Li-Chu Chien

Shape restricted regression with random Bernstein polynomials

Shape restricted regressions, including isotonic regression and concave regression as special cases, are studied using priors on Bernstein polynomials and Markov chain Monte Carlo methods. These priors have large supports, select only smooth functions, can easily incorporate geometric information into the prior, and can be generated without computational difficulty. Algorithms generating priors and posteriors are proposed, and simulation studies are conducted to illustrate the performance of this approach. Comparisons with the density-regression method of Dette et al. (2006) are included.

Temporal Transcription Program of Recombinant Autographa californica Multiple Nucleopolyhedrosis Virus

ABSTRACT Baculoviruses, a family of large, rod-shaped viruses that mainly infect lepidopteran insects, have been widely used to transduce various cells for exogenous gene expression. Nonetheless, how a virus controls its transcription program in cells is poorly understood. With a custom-made baculovirus DNA microarray, we investigated the recombinant Autographa californica multiple nucleopolyhedrosis virus (AcMNPV) gene expression program in lepidopteran Sf21 cells over the time course of infection. Our analysis of transcription kinetics in the cells uncovered sequential viral gene expression patterns possibly regulated by different mechanisms during different phases of infection. To gain further insight into the regulatory network, we investigated the transcription program of a mutant virus deficient in an early transactivator (pe38) and uncovered several pe38-dependent and pe38-independent genes. This study of baculovirus dynamic transcription programs in different virus genetic backgrounds provides new molecular insights into how gene expression in viruses is regulated.

Diagnostic plots in beta-regression models

Two diagnostic plots for selecting explanatory variables are introduced to assess the accuracy of a generalized beta-linear model. The added variable plot is developed to examine the need for adding a new explanatory variable to the model. The constructed variable plot is developed to identify the nonlinearity of the explanatory variable in the model. The two diagnostic procedures are also useful for detecting unusual observations that may affect the regression much. Simulation studies and analysis of two practical examples are conducted to illustrate the performances of the proposed plots.

Generalization of Rare Variant Association Tests for Longitudinal Family Studies.

Given the functional relevance of many rare variants, their identification is frequently critical for dissecting disease etiology. Functional variants are likely to be aggregated in family studies enriched with affected members, and this aggregation increases the statistical power to detect rare variants associated with a trait of interest. Longitudinal family studies provide additional information for identifying genetic and environmental factors associated with disease over time. However, methods to analyze rare variants in longitudinal family data remain fairly limited. These methods should be capable of accounting for different sources of correlations and handling large amounts of sequencing data efficiently. To identify rare variants associated with a phenotype in longitudinal family studies, we extended pedigree‐based burden (BT) and kernel (KS) association tests to genetic longitudinal studies. Generalized estimating equation (GEE) approaches were used to generalize the pedigree‐based BT and KS to multiple correlated phenotypes under the generalized linear model framework, adjusting for fixed effects of confounding factors. These tests accounted for complex correlations between repeated measures of the same phenotype (serial correlations) and between individuals in the same family (familial correlations). We conducted comprehensive simulation studies to compare the proposed tests with mixed‐effects models and marginal models, using GEEs under various configurations. When the proposed tests were applied to data from the Diabetes Heart Study, we found exome variants of POMGNT1 and JAK1 genes were associated with type 2 diabetes.

Profiling time course expression of virus genes—an illustration of Bayesian inference under shape restrictions

There have been several studies of the genome-wide temporal transcriptional program of viruses, based on microarray experiments, which are generally useful in the construction of gene regulation network. It seems that biological interpretations in these studies are directly based on the normalized data and some crude statistics, which provide rough estimates of limited features of the profile and may incur biases. This paper introduces a hierarchical Bayesian shape restricted regression method for making inference on the time course expression of virus genes. Estimates of many salient features of the expression profile like onset time, inflection point, maximum value, time to maximum value, area under curve, etc. can be obtained immediately by this method. Applying this method to a baculovirus microarray time course expression data set, we indicate that many biological questions can be formulated quantitatively and we are able to offer insights into the baculovirus biology.

Simultaneous estimation of the locations and effects of multiple disease loci in case–control studies

The genetic basis of complex diseases often involves multiple causative loci. Under such a disease etiology, assuming one disease locus in linkage disequilibrium mapping is likely to induce bias and lead to efficiency loss in disease locus estimation. An approach is needed for simultaneously localizing multiple functional loci within the same region. However, due to the increasing number of parameters accompanying disease loci, these estimates can be computationally infeasible. To circumvent this problem, we propose to estimate the main and two-adjacent-locus joint effects and a nuisance parameter at the disease loci separately through a linear approximation. Estimates of the genetic effects are entered into a generalized estimating equation to estimate disease loci, and the procedure is conducted iteratively until convergence. The proposed method provides estimates and confidence intervals (CIs) for the disease loci, the genetic main effects, and the joint effects of two adjacent disease loci, with the CIs for the disease loci providing useful regions for further fine-mapping. We apply the proposed approach to a data example of case-control studies. Results of the simulations and data example suggest that the developed method performs well in terms of bias, variance, and coverage probability under scenarios with up to three disease loci.

A robust diagnostic plot for explanatory variables under model mis-specification

A typical added variable plot is a commonly used plot in assessing the accuracy of a normal linear model. This plot is often used to evaluate the effect of adding an explanatory variable into the model and to detect possibly high leverage points or influential observations on the added variable. However, this type of plot is generally in doubt, once the normal distributional assumptions are violated. In this article, we extend the robust likelihood technique introduced by Royall and Tsou [11] to propose a robust added variable plot. The validity of this diagnostic plot requires no knowledge of the true underlying distributions so long as their second moments exist. The usefulness of the robust graphical approach is demonstrated through a few illustrations and simulations.

Regression Diagnostic under Model Misspecification

We propose two novel diagnostic measures for the detection of influential observations for regression parameters in linear regression. Traditional diagnostic statistics focus on the effect of deletion of data points either on parameter estimates, or on predicted values. A data point is regarded as influential by the new methods if its inclusion determines a significantly different likelihood function for the parameter of interest. The concerned likelihood function is asymptotically valid for practically all underlying distributions whose second moments exist.