The aim is the prediction of the failure time of prestressed concrete beams under low cyclic load. Since the experiments last long for low load, accelerated failure tests with higher load are conducted. However, the accelerated tests are expensive so that only few tests are available. To obtain a more precise failure time prediction, the additional information of time points of breakage of tension wires is used. These breakage time points are modeled by a nonlinear birth process. This allows not only point prediction of a critical number of broken tension wires but also prediction intervals which express the uncertainty of the prediction.
Based on accelerated lifetime experiments, we consider the problem of constructing prediction intervals for the time point at which a given number of components of a load-sharing system fails. Our research is motivated by lab experiments with prestressed concrete beams where the tension wires fail successively. Due to an audible noise when breaking, the time points of failure could be determined exactly by acoustic measurements. Under the assumption of equal load sharing between the tension wires, we present a model for the failure times based on a birth process. We provide a model check based on a Q-Q plot including a simulated simultaneous confidence band and four simulation-free prediction methods. Three of the prediction methods are given by confidence sets where two of them are based on classical tests and the third is based on a new outlier-robust test using sign depth. The fourth method uses the implicit function theorem and the-method to get prediction intervals without confidence sets for the unknown parameter. We compare these methods by a leave-one-out analysis of the data on prestressed concrete beams. Moreover, a simulation study is performed to discuss advantages and drawbacks of the individual methods.
BackgroundDisease progression models are important for understanding the critical steps during the development of diseases. The models are imbedded in a statistical framework to deal with random variations due to biology and the sampling process when observing only a finite population. Conditional probabilities are used to describe dependencies between events that characterise the critical steps in the disease process.Many different model classes have been proposed in the literature, from simple path models to complex Bayesian networks. A popular and easy to understand but yet flexible model class are oncogenetic trees. These have been applied to describe the accumulation of genetic aberrations in cancer and HIV data. However, the number of potentially relevant aberrations is often by far larger than the maximal number of events that can be used for reliably estimating the progression models. Still, there are only a few approaches to variable selection, which have not yet been investigated in detail.ResultsWe fill this gap and propose specifically for oncogenetic trees ten variable selection methods, some of these being completely new. We compare them in an extensive simulation study and on real data from cancer and HIV. It turns out that the preselection of events by clique identification algorithms performs best. Here, events are selected if they belong to the largest or the maximum weight subgraph in which all pairs of vertices are connected.ConclusionsThe variable selection method of identifying cliques finds both the important frequent events and those related to disease pathways.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-017-1762-1) contains supplementary material, which is available to authorized users.
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