A New Nonparametric Regression for Longitudinal Data

Background and purpose: in many area of medical research, a relation analysis between oneresponse variable and some explanatory variables is desirable. regression is the most common tool inthis situation. if we have some assumptions for such normality for response variable, we could use it. inthis paper we propose a nonparametric regression that does not have normality assumption for responsevariable and we focus on longitudinal data.materials and methods: consider nonparametric estimation in a varying coefficient model withrepeated measurements ( x tij yij ij, , ), for i=1, …, n and j =1 ,… , ni where xij=txijo xijk( ,..., ) and( x tij yij ij, , ) denote the jth outcome , covariate and time design points, respectively , of the ith subject.the model considered here is y (tij) i (tij)tyij ij? ? ?? , where ( ) ? ( 0 ( ),..., ( )) , for k ? 0ttk? t ? t ? , aresmooth nonparametric functions of interest and (t )? i is a zero-mean stochastic process. themeasurements are assumed to be independent for different subjects but can be correlated at differenttime points within each subject. for evaluating this model, we use data of a cohort of 289 healthyinfants born in shiraz in 2007. the proposed nonparametric regression was fitted to them for obtainingeffect rates of mother weight, mother arm circumference and maternal age at delivery time and maternalage at first menarche on boy’s arm circumference.results: proposed nonparametric regression showed the varied effect of each independent variableover the time but other models achieved constant effect over the time that is in controversy with theinherent property of these natural phenomena.conclusion: this study shows that this model and the spline nonparametric estimator couldbe useful in different areas of medical and health studies.