Decomposing Pearson's χ2 test: A linear regression and its departure from linearity.

Annals of Human Genetics
Zhengyang ZhouChao Xing

Abstract

In case-control genetic association studies, a standard practice is to perform the Cochran-Armitage (CA) trend test under the assumption of the additive model because of its robustness. We could even identify situations in which it outperformed the analysis model consistent with the underlying inheritance mode. In this article, we analytically reveal the statistical basis that leads to the phenomenon. By elucidating the origin of the CA trend test as a linear regression model, we decompose Pearson's χ2 -test statistic into two components-one is the CA trend test statistic that measures the goodness of fit of the linear regression model, and the other measures the discrepancy between data and the linear regression model. Under this framework, we show that the additive coding scheme, as well as the multiplicative coding scheme, increases the coefficient of determination of the regression model by increasing the spread of data points. We also obtain the conditions under which the CA trend test statistic equals the MAX statistic and Pearson's χ2 -test statistic.

References

Dec 1, 1989·American Journal of Medical Genetics·R C Elston
Jan 30, 2008·Genetic Epidemiology·Juan R GonzálezVictor Moreno
Feb 3, 2009·Annals of Human Genetics·Gang ZhengYaning Yang
Dec 22, 2009·Genetic Epidemiology·Chia-Ling Kuo, Eleanor Feingold
Apr 11, 2013·European Journal of Human Genetics : EJHG·Christina LoleyAndreas Ziegler
Feb 9, 2017·Human Heredity·Susan E Hodge, David A Greenberg

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Citations

Nov 29, 2020·Brazilian Journal of Physical Therapy·Dafne Port NascimentoLeonardo Oliveira Pena Costa

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