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CPS2169 Carmen D. Tekwe et al.
                            Percentile-based approaches for assessing
                        impacts of school day energy expenditure on 18-
                         month change in bmi among elementary school-
                                           aged children
                                                                                     3
                               1
                                               2
                                                                       1
             Carmen D. Tekwe , Gilson Honvoh , Roger S. Zoh, Lan Xue , Anand Gupta ,
                                           Mark Benden
                                                        4
                 1  Department of Epidemiology and Biostatistics Indiana University, Bloomington, IN
                     2  Department of Biostatistics, University of North Carolina, Chapel Hill, NC
                                       3  OhioHealth, Columbus, OH
               4  Department of Environmental and Occupational Health, Texas A&M University, College
                                            Station, Texas

            Abstract
            Childhood obesity is defined based on age- and sex- adjusted body mass
            indexes (BMI) within upper percentile ranges. Most studies assessing impacts
            of interventions on BMI rely on traditional linear regression models designed
            to  assess  intervention  effects  on  children  within  "normal"  BMI  percentile
            ranges, limiting assessments of how interventions affect children at higher
            risks  for  overweight  and  obesity.  Thus,  statistical  approaches  that  permit
            evaluations of intervention effects across the full distribution of BMI are more
            desirable  for  determining  their  impacts  on  subjects  at  higher  risks  for
            developing  overweight  or  obesity.  In  this  manuscript,  we  determine  the
            association  between  energy  expenditure  obtained  at  a  prior  time  on
            subsequent risk or progression to obesity. We describe the use of conditional
            functional  quantile  regression  models  to  study  the  relationship  between
            school day energy expenditure, a function-valued covariate, and BMI. Through
            empirical  comparisons,  we  present  the  results  from  mean  regression  and
            quantile regression- based models. The benefits of using quantile regression-
            based methods in assessing intervention effects in obesity research are also
            discussed.

            Keywords
            B-splines, Cluster randomized trial, Functional data analysis, Physical activity,
            Quantile regression

            1.  Introduction
                About  90%  of  children  diagnosed  with  type  2  diabetes  are  either
            overweight or obesity patients (Liu, et al. 2010). While it is well known that
            obesity results from a  chronic imbalance between energy  expenditure and
            energy  intake,  as  well  as  from  environmental  exposures  and  genetic
            predisposition, the exact role of energy expenditure in obesity development is
            unclear  (Bandini,  et  al.  2004).  To  combat  this  growing  epidemic  among
            children,  behavioural  researchers  are  increasingly  interested  in  employing

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