Dose–response modelling for bivariate covariates with and without a spike at zero: theory and application to binary outcomes
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Dose–response modelling for bivariate covariates with and without a spike at zero: theory and application to binary outcomes. / Lorenz, Eva; Jenckner, Carolin; Sauerbrei, Willi; Becher, Heiko.
In: STAT NEERL, Vol. 69, No. 4, 11.2015, p. 374-398.Research output: SCORING: Contribution to journal › SCORING: Journal article › Research › peer-review
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TY - JOUR
T1 - Dose–response modelling for bivariate covariates with and without a spike at zero: theory and application to binary outcomes
AU - Lorenz, Eva
AU - Jenckner, Carolin
AU - Sauerbrei, Willi
AU - Becher, Heiko
PY - 2015/11
Y1 - 2015/11
N2 - In epidemiology and clinical research, there is often a proportion of unexposedindividuals resulting in zero values of exposure, meaning thatsome individuals are not exposed and those exposed have some continuousdistribution. Examples are smoking or alcohol consumption. Wewill call these variables with a spike at zero (SAZ). In this paper, we performeda systematic investigation on how to model covariates with aSAZ and derived theoretical odds ratio functions for selected bivariatedistributions. We consider the bivariate normal and bivariate log normaldistribution with a SAZ. Both confounding and effect modification can beelegantly described by formalizing the covariance matrix given the binaryoutcome variable Y. To model the effect of these variables, weuse a procedure based on fractional polynomials first introduced byRoyston and Altman (1994, Applied Statistics 43: 429–467) and modifiedfor the SAZ situation (Royston and Sauerbrei, 2008, Multivariablemodel-building: a pragmatic approach to regression analysis based onfractional polynomials for modelling continuous variables,Wiley; Becheret al., 2012, Biometrical Journal 54: 686–700). We aim to contribute totheory, practical procedures and application in epidemiology and clinicalresearch to derive multivariable models for variables with a SAZ. As anexample, we use data from a case–control study on lung cancer.
AB - In epidemiology and clinical research, there is often a proportion of unexposedindividuals resulting in zero values of exposure, meaning thatsome individuals are not exposed and those exposed have some continuousdistribution. Examples are smoking or alcohol consumption. Wewill call these variables with a spike at zero (SAZ). In this paper, we performeda systematic investigation on how to model covariates with aSAZ and derived theoretical odds ratio functions for selected bivariatedistributions. We consider the bivariate normal and bivariate log normaldistribution with a SAZ. Both confounding and effect modification can beelegantly described by formalizing the covariance matrix given the binaryoutcome variable Y. To model the effect of these variables, weuse a procedure based on fractional polynomials first introduced byRoyston and Altman (1994, Applied Statistics 43: 429–467) and modifiedfor the SAZ situation (Royston and Sauerbrei, 2008, Multivariablemodel-building: a pragmatic approach to regression analysis based onfractional polynomials for modelling continuous variables,Wiley; Becheret al., 2012, Biometrical Journal 54: 686–700). We aim to contribute totheory, practical procedures and application in epidemiology and clinicalresearch to derive multivariable models for variables with a SAZ. As anexample, we use data from a case–control study on lung cancer.
U2 - 10.1111/stan.12064
DO - 10.1111/stan.12064
M3 - SCORING: Journal article
VL - 69
SP - 374
EP - 398
JO - STAT NEERL
JF - STAT NEERL
SN - 0039-0402
IS - 4
ER -
