by Cohen and Ellis upon the parameters of the multivariate frequency distribution of the data set. The paper shows that the method by which the correct LS estimates of the exponents were obtained from the Cohen-Ellis data is consistent with these constraints and, therefore, this equation is a correct graduation of any other set of treatment regimens which is also consistent with the Cohen and Ellis constraints. The paper further shows that for such data sets there are, in fact, only two independent continuous variables, either D and T or D and N, since the Ellis constraint requires that N and T be collinear. The two characteristic features of the Cohen (Ellis)-type data which impede the construction of useful estimates of the putative separate effects of N and T upon the response of tissues to irradiation are that (1) these data do not include specifications of either a tissue defect or its incidence, and (2) the variables N and T are collinear. Appendices I and II describe methods by which the effects of these features may be eliminated (I) or reduced (II).
- Research Organization:
- University of South Alabama, Department of Radiology, Mobile
- OSTI ID:
- 5404737
- Journal Information:
- Med. Phys.; (United States), Journal Name: Med. Phys.; (United States) Vol. 8:6; ISSN MPHYA
- Country of Publication:
- United States
- Language:
- English
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