Abstract
We introduce a family of tests for regression coefficients based on signs of quantile regression residuals. In our approach, we first fit a quantile regression for the model where an independent variable of interest is not included in the set of model predictors (the null model). Then signs of residuals of this null model are tested for association with the predictor of interest. This conditionally exact testing procedure is applicable for randomized studies. Further, we extend this testing procedure to observational data when co-linearity between the variable of interest and other model predictors is possible. In the presence of possible co-linearity, tests for conditional association controlling for other model predictors are used. Monte Carlo simulation studies show superior performance of the introduced tests over several other widely available testing procedures. These simulations explore situations when normality of regression coefficients is not met. An illustrative example shows the use of the proposed tests for investigating associations of hypertension with quantiles of hemoglobin A1C change.
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Acknowledgements
Funding for this project was provided by the Advancing Healthier Wisconsin Research and Education Program under award 9520277. This publication was also supported by the National Center for Advancing Translational Sciences, National Institutes of Health, through Grant Number UL1TR001436. Its contents are solely the responsibility of the authors and do not necessarily represent the official views of the NIH.
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Tarima, S., Tarassenko, P., Tuyishimire, B., Sparapani, R., Rein, L., Meurer, J. (2018). Signs of Residuals for Testing Coefficients in Quantile Regression. In: Pilz, J., Rasch, D., Melas, V., Moder, K. (eds) Statistics and Simulation. IWS 2015. Springer Proceedings in Mathematics & Statistics, vol 231. Springer, Cham. https://doi.org/10.1007/978-3-319-76035-3_15
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