Robust two-stage approach to repeated measurements analysis of chronic ozone exposure in rats

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Journal Article
Journal of Agricultural, Biological, and Environmental Statistics, 2003, 8 (4), pp. 438 - 454
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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 individuals, leading to the possibility of outliers at each sampling level. By estimating an 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 downweights the aberrant responses arising sporadically within individuals and, 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. © 2003 American Statistical Association and the International Biometric Society.
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