OPTIMAL DESIGNS FOR FITTING A PROPORTIONAL HAZARDS REGRESSION MODEL TO DATA SUBJECT TO CENSORING |
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Authors: | Niels Becker Barry McDonald Celestine Khoo |
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Institution: | La. Trobe University, Bundoora, Victoria |
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Abstract: | Suppose the probability model for failure time data, subject to censoring, is specified by the hazard function λ(t)exp(βT x), where x is a vector of covariates. Analytical difficulties involved in finding the optimal design are avoided by assuming that λ is completely specified and by using D-optimality based on the information matrix for β Optimal designs are found to depend on β, but some results of practical consequence are obtained. It is found that censoring does not affect the choice of design appreciably when βT x ≥ 0 for all points of the feasible region, but may have an appreciable effect when βixi 0, for all i and all points in the feasible experimental region. The nature of the effect is discussed in detail for the cases of one and two parameters. It is argued that in practical biomedical situations the optimal design is almost always the same as for uncensored data. |
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Keywords: | Censored data D-optimal designs proportional hazards model |
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