Abstract
Muscular strength, usually quantified through the grip strength, can be used in humans and animals as an indicator of neuromuscular function or to assess hand function in patients with trauma or congenital problems. Because grip strength cannot be accurately measured, several contaminated measurements are often taken on the same subject. A research interest in grip strength studies is estimating the conditional quantiles of the latent grip strength, which can be used to construct conditional grip strength charts. Current work in the literature often applies conventional quantile regression method using the subject-specific average of the repeated measurements as the response variable. We show that this approach suffers from model misspecification and often leads to biased estimates of the conditional quantiles of the latent grip strength. We propose a new semi-nonparametric estimation approach, which is able to account for measurement errors and allows the subject-specific random effects to follow a flexible distribution. We demonstrate through simulation studies that the proposed method leads to consistent and efficient estimates of the conditional quantiles of the latent response variable. The value of the proposed method is assessed by analyzing a grip strength data set on laboratory mice.
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References
Barreiro, E., Marin-Corral, J., Sanchez, F., Mielgo, V., Alvarez, F.J., Galdiz, J.B., Gea, J.: Reference values of respiratory and peripheral muscle function in rats. J. Anim. Physiol. Anim. Nutr. 94, 393–401 (2010)
Caroll, R.J., Ruppert, D., Stefanski, L.A., Crainiceanu, C.M.: Measurement Error in Nonlinear Models: A Modern Perspective. Chapman & Hall/CRC, Boca Raton, FL (2006)
Chen, J., Zhang, D., Davidian, M.: A Monte Carlo EM algorithm for generalized linear mixed models with flexible random effects distribution, Biostatistics 3, 347–360 (2002)
Cook, J.R., Stefanski, L.A., Simulation-extrapolation estimation in parametric measurement error models, Journal of the American Statistical Association 89, 1314–1328 (1994)
Davidian, M., Gallant, A.R.: The nonlinear mixed effects model with a smooth random effects density, Biometrika. 80, 475–488 (1993)
Davidian, M., Giltinan, D.M.: Nonlinear Models for Repeated Measurement Data. Chapman & Hall, London; New York (1995)
Delaigle, A., Hall, P., Meister, A.: On deconvolution with repeated measurements. The Annals of Statistics 36, 665–685 (2008)
Fenton, V., Gallant, R.: Qualitative and asymptotic performance of SNP density estimators. J. Econ. 74, 77–118 (1996)
Gallant, A.R., Nychka, D.W.: Semi-nonparametric maximum likelihood estimation. Econometrica: Journal of the Econometric Society 55, 363–390 (1987)
Hannan, E.J.: Rational transfer function approximation. Statistical Science 2, 135–151 (1987)
He, X.: Quantile curves without crossing. The American Statistician 51, 186–192 (1997)
Jin, Z., Lin, D.Y., Wei, L.J., Ying, Z.: Rank-based inference for accelerated failure time model. Biometrika 90, 341–353 (2003)
Jin, Z., Ying, Z., Wei, L.J.: A simple resampling method by perturbing the minimand. Biometrika 88, 381–390 (2001)
Koenker, R.: Quantile Regression. First Edition, Cambridge University Press (2005)
Koenker, R., Bassett, G.: Regression quantiles. Econometrica 46, 33–50 (1978)
The Jackson Laboratory: Multi-system analysis of physiology on 7 inbred strains of mice. MPD:Jaxwest1. Mouse Phenome Database web site, The Jackson Laboratory. Bar Harbor, Maine USA, http://phenome.jax.org Accessed 23 October 2012
Li, T., Vuong, Q.: Nonparametric estimation of the measurement error model using multiple indicators. Journal of Multivariate Analysis 65, 139–165 (1998)
Matine, P., van Nes, S., Vanhoutte, E., Bakkers, M., van Doorn, P., Merkies, I., Faber, C.: Revised normative values fro grip strength with the Jamar dynamometer. Journal of Peripheral Nervous System 16, 47–50 (2011)
Molenaar, H.M.T., Selles, R.W., Zuidam, J.M., Willemsen, S.P., Stam, H.J., Hovius, S.E.R.: Growth diagrams for grip strength in children. Clin. Orthop. 468, 217–223 (2010)
Parzen, M.I., Wei, L.J., Ying, Z.: A resampling method basd on pivotal estimating functions. Biometrika 81, 341–350 (1994)
Reich,B.J., Bondell,H.D., Wang,H.J.: Flexible Bayesian quantile regression for independent and clustered data. Biostatistics 11, 337–352 (2010)
Schechtman, E., Spiegelman, C.: Mitigating the effect of measurement errors in quantile estimation. Statistics & Probability Letters 77, 514–524 (2007)
Staudenmayer, J., Ruppert, D., Buonaccorsi, J.P.: Density estimation in the presence of heteroscedastic measurement error. Journal of the American Statistical Association 103, 726–736 (2008)
Takada,T.: Asymptotic and qualitative performance of non-parametric density estimators: a comparative study. Econometrics Journal 11, 573–592 (2008)
Tooze, J.A., Kipnis, V., Buckman, D.W., Carroll, R.J., Freedman, L.S., Guenther, P.M., Krebs-Smith, S.M., Subar, A.F., Dodd, K.W.: A mixed-effects model approach for estimating the distribution of usual intake of nutrients: The NCI method. Stat. Med. 29, 2857–2868 (2010)
Variyam, J.N.: Factors affecting the macronutrient intake of U.S. adults. Electronic Report from the Economic Research Service (2003)
Wang, H.J., Zhou, X.: Estimation of the retransformed conditional mean in health care cost studies. Biometrika 97, 147–158 (2010)
Zhang, D., Davidian, M.: Linear mixed models with flexible distributions of random effects for longitudinal data. Biometrics 57, 795–802 (2001)
Acknowledgements
The research of Torres and Wang was supported by NSF award DMS-1007420 and NSF CAREER award DMS-1149355 and the research of Zhang was supported by the HIH grant R01 CA85848-12 and the NIH/NIAID grant R37 AI031789-20.
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Torres, P.A., Zhang, D., Wang, H.J. (2013). Constructing Conditional Reference Charts for Grip Strength Measured with Error. In: Hu, M., Liu, Y., Lin, J. (eds) Topics in Applied Statistics. Springer Proceedings in Mathematics & Statistics, vol 55. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7846-1_24
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