Proportional Hazards models have been widely used to analyze survival data. In many cases survival data do not verify the assumption of proportional hazards. An alternative to the PH models with more relaxed conditions are Accelerated Failure Time models. These models are fairly commonly used in the field of manufacturing, but they are more and more frequent for modeling clinical trial data. They focus on the direct effect of the explanatory variables on the survival function allowing an easier interpretation of the effect of the corresponding covariates on the survival time. Optimal experimental designs are computed in this framework for Type I and random arrival. The results are applied to clinical models used to prevent tuberculosis in Ugandan adults infected with HIV.
Optimal designs under a survival analysis framework have been rarely considered in the literature. In this paper, an optimal design theory is developed for the typical Cox regression problem. Failure time is modeled according to a probability distribution depending on some explanatory variables through a linear model. At the end of the study, some units will not have failed and thus their time records will be censored. In order to deal with this problem from an experimental design point of view it will be necessary to assume a probability distribution for the time an experimental unit enters the study.Then an optimal conditional design will be computed at the beginning of the study for any possible given time. Thus, every time a new unit enters the study, there is an experimental design to be determined. A particular and simple case is used throughout the paper in order to illustrate the procedure.
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