Likelihood approaches to the non-parametric two-sample problem for right-censored data

2006 ◽  
Vol 25 (13) ◽  
pp. 2284-2298 ◽  
Author(s):  
James F. Troendle ◽  
Kai F. Yu
Keyword(s):  
Censored Data ◽  
Sample Problem ◽  
Right Censored Data ◽  
Two Sample Problem ◽  
Non Parametric

On the fraction of random points by specified nearest-neighbour interrelations and degree of attraction

1987 ◽  
Vol 19 (04) ◽  
pp. 873-895
Author(s):  
Norbert Henze
Keyword(s):  
Nearest Neighbour ◽  
Sample Problem ◽  
Random Vectors ◽  
Almost Everywhere ◽  
Two Sample Problem ◽  
Arbitrary Norm ◽  
Non Parametric

Let Z 1, …, Zn be i.i.d. random vectors (‘points') defined in having common density f(x) that is assumed to be continuous almost everywhere. For a fixed but otherwise arbitrary norm |.| on , consider the fraction Vn of those points Z 1, …, Zn that are the lth nearest neighbour (with respect to |.|) to their own kth nearest neighbour, and write Sn for the fraction of points that are the nearest neighbour of exactly k other points. We derive the stochastic limits of Vn and Sn, as n tends to∞, and show how the results may be applied to the multivariate non-parametric two-sample problem.

scholarly journals Regression Models for Interval Censored Data Using Parametric Pseudo-Observations

2020 ◽  
Author(s):  
Martin Nygård Johansen ◽  
Søren Lundbye-Christensen ◽  
Jacob Moesgaard Larsen ◽  
Erik Thorlund Parner
Keyword(s):  
Censored Data ◽  
Interval Censoring ◽  
Regression Modeling ◽  
Implantable Cardioverter Defibrillators ◽  
Interval Censored Data ◽  
Right Censored Data ◽  
Association Measures ◽  
Real Dataset ◽  
Interval Censored ◽  
Non Parametric

Abstract Background: Time-to-event data that is subject to interval censoring is common in the practice of medical research and versatile statistical methods for estimating associations in such settings have been limited. For right censored data, non-parametric pseudo-observations have been proposed as a basis for regression modeling with the possibility to use different association measures. In this article, we propose a method for calculating pseudo-observations for interval censored data. Methods: We develop an extension of a recently developed set of parametric pseudo-observations based on a spline-based flexible parametric estimator. The inherent competing risk issue with an interval censored event of interest necessitates the use of an illness-death model, and we formulate our method within this framework. To evaluate the empirical properties of the proposed method, we perform a simulation study and calculate pseudo-observations based on our method as well as alternative approaches. We also present an analysis of a real dataset on patients with implantable cardioverter-defibrillators who are monitored for the occurrence of a particular type of device failures by routine follow-up examinations. In this dataset, we have information on exact event times as well as the interval censored data, so we can compare analyses of pseudo-observations based on the interval censored data to those obtained using the non-parametric pseudo-observations for right censored data. Results: Our simulations show that the proposed method for calculating pseudo-observations provides unbiased estimates of the cumulative incidence function as well as associations with exposure variables with appropriate coverage probabilities. The analysis of the real dataset also suggests that our method provides estimates which are in agreement with estimates obtained from the right censored data. Conclusions: The proposed method for calculating pseudo-observations based on the flexible parametric approach provides a versatile solution to the specific challenges that arise with interval censored data. This solution allows regression modeling using a range of different association measures.

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