Screening methods for linear errors-in-variables models in high dimensions.

Microarray studies, in order to identify genes associated with an outcome of interest, usually produce noisy measurements for a large number of gene expression features from a small number of subjects. One common approach to analyzing such high-dimensional data is to use linear errors-in-variables (EIV) models; however, current methods for fitting such models are computationally expensive. In this paper, we present two efficient screening procedures, namely, corrected penalized marginal screening (PMSc) and corrected sure independence screening (SISc), to reduce the number of variables for final model building. Both screening procedures are based on fitting corrected marginal regression models relating the outcome to each contaminated covariate separately, which can be computed efficiently even with a large number of features. Under mild conditions, we show that these procedures achieve screening consistency and reduce the number of features substantially, even when the number of covariates grows exponentially with sample size. In addition, if the true covariates are weakly correlated, we show that PMSc can achieve full variable selection consistency. Through a simulation study and an analysis of gene expression data for bone mineral density of Norwegian women, we demonstrate that the two new screening procedures make estimation of linear EIV models computationally scalable in high-dimensional settings, and improve finite sample estimation and selection performance compared with estimators that do not employ a screening stage.

Assuming independence in spatial latent variable models: Consequences and implications of misspecification.

Multivariate spatial data, where multiple responses are simultaneously recorded across spatially indexed observational units, are routinely collected in a wide variety of disciplines. For example, the Southern Ocean Continuous Plankton Recorder survey collects records of zooplankton communities in the Indian sector of the Southern Ocean, with the aim of identifying and quantifying spatial patterns in biodiversity in response to environmental change. One increasingly popular method for modeling such data is spatial generalized linear latent variable models (GLLVMs), where the correlation across sites is captured by a spatial covariance function in the latent variables. However, little is known about the impact of misspecifying the latent variable correlation structure on inference of various parameters in such models. To address this gap in the literature, we investigate how misspecifying and assuming independence for the latent variables' correlation structure impacts estimation and inference in spatial GLLVMs. Through both theory and numerical studies, we show that performance of maximum likelihood estimation and inference on regression coefficients under misspecification depends on a combination of the response type, the magnitude of true regression coefficient, and the corresponding loadings, and, most importantly, whether the corresponding covariate is (also) spatially correlated. On the other hand, estimation and inference of truly nonzero loadings and prediction of latent variables is consistently not robust to misspecification of the latent variable correlation structure.

Analysis of survey on menstrual disorder among teenagers using Gaussian copula model with graphical lasso prior.

A high prevalence of menstrual disturbance has been reported among teenage girls, and research shows that there are delays in diagnosis of endometriosis among young girls. Using data from the Menstrual Disorder of Teenagers Survey (administered in 2005 and 2016), we propose a Gaussian copula model with graphical lasso prior to identify cohort differences in menstrual characteristics and to predict endometriosis. The model includes random effects to account for clustering by school, and we use the extended rank likelihood copula model to handle variables of mixed-type. The graphical lasso prior shrinks the elements in the precision matrix of a Gaussian distribution to encourage a sparse graphical structure, where the level of shrinkage is adaptable based on the strength of the conditional associations among questions in the survey. Applying our proposed model to the menstrual disorder data set, we found that menstrual disturbance was more pronouncedly reported over a decade, and we found some empirical differences between those girls with higher risk of developing endometriosis and the general population.

Prediction of properties from simulations: a re-examination with modern statistical methods.

We discuss models fit to data collected by Duffy and Jorgensen to predict solvation free energies and partition equilibria of drugs, organic molecules, aromatic heterocycles, and other molecules. These data were originally examined using linear regression, but here more recently developed statistical models are applied. The data set is complicated due to the presence of discrepant observations and also curvature in the response. In some cases it is possible to discard a small number of the observations to get good fit to the data, but, in others, discarding an increasing proportion of the observations does not improve the fit. Our general preference is to use robust parameter estimation which downweights to reduce the influence of discrepant observations on the fitted models. Models are selected for four responses using linear or more complicated representations of the explanatory variables, such as cubic polynomials, B-splines, or smoothers via generalized additive models (GAMs). Variables are chosen using the traditional approach of formal tests to assess contribution to the fit of a model, and resampling methods including bootstrap are also considered to assess the prediction error for given models. Results of our analysis indicate that GAMs are an improvement on linear models for describing the data and making predictions. In general robust regression models and GAMs have the smallest conditional expected loss of prediction over the four responses. In addition, robust regression models offer the advantage of identifying molecules that perform poorly in the fit. In general, models were identified that yielded an improvement of approximately 50% in the conditional expected loss of prediction compared with the original parametrization of Duffy and Jorgensen. It was also found that the use of cross-validation to compare models was unreliable, and bootstrapping is preferred.

Line transect sampling in small regions.

This article develops an approach to estimating population abundance from line transect surveys that uses a calibration survey to estimate the detection function, which is then employed as a weight function in constructing the abundance estimate. Nonparametric methods of estimating the detection function via local regression and via a kernel density estimator are considered. The proposed methods are evaluated using a set of Western Australian plant data and weed enumeration data.

Methodology for estimating the abundance of rare animals: seabird nesting on north east Herald Cay.

We discuss the problem of estimating the number of nests of different species of seabirds on North East Herald Cay based on the data from a 1996 survey of quadrats along transects and data from similar past surveys. We consider three approaches based on different plausible models, namely a conditional negative binomial model that allows for additional zeroes in the data, a weighting approach (based on a heteroscedastic regression model), and a transform-both-sides regression approach. We find that the conditional negative binomial approach and a linear regression approach work well but that the transform-both-sides approach should not be used. We apply the conditional negative binomial and linear regression approaches with poststratification based on data quality and availability to estimate the number of frigatebird nests on North East Herald Cay.

Testing for glaucoma with the spatial frequency doubling illusion.

We examined the performance of tests for glaucoma based on the spatial frequency doubling (FD) illusion. Contrast thresholds for seeing the FD illusion in four large visual field regions were measured from 340 subjects who were tested up to seven times over 2 years. Median sensitivities of 91% at specificities of 95% were obtained. Test-retest variability for the worst hemifield thresholds averaged 2.22 db +/- 0.09 S.E. for all tested groups, and significant progression was observed for glaucoma suspects over the seven visits, indicating that tests based on the FD illusion can detect diffuse early glaucomatous loss.

The association between occlusion and attrition.

The purpose of this study was to identify variables of malocclusion that might be associated with attrition and then to quantify the relationship between these variables and attrition. The results of this study indicate that, with all other factors held constant, a patient's attrition score tends to: increase with age, increase with bite depth, decrease initially with overjet until a critical value and then increase, and be unaffected by sex, interincisal angle, U1 to NA angle, Angle classification, posterior or anterior cross bites. Further, we discuss the statistical treatment of data of this kind and emphasize the importance of a professional approach to analysis.

Sonicated echocardiographic contrast agents: reproducibility studies.

This article describes the production, analysis, and reproducibility of forming microbubbles for contrast ultrasound imaging. The sonication method used to generate microbubbles was tested by four independent observers, and a subsequent laser particle counter analysis of microbubble size and concentration determined the reproducibility of the method. The results indicated that the mean bubble size was 3.3 +/- 1.2 microns for the entire group, based on three trials of each of the four participants. The characteristics of the bubble size of the microbubbles between observers were assessed with a Poisson distribution with the reproducibility based on the sample mean for each observer's trials. Standardization and calibration of the laser particle counter was accomplished with commercially available latex spheres, sonicated albumin microspheres, and a Coulter counter analysis. Our results indicate that the sonication technique generates small microbubbles with a reproducible uniform size distribution. The method of microbubble production is reproducible and can be widely applied for use in contrast echocardiographic perfusion imaging of tissue in a variety of research and clinical studies.