In some long term studies, a series of dependent and possibly censored failure times may be observed. Suppose that the failure times have a common marginal distribution function, and inferences about it are of our interest. The main result of this paper is that of providing, under certain regularity conditions, the Kaplan-Meier estimator can be expressed as the mean of random variables, with a ...

The relative reduction of risk for all-cause mortality among the elderly has been described as attenuated compared to younger subjects, but the risk for all-cause mortality increases with age when absolute risk is considered. The objectives of the present inquiry were to calculate the relative and absolute risks of all-cause mortality based on incidence rate ratios, and summarize these risks fo...

The Kaplan-Meier (KM) method is used to analyze ‘time-toevent’ data. The outcome in KM analysis often includes allcause mortality, but could also include other outcomes such as the occurrence of a cardiovascular event. The purpose of this article is to explain the basic concepts of the KM method, to provide some guidance regarding the presentation of the KM results and to discuss some important...

We estimate the lower bound of the first non-zero eigenvalue of a compact Riemannian manifold with negative lower bound of Ricci curvature in terms of the diameter and the lower bound of Ricci curvature and give an affirmative answer to the conjecture of H. C. Yang.

The nonparametric minimax estimation of an analytic density at a given point, under random censorship, is considered. Although the problem of estimating density is known to be irregular in a certain sense, we make some connections relating this problem to the problem of estimating smooth functionals. Under condition that the censoring is not too severe, we establish the exact limiting behavior ...

The minimum averaged mean squared error nonparametric adaptive weights use data from m possibly different populations to infer about one population of interest. The definition of these weights is based on the properties of the empirical distribution function. We use the Kaplan-Meier estimate to let the weights accommodate right-censored data and use them to define the weighted Kaplan-Meier esti...

BACKGROUND Cardiovascular disease (CVD) prevention guidelines are generally based on the absolute risk of a CVD event, but there is increasing interest in using 'heart age' to motivate lifestyle change when absolute risk is low. Previous studies have not compared heart age to 5-year absolute risk, or investigated the impact of younger heart age, graphical format, and numeracy. OBJECTIVE Compa...

In survival analysis, often times the pattern of instantaneous risk over time is more interesting than that of the cumulative risk. For this case, a nonparametric hazard function estimate is more appropriate for summarizing the risk experience of a group of patients than the corresponding Kaplan-Meier estimate. In comparing a new treatment with a standard therapy, it is important to know if the...