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• W85832130 abstract "Y1=(X2+f2xi+ei, i=zT+l,..., (1) where the ei are independently, normally distributed, N(O, a2), 1 < T < T (al f,) $ (a2, ,B2) and all the parameters a,, f1 a25 ,B25 a2, T are unknown. The two straight lines in (1) intersect at a point with x coordinate v = (a1 a2)/(12 fl1). If we further assume that X1 < X2 <... < XT (in many applications, x will denote time), it is useful to distinguish two versions of (1) according to whether v satisfies x, < v < x+ 1 or not. When this constraint is assumed, we shall refer to the constrained case of switching straight lines. It has been found see, for example, Knapp et al. (1977)-that the constrained version provides a satisfactory statistical model for monitoring the function of renal transplants. Following a transplant, daily measurements are made of serum-creatinine, a substance which indicates the level of functioning of the patient's kidney and a plot of the reciprocal of bodyweight corrected serum-creatinine (y) is then made against time (x). Fig. 1 shows part of two typical plots obtained from patients undergoing treatment at the City Hospital, Nottingham. An increasing straight line indicates successful functioning of the transplanted kidney. A sudden switch to a decreasing straight line indicates that rejection has occurred. It might be argued that rejection is not an instantaneous process, so that the sharp intersection of the two lines is a fiction, and an approach assuming a less sharp transition, such as that of Bacon and Watts (1971), might be more reasonable. On present evidence, however, any transition period would appear to be usually very short compared with the interval between measurements, and so the switching straight line model provides a reasonable approximation. With this assumption, in the renal transplant application the intersection point, y, corresponds to the time at which a rejection occurs. This parameter is of very great interest, both in the treatment of individual patients and because inferences about v for each of a number of patients permit inferences about daily and hourly variations in the rates of rejection. This, in turn, has implications for treatment and monitoring procedures in the hospital (see Knapp et al., 1979)." @default.
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• W85832130 date "1980-01-01" @default.
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• W85832130 title "Straight Lines with a Change-Point: A Bayesian Analysis of Some Renal Transplant Data" @default.
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• W85832130 doi "https://doi.org/10.2307/2986304" @default.
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