A New Nonparametric Regression for Longitudinal Data

Background and purpose: In many area of medical research, a relation analysis between one response variable and some explanatory variables is desirable. Regression is the most common tool in this situation. If we have some assumptions for such normality for response variable, we could use it. In this paper we propose a nonparametric regression that does not have normality assumption for response variable and we focus on longitudinal data. Materials and Methods: Consider nonparametric estimation in a varying coefficient model with repeated measurements ( X tij Yij ij , , ), for i=1, …, n and j =1 ,… , ni where Xij= T Xijo 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) T Yij ij ? ? ?? , where ( ) ? ( 0 ( ),..., ( )) , for k ? 0 T t k ? t ? t ? , are smooth nonparametric functions of interest and (t ) ? i is a zero-mean stochastic process. The measurements are assumed to be independent for different subjects but can be correlated at different time points within each subject. For evaluating this model, we use data of a cohort of 289 healthy infants born in Shiraz in 2007. The proposed nonparametric regression was fitted to them for obtaining effect rates of mother weight, mother arm circumference and maternal age at delivery time and maternal age at first menarche on boy’s arm circumference. Results: proposed nonparametric regression showed the varied effect of each independent variable over the time but other models achieved constant effect over the time that is in controversy with the inherent property of these natural phenomena. Conclusion: This study shows that this model and the spline nonparametric estimator could be useful in different areas of medical and health studies.