Semiparametric estimation of count regression models

This paper develops a semiparametric estimation approach for mixed count regression models based on series expansion for the unknown density of the unobserved heterogeneity. We use the generalized Laguerre series expansion around a gamma baseline density to model unobserved heterogeneity in a Poisson mixture model. We establish the consistency of the estimator and present a computational strategy to implement the proposed estimation techniques in the standard count model as well as in truncated, censored, and zero-inflated count regression models. Monte Carlo evidence shows that the finite sample behavior of the estimator is quite good. The paper applies the method to a model of individual shopping behavior. © 1999 Elsevier Science S.A. All rights reserved.

The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

Head and neck squamous-cell cancer and its association with polymorphic enzymes of xenobiotic metabolism and repair

Tobacco smoking, alcohol drinking, and occupational exposures to polycyclic aromatic hydrocarbons are the major proven risk factors for human head and neck squamous-cell cancer (HNSCC). Major research focus on gene-environment interactions concerning HNSCC has been on genes encoding enzymes of metabolism for tobacco smoke constituents and repair enzymes. To investigate the role of genetically determined individual predispositions in enzymes of xenobiotic metabolism and in repair enzymes under the exogenous risk factor tobacco smoke in the carcinogenesis of HNSCC, we conducted a case-control study on 312 cases and 300 noncancer controls. We focused on the impact of 22 sequence variations in CYP1A1, CYP1B1, CYP2E1, ERCC2/XPD, GSTM1, GSTP1, GSTT1, NAT2, NQO1, and XRCC1. To assess relevant main and interactive effects of polymorphic genes on the susceptibility to HNSCC we used statistical models such as logic regression and a Bayesian version of logic regression. In subgroup analysis of nonsmokers, main effects in ERCC2 (Lys751Gln) C/C genotype and combined ERCC2 (Arg156Arg) C/A and A/A genotypes were predominant. When stratifying for smokers, the data revealed main effects on combined CYP1B1 (Leu432Val) C/G and G/G genotypes, followed by CYP1B1 (Leu432Val) G/G genotype and CYP2E1 (-70G>T) G/T genotype. When fitting logistic regression models including relevant main effects and interactions in smokers, we found relevant associations of CYP1B1 (Leu432Val) C/G genotype and CYP2E1 (-70G>T) G/T genotype (OR, 10.84; 95% CI, 1.64-71.53) as well as CYP1B1 (Leu432Val) G/G genotype and GSTM1 null/null genotype (OR, 11.79; 95% CI, 2.18-63.77) with HNSCC. The findings underline the relevance of genotypes of polymorphic CYP1B1 combined with exposures to tobacco smoke.

An evaluation of crowd counting methods, features and regression models

Existing crowd counting algorithms rely on holistic, local or histogram based features to capture crowd properties. Regression is then employed to estimate the crowd size. Insufficient testing across multiple datasets has made it difficult to compare and contrast different methodologies. This paper presents an evaluation across multiple datasets to compare holistic, local and histogram based methods, and to compare various image features and regression models. A K-fold cross validation protocol is followed to evaluate the performance across five public datasets: UCSD, PETS 2009, Fudan, Mall and Grand Central datasets. Image features are categorised into five types: size, shape, edges, keypoints and textures. The regression models evaluated are: Gaussian process regression (GPR), linear regression, K nearest neighbours (KNN) and neural networks (NN). The results demonstrate that local features outperform equivalent holistic and histogram based features; optimal performance is observed using all image features except for textures; and that GPR outperforms linear, KNN and NN regression

A national satellite-based land-use regression model for air pollution exposure assessment in Australia

Land-use regression (LUR) is a technique that can improve the accuracy of air pollution exposure assessment in epidemiological studies. Most LUR models are developed for single cities, which places limitations on their applicability to other locations. We sought to develop a model to predict nitrogen dioxide (NO2) concentrations with national coverage of Australia by using satellite observations of tropospheric NO2 columns combined with other predictor variables. We used a generalised estimating equation (GEE) model to predict annual and monthly average ambient NO2 concentrations measured by a national monitoring network from 2006 through 2011. The best annual model explained 81% of spatial variation in NO2 (absolute RMS error=1.4 ppb), while the best monthly model explained 76% (absolute RMS error=1.9 ppb). We applied our models to predict NO2 concentrations at the ~350,000 census mesh blocks across the country (a mesh block is the smallest spatial unit in the Australian census). National population-weighted average concentrations ranged from 7.3 ppb (2006) to 6.3 ppb (2011). We found that a simple approach using tropospheric NO2 column data yielded models with slightly better predictive ability than those produced using a more involved approach that required simulation of surface-to-column ratios. The models were capable of capturing within-urban variability in NO2, and offer the ability to estimate ambient NO2 concentrations at monthly and annual time scales across Australia from 2006–2011. We are making our model predictions freely available for research.

A Gaussian pseudolikelihood approach for quantile regression with repeated measurements

To enhance the efficiency of regression parameter estimation by modeling the correlation structure of correlated binary error terms in quantile regression with repeated measurements, we propose a Gaussian pseudolikelihood approach for estimating correlation parameters and selecting the most appropriate working correlation matrix simultaneously. The induced smoothing method is applied to estimate the covariance of the regression parameter estimates, which can bypass density estimation of the errors. Extensive numerical studies indicate that the proposed method performs well in selecting an accurate correlation structure and improving regression parameter estimation efficiency. The proposed method is further illustrated by analyzing a dental dataset.

Approximation of Bayesian predictive p-values with regression ABC

In the Bayesian framework a standard approach to model criticism is to compare some function of the observed data to a reference predictive distribution. The result of the comparison can be summarized in the form of a p-value, and it's well known that computation of some kinds of Bayesian predictive p-values can be challenging. The use of regression adjustment approximate Bayesian computation (ABC) methods is explored for this task. Two problems are considered. The first is the calibration of posterior predictive p-values so that they are uniformly distributed under some reference distribution for the data. Computation is difficult because the calibration process requires repeated approximation of the posterior for different data sets under the reference distribution. The second problem considered is approximation of distributions of prior predictive p-values for the purpose of choosing weakly informative priors in the case where the model checking statistic is expensive to compute. Here the computation is difficult because of the need to repeatedly sample from a prior predictive distribution for different values of a prior hyperparameter. In both these problems we argue that high accuracy in the computations is not required, which makes fast approximations such as regression adjustment ABC very useful. We illustrate our methods with several samples.

The epidemiological modelling of major depressive disorder : application for the global burden of disease study 2010

Background Although the detrimental impact of major depressive disorder (MDD) at the individual level has been described, its global epidemiology remains unclear given limitations in the data. Here we present the modelled epidemiological profile of MDD dealing with heterogeneity in the data, enforcing internal consistency between epidemiological parameters and making estimates for world regions with no empirical data. These estimates were used to quantify the burden of MDD for the Global Burden of Disease Study 2010 (GBD 2010). Method Analyses drew on data from our existing literature review of the epidemiology of MDD. DisMod-MR, the latest version of the generic disease modelling system redesigned as a Bayesian meta-regression tool, derived prevalence by age, year and sex for 21 regions. Prior epidemiological knowledge, study- and country-level covariates adjusted sub-optimal raw data. Results There were over 298 million cases of MDD globally at any point in time in 2010, with the highest proportion of cases occurring between 25 and 34 years. Global point prevalence was very similar across time (4.4% (95% uncertainty: 4.2–4.7%) in 1990, 4.4% (4.1–4.7%) in 2005 and 2010), but higher in females (5.5% (5.0–6.0%) compared to males (3.2% (3.0–3.6%) in 2010. Regions in conflict had higher prevalence than those with no conflict. The annual incidence of an episode of MDD followed a similar age and regional pattern to prevalence but was about one and a half times higher, consistent with an average duration of 37.7 weeks. Conclusion We were able to integrate available data, including those from high quality surveys and sub-optimal studies, into a model adjusting for known methodological sources of heterogeneity. We were also able to estimate the epidemiology of MDD in regions with no available data. This informed GBD 2010 and the public health field, with a clearer understanding of the global distribution of MDD.

Burden of depressive disorders by country, sex, age, and year : findings from the Global Burden of Disease Study 2010

Background Depressive disorders were a leading cause of burden in the Global Burden of Disease (GBD) 1990 and 2000 studies. Here, we analyze the burden of depressive disorders in GBD 2010 and present severity proportions, burden by country, region, age, sex, and year, as well as burden of depressive disorders as a risk factor for suicide and ischemic heart disease. Methods and Findings Burden was calculated for major depressive disorder (MDD) and dysthymia. A systematic review of epidemiological data was conducted. The data were pooled using a Bayesian meta-regression. Disability weights from population survey data quantified the severity of health loss from depressive disorders. These weights were used to calculate years lived with disability (YLDs) and disability adjusted life years (DALYs). Separate DALYs were estimated for suicide and ischemic heart disease attributable to depressive disorders.Depressive disorders were the second leading cause of YLDs in 2010. MDD accounted for 8.2% (5.9%-10.8%) of global YLDs and dysthymia for 1.4% (0.9%-2.0%). Depressive disorders were a leading cause of DALYs even though no mortality was attributed to them as the underlying cause. MDD accounted for 2.5% (1.9%-3.2%) of global DALYs and dysthymia for 0.5% (0.3%-0.6%). There was more regional variation in burden for MDD than for dysthymia; with higher estimates in females, and adults of working age. Whilst burden increased by 37.5% between 1990 and 2010, this was due to population growth and ageing. MDD explained 16 million suicide DALYs and almost 4 million ischemic heart disease DALYs. This attributable burden would increase the overall burden of depressive disorders from 3.0% (2.2%-3.8%) to 3.8% (3.0%-4.7%) of global DALYs. Conclusions GBD 2010 identified depressive disorders as a leading cause of burden. MDD was also a contributor of burden allocated to suicide and ischemic heart disease. These findings emphasize the importance of including depressive disorders as a public-health priority and implementing cost-effective interventions to reduce its burden.Please see later in the article for the Editors' Summary.

Design, construction and evaluation of systems to predict risk in obstetrics

We present a systematic, practical approach to developing risk prediction systems, suitable for use with large databases of medical information. An important part of this approach is a novel feature selection algorithm which uses the area under the receiver operating characteristic (ROC) curve to measure the expected discriminative power of different sets of predictor variables. We describe this algorithm and use it to select variables to predict risk of a specific adverse pregnancy outcome: failure to progress in labour. Neural network, logistic regression and hierarchical Bayesian risk prediction models are constructed, all of which achieve close to the limit of performance attainable on this prediction task. We show that better prediction performance requires more discriminative clinical information rather than improved modelling techniques. It is also shown that better diagnostic criteria in clinical records would greatly assist the development of systems to predict risk in pregnancy. We present a systematic, practical approach to developing risk prediction systems, suitable for use with large databases of medical information. An important part of this approach is a novel feature selection algorithm which uses the area under the receiver operating characteristic (ROC) curve to measure the expected discriminative power of different sets of predictor variables. We describe this algorithm and use it to select variables to predict risk of a specific adverse pregnancy outcome: failure to progress in labour. Neural network, logistic regression and hierarchical Bayesian risk prediction models are constructed, all of which achieve close to the limit of performance attainable on this prediction task. We show that better prediction performance requires more discriminative clinical information rather than improved modelling techniques. It is also shown that better diagnostic criteria in clinical records would greatly assist the development of systems to predict risk in pregnancy.

Bivariate genome-wide association study of genetically correlated neuroimaging phenotypes from DTI and MRI through a seemingly unrelated regression model

Large multisite efforts (e.g., the ENIGMA Consortium), have shown that neuroimaging traits including tract integrity (from DTI fractional anisotropy, FA) and subcortical volumes (from T1-weighted scans) are highly heritable and promising phenotypes for discovering genetic variants associated with brain structure. However, genetic correlations (rg) among measures from these different modalities for mapping the human genome to the brain remain unknown. Discovering these correlations can help map genetic and neuroanatomical pathways implicated in development and inherited risk for disease. We use structural equation models and a twin design to find rg between pairs of phenotypes extracted from DTI and MRI scans. When controlling for intracranial volume, the caudate as well as related measures from the limbic system - hippocampal volume - showed high rg with the cingulum FA. Using an unrelated sample and a Seemingly Unrelated Regression model for bivariate analysis of this connection, we show that a multivariate GWAS approach may be more promising for genetic discovery than a univariate approach applied to each trait separately.

Discovery and replication of gene influences on brain structure using LASSO regression

We implemented least absolute shrinkage and selection operator (LASSO) regression to evaluate gene effects in genome-wide association studies (GWAS) of brain images, using an MRI-derived temporal lobe volume measure from 729 subjects scanned as part of the Alzheimer's Disease Neuroimaging Initiative (ADNI). Sparse groups of SNPs in individual genes were selected by LASSO, which identifies efficient sets of variants influencing the data. These SNPs were considered jointly when assessing their association with neuroimaging measures. We discovered 22 genes that passed genome-wide significance for influencing temporal lobe volume. This was a substantially greater number of significant genes compared to those found with standard, univariate GWAS. These top genes are all expressed in the brain and include genes previously related to brain function or neuropsychiatric disorders such as MACROD2, SORCS2, GRIN2B, MAGI2, NPAS3, CLSTN2, GABRG3, NRXN3, PRKAG2, GAS7, RBFOX1, ADARB2, CHD4, and CDH13. The top genes we identified with this method also displayed significant and widespread post hoc effects on voxelwise, tensor-based morphometry (TBM) maps of the temporal lobes. The most significantly associated gene was an autism susceptibility gene known as MACROD2.We were able to successfully replicate the effect of the MACROD2 gene in an independent cohort of 564 young, Australian healthy adult twins and siblings scanned with MRI (mean age: 23.8±2.2 SD years). Our approach powerfully complements univariate techniques in detecting influences of genes on the living brain.