Cholesky Residuals for Assessing Normal Errors in a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional variance matrix. The resulting rotated residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and Ryan (1989), Pierce (1982), and Randles (1982). Our method appears to work well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series). Our methods can produce satisfactory results even for models that do not satisfy all of the technical conditions stated in our theory

A Functional-Based Distribution Diagnostic for a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed modesl and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated marginal residual vector by the Cholesky decomposition of the inverse of the estimated marginal variance matrix. Linear functions or the resulting rotated residuals are used to construct an empirical cumulative distribution function (ECDF), whose stochastic limit is characterized. We describe a resampling technique that serves as a computationally efficient parametric bootstrap for generating representatives of the stochastic limit of the ECDF. Through functionals, such representatives are used to construct global tests for the hypothesis of normal margional errors. In addition, we demonstrate that the ECDF of the predicted random effects, as described by Lange and Ryan (1989), can be formulated as a special case of our approach. Thus, our method supports both omnibus and directed tests. Our method works well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series)

A Nonstationary Negative Binomial Time Series with Time-Dependent Covariates: Enterococcus Counts in Boston Harbor

Boston Harbor has had a history of poor water quality, including contamination by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. Motivated by the ineffectiveness of standard Poisson mixture models and their zero-inflated counterparts, we propose a new negative binomial model for time series of Enterococcus counts in Boston Harbor, where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor. Without further restrictions, this function is not identifiable in the presence of time-dependent covariates; consequently we use a basis orthogonal to the space spanned by the covariates and use penalized quasi-likelihood (PQL) for estimation. We conclude that Enterococcus counts were greatly reduced near the Nut Island Treatment Plant (NITP) outfalls following the transfer of wastewaters from NITP to the Deer Island Treatment Plant (DITP) and that the transfer of wastewaters from Boston Harbor to the offshore diffusers in Massachusetts Bay reduced the Enterococcus counts near the DITP outfalls

Genome-wide characterization of cytosine-specific 5-hydroxymethylation in normal breast tissue.

Despite recent evidence that 5-hydroxymethylcytosine (5hmC) possesses roles in gene regulation distinct from 5-methylcytosine (5mC), relatively little is known regarding the functions of 5hmC in mammalian tissues. To address this issue, we utilized an approach combining both paired bisulfite (BS) and oxidative bisulfite (oxBS) DNA treatment, to resolve genome-wide patterns of 5hmC and 5mC in normal breast tissue from disease-free women. Although less abundant than 5mC, 5hmC was differentially distributed, and consistently enriched among breast-specific enhancers and transcriptionally active chromatin. In contrast, regulatory regions associated with transcriptional inactivity, such as heterochromatin and repressed Polycomb regions, were relatively depleted of 5hmC. Gene regions containing abundant 5hmC were significantly associated with lactate oxidation, immune cell function, and prolactin signaling pathways. Furthermore, genes containing abundant 5hmC were enriched among those actively transcribed in normal breast tissue. Finally, in independent data sets, normal breast tissue 5hmC was significantly enriched among CpG loci demonstrated to have altered methylation in pre-invasive breast cancer and invasive breast tumors. Primarily, our findings identify genomic loci containing abundant 5hmC in breast tissues and provide a genome-wide map of nucleotide-level 5hmC in normal breast tissue. Additionally, these data suggest 5hmC may participate in gene regulatory programs that are dysregulated during breast-related carcinogenesis

Genetic Determinants of UV-Susceptibility in Non-Melanoma Skin Cancer

A milieu of cytokines and signaling molecules are involved in the induction of UV-induced immune suppression and thus the etiology of non-melanoma skin cancer (NMSC). Targeting the UV-induced immunosuppression pathway, and using a large population based study of NMSC, we have investigated the risk associated with functional variants in 10 genes (IL10, IL4, IL4R, TNF, TNFR2, HTR2A, HRH2, IL12B, PTGS2, and HAL). The most prominent single genetic effect was observed for IL10. There was increasing risk for both basal cell carcinoma (BCC) and squamous cell carcinoma (SCC) with increasing number of variant IL10 haplotypes (BCC: ptrend = 0.0048; SCC: ptrend = 0.031). Having two IL10 GC haplotypes was associated with increased odds ratios of BCC and SCC (ORBCC = 1.5, 95% CI 1.1–1.9; ORSCC = 1.4, 95% CI 1.0–1.9), and these associations were largely confined to women (ORBCC = 2.2, 95% CI 1.4–3.4; SCC: ORSCC = 1.8, 95% CI 1.1–3.0). To examine how combinations of these variants contribute to risk of BCC and SCC, we used multifactor dimensionality reduction (MDR) and classification and regression trees (CART). Results from both of these methods found that in men, a combination of skin type, burns, IL10, IL4R, and possibly TNFR2 were important in both BCC and SCC. In women, skin type, burns, and IL10 were the most critical risk factors in SCC, with risk of BCC involving these same factors plus genetic variants in HTR2A, IL12B and IL4R. These data suggest differential genetic susceptibility to UV-induced immune suppression and skin cancer risk by gender