The construction of the simultaneous confidence bands for the integrated hazard function is considered. The Nelson–Aalen estimator is used. The simultaneous confidence bands based on bootstrap methods are presented. Two methods of construction of such confidence bands are proposed. The weird bootstrap method is used for resampling. Simulations are made to compare the actual coverage probability...

Incompleteness is a major feature of time-to-event data. As one type of incompleteness, truncation refers to the unobservability of the time-to-event variable because it is smaller (or greater) than the truncation variable. A truncated sample always involves left and right truncation. Left truncation has been studied extensively while right truncation has not received the same level of attentio...

This thesis centers on nonparametric inferences of the cumulative hazard function of a right truncated variable. We present three variance estimators for the Nelson-Aalen estimator of the cumulative hazard function and conduct a simulation study to investigate their performances. A close match between the sampling standard deviation and the estimated standard error is observed when an estimated...

The aim of fitting a Cox model to time-to-event data is to estimate the effect of covariates on the baseline hazard function. The baseline hazard function, not itself estimated within the model, is the hazard function obtained when all covariate are set to zero. In several applications, it is important to have an explicit, preferably smooth, estimate of the baseline hazard function, or more gen...

HAZOP studies are widely accepted in chemical and petroleum industries as the method for conducting process hazard analysis related to design, maintenance and operation of the systems. In this paper, a HAZOP reasoning method based on function-oriented modelling, multilevel flow modelling (MFM) is extended with function roles to complete HAZOP studies in principle. A graphical MFM editor, which ...

We investigate the problem of estimating the best binary decision tree approximation to the baseline hazard function in the Cox proportional hazards model. Our motivation is to find an effective way of condensing key functional information in the baseline hazard into a small number of estimable parameters. The parameters consist of a threshold and two hazard levels, one to the left of the thres...

Drought risk reduction and its direct indirect impacts have gained worldwide relevance during the last decades. This paper presents a review of basic conceptual methodological tools to analyze drought in given system. The fundamental components are described, conceived primarily as function hazard (or specific danger, which this case is phenomenon); exposure (people, property, livelihoods, syst...

BACKGROUND An inverse relationship between experience and risk of injury has been observed in many occupations. Due to statistical challenges, however, it has been difficult to characterize the role of experience on the hazard of injury. In particular, because the time observed up to injury is equivalent to the amount of experience accumulated, the baseline hazard of injury becomes the main par...