Semiparametric Regression During 2003–2007

Semiparametric regression is a fusion between parametric regression and nonparametric regression and the title of a book that we published on the topic in early 2003. We review developments in the field during the five year period since the book was written. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application

Topics in Partially Linear Single-Index Models for Longitudinal Data

The partially linear single-index model is a semiparametric model proposed to the case when some predictors are linearly associated with the response variable, while some other predictors are nonlinearly associated with the response variable. It is widely used for its flexibility in statistical modeling. Furthermore, its generalized version is a generalization of some popular models such as the generalized linear model, the partially linear model and the single-index model. However, the proper estimation in partially linear single-index models for longitudinal data, where multiple measurements are observed for each subject, is still open to discussion. Our main purpose is to establish a unified estimation method for the longitudinal partially linear single-index model and its generalized version. With this question in mind, we propose a new iterative three-stage estimation method in partially linear single-index models and generalized partially linear single-index models for longitudinal data. With the proposed method, the within-subject correlation is properly taken into consideration in the estimation of both the parameters and the nonparametric single-index function. The parameter estimators are shown to be asymptotically semiparametric efficient. The asymptotic variance of the single-index function estimator is shown to be generally less than that of existing estimators. Simulation studies are performed to demonstrate the finite sample performance. Three real data examples are also analyzed to illustrate the methodology

Topics in Partially Linear Single-Index Models for Longitudinal Data

The partially linear single-index model is a semiparametric model proposed to the case when some predictors are linearly associated with the response variable, while some other predictors are nonlinearly associated with the response variable. It is widely used for its flexibility in statistical modeling. Furthermore, its generalized version is a generalization of some popular models such as the generalized linear model, the partially linear model and the single-index model. However, the proper estimation in partially linear single-index models for longitudinal data, where multiple measurements are observed for each subject, is still open to discussion. Our main purpose is to establish a unified estimation method for the longitudinal partially linear single-index model and its generalized version. With this question in mind, we propose a new iterative three-stage estimation method in partially linear single-index models and generalized partially linear single-index models for longitudinal data. With the proposed method, the within-subject correlation is properly taken into consideration in the estimation of both the parameters and the nonparametric single-index function. The parameter estimators are shown to be asymptotically semiparametric efficient. The asymptotic variance of the single-index function estimator is shown to be generally less than that of existing estimators. Simulation studies are performed to demonstrate the finite sample performance. Three real data examples are also analyzed to illustrate the methodology

Hierarchical models for semi-competing risks data with application to quality of end-of-life care for pancreatic cancer

Readmission following discharge from an initial hospitalization is a key marker of quality of health care in the United States. For the most part, readmission has been used to study quality of care for patients with acute health conditions, such as pneumonia and heart failure, with analyses typically based on a logistic-Normal generalized linear mixed model. Applying this model to the study readmission among patients with increasingly prevalent advanced health conditions such as pancreatic cancer is problematic, however, because it ignores death as a competing risk. A more appropriate analysis is to imbed such studies within the semi-competing risks framework. To our knowledge, however, no comprehensive statistical methods have been developed for cluster-correlated semi-competing risks data. In this paper we propose a novel hierarchical modeling framework for the analysis of cluster-correlated semi-competing risks data. The framework permits parametric or non-parametric specifications for a range of model components, including baseline hazard functions and distributions for key random effects, giving analysts substantial flexibility as they consider their own analyses. Estimation and inference is performed within the Bayesian paradigm since it facilitates the straightforward characterization of (posterior) uncertainty for all model parameters including hospital-specific random effects. The proposed framework is used to study the risk of readmission among 5,298 Medicare beneficiaries diagnosed with pancreatic cancer at 112 hospitals in the six New England states between 2000-2009, specifically to investigate the role of patient-level risk factors and to characterize variation in risk across hospitals that is not explained by differences in patient case-mix

Semiparametric approach to characterize unique gene expression trajectories across time

BACKGROUND: A semiparametric approach was used to identify groups of cDNAs and genes with distinct expression profiles across time and overcome the limitations of clustering to identify groups. The semiparametric approach allows the generalization of mixtures of distributions while making no specific parametric assumptions about the distribution of the hidden heterogeneity of the cDNAs. The semiparametric approach was applied to study gene expression in the brains of Apis mellifera ligustica honey bees raised in two colonies (A. m. mellifera and ligustica) with consistent patterns across five maturation ages. RESULTS: The semiparametric approach provided unambiguous criteria to detect groups of genes, trajectories and probability of gene membership to groups. The semiparametric results were cross-validated in both colony data sets. Gene Ontology analysis enhanced by genome annotation helped to confirm the semiparametric results and revealed that most genes with similar or related neurobiological function were assigned to the same group or groups with similar trajectories. Ten groups of genes were identified and nine groups had highly similar trajectories in both data sets. Differences in the trajectory of the reminder group were consistent with reports of accelerated maturation in ligustica colonies compared to mellifera colonies. CONCLUSION: The combination of microarray technology, genomic information and semiparametric analysis provided insights into the genomic plasticity and gene networks linked to behavioral maturation in the honey bee