In laboratory experiments with mice, the drug effect on the muscular strength can be measured through the grip strength. Since the grip strength is hard to quantify, multiple measurements are taken on the same mouse, and those observations have considerable measurement errors inherent to the measuring process. One of the research interests lies in studying how the quantiles of the grip strength depend on the other covariates such as weight and drug treatment (i.e. conditional quantiles). Quantile regression provides a convenient tool since it helps capture different effects of covariates at different tails of the grip strength distribution and thus provides a comprehensive understanding of the study. As an example, biometric charts of the grip strength as a function of the weight can be generated in order to have reference values for quality control in laboratory experiments. However, due to the measurement error, conventional quantile regression method often leads to biased estimates of the conditional quantiles of the latent grip strength. In this paper, we propose a semi-parametric approach, which accounts for the measurement error via mixed models with a flexible distribution for the random effects associated with mice. We apply the proposed method to the mice data and compare it to the conventional approach. Using statistical theory and simulation studies, we argue that our method outperforms the conventional approach when estimating the true quantiles of the latent grip strength. We also demonstrate through simulation that the proposed method leads to consistent and efficient estimation of conditional quantiles.
Quantile Regression for Repeated Measurements Under the Presence of Measurement Error
Friday, October 28, 2011
Hall 1-2 (San Jose Convention Center)