Economou Polychronis, Batsidis Apostolos, Tzavelas George, Alexopoulos Panagiotis
Department of Civil Engineering, University of Patras, Rion-Patras, Greece.
Department of Mathematics, University of Ioannina, Ioannina, Greece.
Biom J. 2020 Jan;62(1):238-249. doi: 10.1002/bimj.201900046. Epub 2019 Nov 7.
One reason for observing in practice a false positive or negative correlation between two random variables, which are either not correlated or correlated with a different direction, is the overrepresentation in the sample of individuals satisfying specific properties. In 1946, Berkson first illustrated the presence of a false correlation due to this last reason, which is known as Berkson's paradox and is one of the most famous paradox in probability and statistics. In this paper, the concept of weighted distributions is utilized to describe Berskon's paradox. Moreover, a proper procedure is suggested to make inference for the population given a biased sample which possesses all the characteristics of Berkson's paradox. A real data application for patients with dementia due to Alzheimer's disease demonstrates that the proposed method reveals characteristics of the population that are masked by the sampling procedure.
在实践中观察到两个随机变量之间存在假正相关或假负相关（这两个随机变量要么不相关，要么呈不同方向的相关）的一个原因是，满足特定属性的个体在样本中的过度代表性。1946年，伯克森首次阐述了由于这最后一个原因而出现的假相关，这被称为伯克森悖论，是概率和统计学中最著名的悖论之一。在本文中，加权分布的概念被用于描述伯克森悖论。此外，针对具有伯克森悖论所有特征的有偏样本，建议了一种合适的程序来对总体进行推断。一项针对阿尔茨海默病所致痴呆患者的实际数据应用表明，所提出的方法揭示了被抽样程序掩盖的总体特征。
