Non-Parametric Modeling of Longitudinal Data
Longitudinal data or repeated measurements taken on each of a number of subjects arise frequently in many biomedical applications. The key difference between longitudinal data and cross-sectional data is that longitudinal data are usually correlated within a subject and data analysis must account for the within-subject variation. Linear and nonlinear regression models such as mixed-effects models have been very popular for longitudinal data analysis. However, in many applications, the functional form describing the time patterns of longitudinal data or relationship between a longitudinal response and covariates may not be available, such as for some preliminary data analyses or long-term follow-up studies. In the past decade, semiparametric and nonparametric regression models (including functional or time-varying coefficient models) have been developed for longitudinal data to deal with this problem. Standard nonparametric smoothing techniques such as kernel smoothing, regression splines, smoothing splines and penalized splines have been proposed and adjusted to estimate the nonparametric components or functional coefficients in the semiparametric/nonparametric models for longitudinal data. Functional data analysis techniques with some modifications can also be applied to longitudinal data analysis. Some difficulties in longitudinal data analysis such as missing data issues, lost follow-ups, data truncation and censoring, measurement errors in covariates, and data sparseness from individuals need to be carefully addressed. Other unresolved problems in the area of nonparametric modeling of longitudinal data include hypothesis testing, pattern classification and clustering, model selection and evaluation, and other statistical inferences. Our research group has made great strides in introducing ideas of mixed-effects modeling to semiparametric/nonparametric models for longitudinal data analysis with practical application to biomarker data analysis from AIDS clinical trials. Currently we are trying to develop more practical and useful statistical inference methods for longitudinal data under nonparametric model settings.