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• W2130955501 abstract "In this chapter, two theoretical developments, motivated by practice, are discussed. These are (1) the construction of simultaneous confidence bands for the survival function S(t|z) = S(t|z1, …, zk), and (2) the implementation of the results of multivariable survival analysis, as described in Chapter 14, in decision analysis. This implementation is performed from the medical as well as from the mathematical side. A (two-sided) simultaneous confidence band is a generalisation of a confidence interval for a fixed time t. It consists of a lower boundary S(t|z) and an upper boundary S¯(t|z) such that, for a given interval [tmin, tmax] and a given α ∈ [0, 1], the probability that the unknown survival function lies between S(t|z) and S¯(t|z) for every t ∈ [tmin, tmax] is equal to 1 - α. The calculation of the width of a band with a realistic shape presents a non-trivial mathematical problem, which is solved by using an integral equation approach. Such a confidence band can be used (among others) to test the null hypothesis H0:S(t|z) = S0(t), where S0(t) is a reference survival function (for example, of the normal population at a certain age). In Section 2 of this chapter, the following problem is considered. Suppose one is interested in choosing between two treatments, which we shall call A and B. (A may denote ‘to treat’ and B ‘not to treat’, according to some method.) We further assume that data are available from patients who have been treated according to A and from (other) patients who have been treated according to B. The question is whether for a new patient with covariables z1, …, zk, on the basis of the available data, (1) treatment A has to be recommended, (2) treatment B has to be recommended, or (3) no recommendation should be made. Our analysis of this problem is based on the estimated survival functions of the ‘effective lifetime’ under each treatment. The effective lifetime is determined by subjective ratios, established in a discussion with the patient, of the qualities of life under various conditions. Sometimes, the difference between two ‘effective’ survival functions is well expressed by a one-dimensional parameter (such as the ratio of the mean, or median, effective survival times), the estimator of which is asymptotically normally distributed. For such a situation, the (two-sided) Neyman-Pearson testing theory is replaced by a loss-function formulation. This formulation leads to the same partition of the outcome space R as does some two-sided test. It adequately reflects, however, the three-decision character of the above mentioned problem, and allows a motivated choice of the level α of the corresponding (two-sided) test. In a traditional approach, this level is often set to 5% or 1%. The same remarks about notation and the list of references apply as in Chapter 14." @default.
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• W2130955501 date "1991-01-01" @default.
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• W2130955501 title "15 Confidence bands for the survival function S(t|z) and the relation with decision analysis: Theory" @default.
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• W2130955501 doi "https://doi.org/10.1016/s0169-7161(05)80171-3" @default.
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