GEE‐Smoothing Spline in Semiparametric Model with Correlated Nominal Data

Ibrahim, Noor Akma; Suliadi, Suliadi

doi:10.1063/1.3525149

Cited by 2 publications

(1 citation statement)

References 19 publications

(35 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, it is not straightforward to apply kernel smoothing to accommodate the multilevel data structure. A few other works that propose marginal models fitted by smoothing splines include Ibrahim and Suliadi (2010a, 2010b). In a variable selection setting, Fu (2003) proposed penalized generalized estimating equation to handle collinearity among variables.…”

Section: Introductionmentioning

confidence: 99%

A Marginal Approach to Reduced-Rank Penalized Spline Smoothing With Application to Multilevel Functional Data

Chen

Wang

Paik

et al. 2013

Journal of the American Statistical Association

View full text Add to dashboard Cite

Multilevel functional data is collected in many biomedical studies. For example, in a study of the effect of Nimodipine on patients with subarachnoid hemorrhage (SAH), patients underwent multiple 4-hour treatment cycles. Within each treatment cycle, subjects’ vital signs were reported every 10 minutes. This data has a natural multilevel structure with treatment cycles nested within subjects and measurements nested within cycles. Most literature on nonparametric analysis of such multilevel functional data focus on conditional approaches using functional mixed effects models. However, parameters obtained from the conditional models do not have direct interpretations as population average effects. When population effects are of interest, we may employ marginal regression models. In this work, we propose marginal approaches to fit multilevel functional data through penalized spline generalized estimating equation (penalized spline GEE). The procedure is effective for modeling multilevel correlated generalized outcomes as well as continuous outcomes without suffering from numerical difficulties. We provide a variance estimator robust to misspecification of correlation structure. We investigate the large sample properties of the penalized spline GEE estimator with multilevel continuous data and show that the asymptotics falls into two categories. In the small knots scenario, the estimated mean function is asymptotically efficient when the true correlation function is used and the asymptotic bias does not depend on the working correlation matrix. In the large knots scenario, both the asymptotic bias and variance depend on the working correlation. We propose a new method to select the smoothing parameter for penalized spline GEE based on an estimate of the asymptotic mean squared error (MSE). We conduct extensive simulation studies to examine property of the proposed estimator under different correlation structures and sensitivity of the variance estimation to the choice of smoothing parameter. Finally, we apply the methods to the SAH study to evaluate a recent debate on discontinuing the use of Nimodipine in the clinical community.

show abstract

Section: Introductionmentioning

confidence: 99%