Timothy Hanson

Modeling Regression Error With a Mixture of Polya Trees

We model the error distribution in the standard linear model as a mixture of absolutely continuous Polya trees constrained to have median 0. By considering a mixture, we smooth out the partitioning effects of a simple Polya tree and the predictive error density has a derivative everywhere except 0. The error distribution is centered around a standard parametric family of distributions and thus may be viewed as a generalization of standard models in which important, data-driven features, such as skewness and multimodality, are allowed. By marginalizing the Polya tree, exact inference is possible up to Markov chain Monte Carlo error.

Inference for Mixtures of Finite Polya Tree Models

Mixtures of Polya tree models provide a flexible alternative when a parametric model may only hold approximately. I provide computational strategies for obtaining full semiparametric inference for mixtures of finite Polya tree models given a standard parameterization, including models that would be troublesome to fit using Dirichlet process mixtures. Recommendations are put forth on choosing the level of a finite Polya tree, and model comparison is discussed. Several examples demonstrate the utility of finite Polya tree modeling, including data fit to generalized linear mixed models and several survival models.

Identifiability of Models for Multiple Diagnostic Testing in the Absence of a Gold Standard

We discuss the issue of identifiability of models for multiple dichotomous diagnostic tests in the absence of a gold standard (GS) test. Data arise as multinomial or product-multinomial counts depending upon the number of populations sampled. Models are generally posited in terms of population prevalences, test sensitivities and specificities, and test dependence terms. It is commonly believed that if the degrees of freedom in the data meet or exceed the number of parameters in a fitted model then the model is identifiable. Goodman (1974, Biometrika 61, 215-231) established that this was not the case a long time ago. We discuss currently available models for multiple tests and argue in favor of an extension of a model that was developed by Dendukuri and Joseph (2001, Biometrics 57, 158-167). Subsequently, we further develop Goodmans technique, and make geometric arguments to give further insight into the nature of models that lack identifiability. We present illustrations using simulated and real data.

Do microbial interactions and cultivation media decrease the accuracy of Salmonella surveillance systems and outbreak investigations

Cultivation methods are commonly used in Salmonella surveillance systems and outbreak investigations, and consequently, conclusions about Salmonella evolution and transmission are highly dependent on the performance characteristics of these methods. Past studies have shown that Salmonella serotypes can exhibit different growth characteristics in the same enrichment and selective media. This could lead not only to biased conclusions about the dominant strain present in a sample with mixed Salmonella populations, but also to a low sensitivity for detecting a Salmonella strain in a sample with only a single strain present. The objective of this study was to determine whether cultivation media select preferentially for specific strains of Salmonella in heterogeneous cultures. In this study, four different Salmonella strains (one Salmonella Newport, two Salmonella Typhimurium, and one Salmonella Enteritidis) were competed in a broth-based experiment and a bovine fecal experiment with varied combinations and concentrations of each strain. In all experiments, the strain of Salmonella Newport was the most competitive, regardless of the starting concentration and cultivation protocol. One strain of Salmonella Typhimurium was rarely detected in competition, even when it was the only strain present in bovine feces. Overall, the probability of detecting a specific Salmonella strain had little to do with its starting concentration in the sample. The bias introduced by culture could be dramatically biasing Salmonella surveillance systems and hindering traceback investigations during Salmonella outbreaks. Future studies should focus on the microbiological explanations for this Salmonella interstrain variability, approaches for minimizing the bias, and estimations of the public health significance of this bias.

Hierarchical Models for Estimating Herd Prevalence and Test Accuracy in the Absence of a Gold Standard

A common assumption made in studies involving two or more binary diagnostic tests in the absence of a gold standard is one of conditional independence among tests given disease status. Although reasonable in some cases, often this assumption is untenable or untested and may lead to biased results. We proposed a class of hierarchical models for the purpose of estimating the herd-level prevalence distribution and the accuracies of two tests in the absence of a gold standard when several exchangeable populations with differing disease prevalence are available for sampling, relaxing the assumption of conditional independence between tests. The models are used to estimate the prevalence of bovine brucellosis in Mexican cow herds and to estimate the error rates of two tests for the detection of swine pneumonia.

Bayesian Nonparametric Data Analysis

This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the books structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in online software pages.

A Bayesian Semiparametric Temporally–Stratified Proportional Hazards Model with Spatial Frailties

Incorporating temporal and spatial variation could potentially enhance information gathered from survival data. This paper proposes a Bayesian semiparametric model for capturing spatio-temporal heterogeneity within the proportional hazards framework. The spatial correlation is introduced in the form of county-level frailties. The temporal effect is introduced by considering the stratification of the proportional hazards model, where the time-dependent hazards are indirectly modeled using a probability model for related probability distributions. With this aim, an autoregressive dependent tailfree process is introduced. The full Kullback-Leibler support of the proposed process is provided. The approach is illustrated using simulated and data from the Surveillance Epidemiology and End Results database of the National Cancer Institute on patients in Iowa diagnosed with breast cancer.

T1ρ and T2ρ MRI in the evaluation of Parkinson’s disease

Prior work has shown that adiabatic T1ρ and T2ρ relaxation time constants may have sensitivity to cellular changes and the presence of iron, respectively, in Parkinson’s disease (PD). Further understanding of these magnetic resonance imaging (MRI) methods and how they relate to measures of disease severity and progression in PD is needed. Using T1ρ and T2ρ on a 4T MRI scanner, we assessed the substantia nigra (SN) of nine non-demented moderately affected PD and ten gender- and age-matched control participants. When compared to controls, the SN of PD subjects had increased T1ρ and reduced T2ρ. We also found a significant correlation between asymmetric motor features and asymmetry based on T1ρ. This study provides additional validation of T1ρ and T2ρ as a means to separate PD from control subjects, and T1ρ may be a useful marker of asymmetry in PD.

A Bayesian Semiparametric AFT Model for Interval-Censored Data

We model the baseline distribution in the accelerated failure-time (AFT) model as a mixture of Dirichlet processes for interval-censored data. This mixture is distinct from Dirichlet process mixtures, and can be viewed as a simple extension of existing parametric models, which we believe is an advantage in the practical modeling of data. We introduce a novel MCMC scheme for the purpose of making posterior inferences for the AFT regression model and illustrate our methods with several real examples.

Chemopreventive Effect of Kava on 4-(Methylnitrosamino)-1-(3-pyridyl)-1-butanone plus Benzo[a]pyrene–Induced Lung Tumorigenesis in A/J Mice

Lung cancer is the leading cause of cancer death, and chemoprevention is a potential strategy to help control this disease. Epidemiologic survey indicates that kava may be chemopreventive for lung cancer, but there is a concern about its potential hepatotoxicity. In this study, we evaluated whether oral kava could prevent 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK) plus benzo[a]pyrene (B[a]P)–induced lung tumorigenesis in A/J mice. We also studied the effect of kava to liver. At a dose of 10 mg/g diet, 30-week kava treatment (8 weeks concurrent with NNK and B[a]P treatment followed by 22 weeks post-carcinogen treatment) effectively reduced lung tumor multiplicity by 56%. Kava also reduced lung tumor multiplicity by 47% when administered concurrently with NNK and B[a]P for 8 weeks. Perhaps most importantly, kava reduced lung tumor multiplicity by 49% when administered after the final NNK and B[a]P treatment. These results show for the first time the chemopreventive potential of kava against lung tumorigenesis. Mechanistically, kava inhibited proliferation and enhanced apoptosis in lung tumors, as shown by a reduction in proliferating cell nuclear antigen (PCNA), an increase in caspase-3, and cleavage of poly(ADP-ribose) polymerase (PARP). Kava treatment also inhibited the activation of nuclear factor κBNF-κB, a potential upstream mechanism of kava chemoprevention. Although not rigorously evaluated in this study, our preliminary data were not suggestive of hepatotoxicity. Based on these results, further studies are warranted to explore the chemopreventive potential and safety of kava.