Nonparametric estimation of the survival function from censored data based on relative risk function

1998 ◽  
Vol 27 (8) ◽  
pp. 1991-2012 ◽  
Author(s):  
A.A. Abdushukurov
2020 ◽  
Vol 72 (2) ◽  
pp. 111-121
Author(s):  
Abdurakhim Akhmedovich Abdushukurov ◽  
Rustamjon Sobitkhonovich Muradov

At the present time there are several approaches to estimation of survival functions of vectors of lifetimes. However, some of these estimators either are inconsistent or not fully defined in range of joint survival functions and therefore not applicable in practice. In this article, we consider three types of estimates of exponential-hazard, product-limit, and relative-risk power structures for the bivariate survival function, when replacing the number of summands in empirical estimates with a sequence of Poisson random variables. It is shown that these estimates are asymptotically equivalent. AMS 2000 subject classification: 62N01


Author(s):  
Rustamjon S. Muradov

At present there are several approaches to estimate survival functions of vectors of lifetimes. However, some of these estimators are either inconsistent or not fully defined in the range of joint survival functions. Therefore they are not applicable in practice. In this paper three types of estimates of exponential-hazard, product-limit and relative-risk power structures for the bivariate survival function are considered when the number of summands in empirical estimates is replaced with a sequence of Poisson random variables. It is shown that proposed estimates are asymptotically equivalent. Keywords: bivariate survival function, Poisson random variables, empirical estimates


2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Ian D. Buller ◽  
Derek W. Brown ◽  
Timothy A. Myers ◽  
Rena R. Jones ◽  
Mitchell J. Machiela

Abstract Background Cancer epidemiology studies require sufficient power to assess spatial relationships between exposures and cancer incidence accurately. However, methods for power calculations of spatial statistics are complicated and underdeveloped, and therefore underutilized by investigators. The spatial relative risk function, a cluster detection technique that detects spatial clusters of point-level data for two groups (e.g., cancer cases and controls, two exposure groups), is a commonly used spatial statistic but does not have a readily available power calculation for study design. Results We developed sparrpowR as an open-source R package to estimate the statistical power of the spatial relative risk function. sparrpowR generates simulated data applying user-defined parameters (e.g., sample size, locations) to detect spatial clusters with high statistical power. We present applications of sparrpowR that perform a power calculation for a study designed to detect a spatial cluster of incident cancer in relation to a point source of numerous environmental emissions. The conducted power calculations demonstrate the functionality and utility of sparrpowR to calculate the local power for spatial cluster detection. Conclusions sparrpowR improves the current capacity of investigators to calculate the statistical power of spatial clusters, which assists in designing more efficient studies. This newly developed R package addresses a critically underdeveloped gap in cancer epidemiology by estimating statistical power for a common spatial cluster detection technique.


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