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Testing the product of slopes in related regressions.

MedStar author(s):

Citation: Advances & Applications in Statistics. 36(1):29-46, 2013 Sep 01PMID: 25346580Institution: MedStar Health Research InstituteForm of publication: Journal ArticleMedline article type(s): Journal ArticleYear: 2013 ISSN:

0972-3617

Name of journal: Advances and applications in statisticsAbstract: A study was conducted of the relationships among neuroprotective factors and cytokines in brain tissue of mice at different ages that were examined on the effect of dietary restriction on protection after experimentally induced brain stroke. It was of interest to assess whether the cross-product of the slopes of pairs of variables vs. age was positive or negative. To accomplish this, the product of the slopes was estimated and tested to determine if it is significantly different from zero. Since the measurements are taken on the same animals, the models used must account for the non-independence of the measurements within animals. A number of approaches are illustrated. First a multivariate multiple regression model is employed. Since we are interested in a nonlinear function of the parameters (the product) the delta method is used to obtain the standard error of the estimate of the product. Second, a linear mixed-effects model is fit that allows for the specification of an appropriate correlation structure among repeated measurements. The delta method is again used to obtain the standard error. Finally, a non-linear mixed-effects approach is taken to fit the linear-mixed-effects model and conduct the test. A simulation study investigates the properties of the procedure.All authors: Arumugam TV, Mattson MP, Morrell CH, Phillips T, Shetty V, Wan RFiscal year: FY2014Date added to catalog: 2018-05-08

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Item type	Current library	Collection	Call number	Status	Date due	Barcode
Journal Article	MedStar Authors Catalog	Article	25346580	Available		25346580

A study was conducted of the relationships among neuroprotective factors and cytokines in brain tissue of mice at different ages that were examined on the effect of dietary restriction on protection after experimentally induced brain stroke. It was of interest to assess whether the cross-product of the slopes of pairs of variables vs. age was positive or negative. To accomplish this, the product of the slopes was estimated and tested to determine if it is significantly different from zero. Since the measurements are taken on the same animals, the models used must account for the non-independence of the measurements within animals. A number of approaches are illustrated. First a multivariate multiple regression model is employed. Since we are interested in a nonlinear function of the parameters (the product) the delta method is used to obtain the standard error of the estimate of the product. Second, a linear mixed-effects model is fit that allows for the specification of an appropriate correlation structure among repeated measurements. The delta method is again used to obtain the standard error. Finally, a non-linear mixed-effects approach is taken to fit the linear-mixed-effects model and conduct the test. A simulation study investigates the properties of the procedure.

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