Abstract
A robust two-stage approach is used to reanalyze the repeated measurements from an experiment of airway responsiveness in rats randomized to long-term exposure at four ozone doses. The concentration-response data generated for each rat may be represented as a hierarchical nonlinear model encompasing the sources of variation within and between individual profile for each rat, the conditional modeling approach can assess the adequacy of an assumed mean model, a fundamental advantage not intrinsic to marginal techniques. The two-stage population inference is based on the estimated individual parameters, thus maintaining an intuitive appeal to the toxicologists who traditionally have fitted a separate curve for each animal and then applied ANOVA to the summary statistics. However, we formally adjust the standard errors for the extra variability due to the initial estimation of the individual parameters and also allow for their within-rat correlation. The robust two-stage method appropriately down weights the a berrant responses arising sporadically within individualsand, more importantly, the rats which may be outlying relative to the usual population variation. The true effect of chronic ozone exposure, including a significant gender interaction, may be masked by a few rats which exert undue influence on the population estimates in a nonrobust analysis.
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Boorman, G. A., Catalano, P. J., Jacobson, B. J., Kaden, D. A., Mellick, P. W., Nauss, K. M., and Ryan L. M. (1995), “Consequences of Prolonged Inhalation of Ozone on F344/N rats: Collaborative Studies, Part VI: Background and Project Design,” Research Report No. 65. Health Effects Institute, Cambridge, MA.
Davidian, M., and Giltinan, D. M. (1993), “Some Simple Methods for Estimating Intraindividual Variability in Nonlinear Mixed Effects Models,” Biometrics, 49, 59–73.
— (1995), Nonlinear Models for Repeated Measurement Data, London: Chapman and Hall.
Farmer, S. G., and Hay, D. W. P. (1991), “Airway Epithelial Modulation of Smooth-muscle Function: the Evidence for Epithelium-derived Inhibitory Factor,” in Lung Biology in Health and Disease 55, The Airway Epithelium: Physiology, Pathophysiology and Pharmacology, eds. S. G. Farmer and D. W. P. Hay. New York: Marcel Dekker.
Harkema, J. R., and Mauderly, J. L. (1994), “Consequences of Prolonged Inhalation of Ozone on F344/N rats: Collaborative Studies, Part V: Effects on Pulmonary Function,” Research Report No. 65. Health Effects Institute, Cambridge, MA.
Huber, P. J. (1981), Robust Statistics, New York: Wiley.
Lindsey, J. K., and Lambert, P. (1998), “On the Appropriateness of Margin al Models for Repeated Measurements in Clinical Trials,” Statistics in Medicine, 17, 447–469.
Lindstrom, M. J., and Bates, D. M. (1990), “Nonlinear Mixed Effects Model for Repeated Measures Data,” Biometrics, 46, 673–687.
Lippman, M. (1989), “Health Effects of Ozone: A Critical Review,” Journal of the Air Pollution Control Association, 39, 672–695.
— (1993), “Health Effects of Tropospheric Ozone: A Review of Recent Research Findings and their Implications to Ambient Air Quality Standards,” Journal of Exposure Analysis and Environmental Epidemiology, 3, 103–129.
Plopper, C. G., Chu, F-P., Haselton, C. J., Peake, J., Wu, J., and Pinkerton, K. E. (1994a), “Dose-dependent Tolerance to Ozone 1: Tracheobronchial Epithelial Reorganization in Rats after 20 Months’ Exposure,” American Journal of Pathology, 144, 404–421.
Plopper, C. G., Duan, X., Buckpitt, A. R., and Pinkerton, K. E. (1994b), “Dose-dependent Tolerance to Ozone IV: Site-specific Elevation in Antioxidant Enzymes in the Lungs of Rats Exposed for 90 Days or 20 Months,” Toxicology and Applied Pharmacology, 127, 124–131.
Seber, G. A. F., and Wild, C. J. (1988), Nonlinear Regression, New York: Wiley.
Steimer, J.-L., Mallet, A., Golmard, J. L., and Boisvieux, J. F. (1984), “Alternative Approaches to Estimation of Population Pharmacokinetic Parameters: Comparison with the Nonlinear Mixed Effect Model,” Drug Metabolism Reviews, 15, 265–292.
Szarek, J. L. (1994), “Consequences of Prolonged Inhalation of Ozone on F344/N rats: Collaborative Studies, Part II: Mechanical Properties, Responses to Bronchoactive Stimuli, and Eicosanoid Release in Isolated Large and Small Airways,” Research Report No. 65. Health Effects Institute, Cambridge, MA.
Szarek, J. L., Stewart, N. L., Zhang, J. Z., Webb, J. A., Valentovic, M. A., and Catalano, P. (1995), “Contractile Responses and Structure of Small Bronchi Isolated from Rats after 20 Months’ Exposure to Ozone,” Fundamental and Applied Toxicology, 28, 199–208.
U.S. Environmental Protection Agency (1986), “Air Quality Criteria for Ozone,” Washington, DC: U.S. EPA.
— (1994), “Air Quality Criteria for Ozone and Related Photochemical Oxidants: External Review Draft, 1993,” Washington, DC: U.S. EPA.
Vonesh, E. F., and Carter, R. L. (1992), “Mixed Effects Nonlinear Regression for Unbalanced Repeated Measures,” Biometrics, 48, 1–18.
Yeap, B. Y., and Davidian, M. (2001), “Robust Two-stage Estimation in Hierarchical Nonlinear Models,” Biometrics, 57, 266–272.
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Yeap, B.Y., Catalano, P.J., Ryan, L.M. et al. Robust two-stage approach to repeated measurements analysis of chronic ozone exposure in rats. JABES 8, 438 (2003). https://doi.org/10.1198/1085711032552
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DOI: https://doi.org/10.1198/1085711032552