Additive quantile regression for clustered data with an application to children's physical activity

Adaptive aggregation for longitudinal quantile regression based on censored history process

Most of the studies for longitudinal quantile regression are based on the correct specification. Nevertheless, one specific model can hardly perform precisely under different conditions and assessing which conditions are (approximately) satisfied to determine the optimal one is rather difficult. In the case of the mixed effect model, the misspecification of the fixed effect part will cause a lack of predicting accuracy of random effects, and affect the efficiency of the cumulative function estimator. On the other hand, limited research has focused on incorporating multiple candidate procedures in longitudinal data analysis, which is of current emergency. This paper proposes an exponential aggregation weighting algorithm for longitudinal quantile regression. Based on the secondary smoothing loss function, we establish oracle inequalities for aggregated estimator. The proposed method is applied to evaluate the cumulative τ th quantile function for additive mixed effect model with right-censored history process, and an aggregation-based best linear prediction for random effects is constructed as well. We show that the asymptotic properties are conveniently imposed owing to the smoothing scheme. Simulation studies are carried out to exhibit the rationality, and our method is illustrated to analyze the data set from a multicenter automatic defibrillator implantation trial.

Joint regression modelling of intensity and timing of accelerometer counts

Accelerometers are commonly used in human medical and public health research to measure physical movement, which is relevant in a wide range of studies, from physical activity and sleep behaviours studies, to identification of movement patterns in people affected by diseases of the locomotor system and prediction of risk of injury in high performance sports. The accelerometer output provides the intensity (activity count) and timing (timestamp) of the movement, which can be used to define bouts of activity (periods of sustained movement of a given intensity). In some contexts, it may be important to include both dimensions to obtain a broader and deeper understanding of the phenomenon under study. Such is the case of a large-scale epidemiological investigation on the daily and weekly physical activity behaviours of school-aged children enrolled in the UK Millennium Cohort Study, which has motivated the present article. I present a statistical approach to joint modelling of intensity and timing of activity bouts that takes advantage of the circular nature of the timing. The model, which accounts for the longitudinal structure of the observations, is remarkably simple to implement using standard statistical software.

Additive quantile mixed effects modelling with application to longitudinal CD4 count data

Quantile regression offers an invaluable tool to discern effects that would be missed by other conventional regression models, which are solely based on modeling conditional mean. Quantile regression for mixed-effects models has become practical for longitudinal data analysis due to the recent computational advances and the ready availability of efficient linear programming algorithms. Recently, quantile regression has also been extended to additive mixed-effects models, providing an efficient and flexible framework for nonparametric as well as parametric longitudinal forms of data analysis focused on features of the outcome beyond its central tendency. This study applies the additive quantile mixed model to analyze the longitudinal CD4 count of HIV-infected patients enrolled in a follow-up study at the Centre of the AIDS Programme of Research in South Africa. The objective of the study is to justify how the procedure developed can obtain robust nonlinear and linear effects at different conditional distribution locations. With respect to time and baseline BMI effect, the study shows a significant nonlinear effect on CD4 count across all fitted quantiles. Furthermore, across all fitted quantiles, the effect of the parametric covariates of baseline viral load, place of residence, and the number of sexual partners was found to be major significant factors on the progression of patients' CD4 count who had been initiated on the Highly Active Antiretroviral Therapy study.

Modelling and estimation of nonlinear quantile regression with clustered data

In regression applications, the presence of nonlinearity and correlation among observations offer computational challenges not only in traditional settings such as least squares regression, but also (and especially) when the objective function is nonsmooth as in the case of quantile regression. Methods are developed for the modelling and estimation of nonlinear conditional quantile functions when data are clustered within two-level nested designs. The proposed estimation algorithm is a blend of a smoothing algorithm for quantile regression and a second order Laplacian approximation for nonlinear mixed models. This optimization approach has the appealing advantage of reducing the original nonsmooth problem to an approximated L 2 problem. While the estimation algorithm is iterative, the objective function to be optimized has a simple analytic form. The proposed methods are assessed through a simulation study and two applications, one in pharmacokinetics and one related to growth curve modelling in agriculture.

Quantile Regression Modeling of Latent Trajectory Features with Longitudinal Data

Quantile regression has demonstrated promising utility in longitudinal data analysis. Existing work is primarily focused on modeling cross-sectional outcomes, while outcome trajectories often carry more substantive information in practice. In this work, we develop a trajectory quantile regression framework that is designed to robustly and flexibly investigate how latent individual trajectory features are related to observed subject characteristics. The proposed models are built under multilevel modeling with usual parametric assumptions lifted or relaxed. We derive our estimation procedure by novelly transforming the problem at hand to quantile regression with perturbed responses and adapting the bias correction technique for handling covariate measurement errors. We establish desirable asymptotic properties of the proposed estimator, including uniform consistency and weak convergence. Extensive simulation studies confirm the validity of the proposed method as well as its robustness. An application to the DURABLE trial uncovers sensible scientific findings and illustrates the practical value of our proposals.