Statistics for Spatial Data.

In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

The t distribution provides a useful extension of the normal for statistical modeling of data sets involving errors with longer-than-normal tails. An analytical strategy based on maximum likelihood for a general model with multivariate t errors is suggested and applied to a variety of problems, including linear and nonlinear regression, robust estimation of the mean and covariance matrix with missing data, unbalanced multivariate repeated-measures data, multivariate modeling of pedigree data, and multivariate nonlinear regression. The degrees of freedom parameter of the t distribution provides a convenient dimension for achieving robust statistical inference, with moderate increases in computational complexity for many models. Estimation of precision from asymptotic theory and the bootstrap is discussed, and graphical methods for checking the appropriateness of the t distribution are presented.

/pdf/robust-statistical-modeling-using-the-t-distribution-7l58dinnf1.pdf

Robust Statistical Modeling Using the t Distribution

Normal mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster sets of continuous multivariate data. However, for a set of data containing a group or groups of observations with longer than normal tails or atypical observations, the use of normal components may unduly affect the fit of the mixture model. In this paper, we consider a more robust approach by modelling the data by a mixture of t distributions. The use of the ECM algorithm to fit this t mixture model is described and examples of its use are given in the context of clustering multivariate data in the presence of atypical observations in the form of background noise.

/pdf/robust-mixture-modelling-using-the-t-distribution-52huig0ns2.pdf

Robust mixture modelling using the t distribution

Human immunodeficiency virus (HIV) persistence in latently infected resting memory CD4+ T-cells is the major barrier to HIV cure. Cellular histone deacetylases (HDACs) are important in maintaining HIV latency and histone deacetylase inhibitors (HDACi) may reverse latency by activating HIV transcription from latently infected CD4+ T-cells. We performed a single arm, open label, proof-of-concept study in which vorinostat, a pan-HDACi, was administered 400 mg orally once daily for 14 days to 20 HIV-infected individuals on suppressive antiretroviral therapy (ART). The primary endpoint was change in cell associated unspliced (CA-US) HIV RNA in total CD4+ T-cells from blood at day 14. The study is registered at ClinicalTrials.gov (NCT01365065). Vorinostat was safe and well tolerated and there were no dose modifications or study drug discontinuations. CA-US HIV RNA in blood increased significantly in 18/20 patients (90%) with a median fold change from baseline to peak value of 7.4 (IQR 3.4, 9.1). CA-US RNA was significantly elevated 8 hours post drug and remained elevated 70 days after last dose. Significant early changes in expression of genes associated with chromatin remodeling and activation of HIV transcription correlated with the magnitude of increased CA-US HIV RNA. There were no statistically significant changes in plasma HIV RNA, concentration of HIV DNA, integrated DNA, inducible virus in CD4+ T-cells or markers of T-cell activation. Vorinostat induced a significant and sustained increase in HIV transcription from latency in the majority of HIV-infected patients. However, additional interventions will be needed to efficiently induce virus production and ultimately eliminate latently infected cells.

/pdf/activation-of-hiv-transcription-with-short-course-vorinostat-2wt8d0p99z.pdf

Activation of HIV transcription with short-course vorinostat in HIV-infected patients on suppressive antiretroviral therapy.

SUMMARY Liang & Zeger (1986) introduced a generalised estimating equations approach based on a 'working' correlation matrix to obtain consistent and efficient estimators of regression parameters in the class of generalised linear models for repeated measures data. As demonstrated by Crowder (1995), because of the uncertainty of definition of the working correlation matrix, the Liang-Zeger approach may in some cases lead to a complete breakdown of the estimation of the regression parameters. In this paper we show that, even though the Liang-Zeger approach in many situations yields consistent estimators for the regression parameters, these estimators are usually inefficient as compared to the regression estimators obtained by using the independence estimating equations approach.

Miscellanea. On the efficiency of regression estimators in generalised linear models for longitudinal data

In the longitudinal regression setup, interest may be focused primarily on the regression parameters for the marginal expectations of the longitudinal responses, the longitudinal correlation parameters being of secondary interest. Second, interest may be focused on both the regression and the longitudinal correlation parameters. Under the first setup, there exists a "working'' correlation matrix based generalized estimating equation (GEE) approach for the estimation of the regression parameters. Under the second setup, there exist two approaches for the joint estimation of the regression and the longitudinal correlations. In one approach, true longitudinal correlations are modeled and the regression and the true correlation parameters are jointly estimated based on a GEE approach. The second approach avoids the specification of the true longitudinal correlation structure and deals with the joint estimation of the regression and a vector of "working'' correlation parameters. In this second approach under the second setup, there again exist two joint estimation methods, one requiring moments up to order 4 and the other somehow using moments up to order 2 for the construction of the estimating equations for the "working'' correlation parameters. In this paper, we first provide an outline of the desirable features and drawbacks of each of these four existing approaches. By using a general autocorrelation structure to model the true longitudinal correlations, we then provide an outline of the advantages of three new approaches. In the first new approach, the true longitudinal correlations are estimated by the method of moments, whereas the regression estimates are obtained based on a generalized quasi-likelihood (GQL) estimation approach. The other two new approaches simultaneously estimate the regression and the true longitudinal correlation parameters. It is shown through a simulation study that, among these three new approaches, the first approach performs the best in estimating both the regression and the true correlation parameters, even though the longitudinal correlations are estimated separately by the method of moments.

/pdf/an-overview-on-regression-models-for-discrete-longitudinal-2c77math37.pdf

An Overview on Regression Models for Discrete Longitudinal Responses

This paper deals with a regression model for several vari¬ables under the assumption that the errors have a multivariate t-distribution. The parameters of the model, the regression parameters, as well as the scale parameters and the degress of freedom of the error variable are estimated and the estimation procedure is illustrated by a numerical example, Also, the prop¬erties of the estimators and tests for the regression parameters are discussed.

Estimation of the parameters of a regression model with a multivariate t error variable

To examine longitudinal and gestational effects of mineral content in human milk, we analyzed human milk from lactating mothers of premature (PRT, n = 24, 2500 g, 39-41 wk gestation), living in Newfoundland, Canada. Samples were collected once a week for 8 wk with one final sample collected at 3 mo. Milk samples collected in acid-washed containers were wet ashed with concentrated HNO3, and barium, cadmium, calcium, cesium, cobalt, copper, cerium, lanthanum, magnesium, manganese, molybdenum, nickel, lead, rubidium, tin, strontium, and zinc were measured using inductively coupled plasma-mass spectrometry. Data were analyzed using standard multiple-regression procedures with correlated data analyses to take account of the relationship between successive weeks. Results indicated lower Ca and Pb in PRT milk. Calcium was the only nutritionally significant element to differ between groups. Molybdenum in both PRT and FT milk showed a definite decrease with time, suggesting that the Mo content in milk is homeostatically regulated. However, Ce, La, Ba, and Sn did not display any pattern indicative of biological regulation and potential human requirement.

Elemental composition of human milk from mothers of premature and full-term infants during the first 3 months of lactation

SUMMARY In many biomedical studies, longitudinal count data comprise repeated responses and a set of multidimensional covariates for a large number of individuals. When the response variable in such models is subject to overdispersion, the overdispersion parameter influences the marginal variance. In such cases, the overdispersion parameter plays a significant role in efficient estimation of the regression parameters. This raises the need for joint estimation of the regression parameters and the overdispersion parameter, the longitudinal correlations being nuisance parameters. In this paper, we develop a generalised estimating equations approach based on a general autocorrelation structure for the repeated overdispersed data. The asymptotic properties of the estimators of the main parameters are discussed, and the estimation methodology is illustrated by analysing data on epileptic seizure counts.

https://www.jstor.org/stable/pdfplus/4140584.pdf

Brajendra C. Sutradhar

Papers

Miscellanea. On the efficiency of regression estimators in generalised linear models for longitudinal data

An Overview on Regression Models for Discrete Longitudinal Responses

Estimation of the parameters of a regression model with a multivariate t error variable

Elemental composition of human milk from mothers of premature and full-term infants during the first 3 months of lactation

Analysing longitudinal count data with overdispersion