Influence of human immunodeficiency virus infection on neurological impairment: an analysis of longitudinal binary data with informative drop-out

A study to investigate the human immunodeficiency virus (HIV) status on the course of neurological impairment, conducted by the HIV Center at Columbia University, followed a cohort of HIV positive and negative gay men for 5 years and assessed the presence or absence of neurological impairment every 6 months. Almost half of the subjects dropped out before the end of the study for reasons that might have been related to the missing neurological data. We propose likelihood-based methods for analysing such binary longitudinal data under informative and non-informative drop-out. A transition model is assumed for the binary response, and several models for the drop-out processes are considered which are functions of the response variable (neurological impairment). The likelihood ratio test is used to compare models with informative and non-informative drop-out mechanisms. Using simulations, we investigate the percentage bias and mean-squared error (MSE) of the parameter estimates in the transition model under various assumptions for the drop-out. We find evidence for informative drop-out in the study, and we illustrate that the bias and MSE for the parameters of the transition model are not directly related to the observed drop-out or missing data rates. The effect of HIV status on the neurological impairment is found to be statistically significant under each of the models considered for the drop-out, although the regression coefficient may be biased in certain cases. The presence and relative magnitude of the bias depend on factors such as the probability of drop-out conditional on the presence of neurological impairment and the prevalence of neurological impairment in the population under study.     

Stochastic models for fractal processes

This paper considers the situation where a stochastic process may display both long-range dependence (LRD) and intermittency. The existence of such a process is established in Anh et al. (1999). Existing works have commonly paid attention either to LRD or intermittency quite separately. This paper offers a convenient framework to study both effects simultaneously. A method is given to estimate and separate the two effects. The wavelet theory plays an essential role in this procedure. Numerical experiments on fractional Brownian motion and multiplicative cascade processes confirm the power of the method.     

Efficacy of programmes for the unemployed: discrete time modelling of duration data from a matched-comparison study

An evaluation is described of two UK Government programmes for the long-term unemployed in Great Britain, Employment Training and Employment Action, using discrete time hazard modelling of event histories. The study design employed a closely matched comparison group and carefully chosen control variables to minimize the effect of selection bias on conclusions. The effect of unobserved heterogeneity is investigated by using some standard random effect model formulations.     

Study of a Markov model for a high-quality dependent process

For high-quality processes, non-conforming items are seldom observed and the traditional p (or np) charts are not suitable for monitoring the state of the process. A type of chart based on the count of cumulative conforming items has recently been introduced and it is especially useful for automatically collected one-at-a-time data. However, in such a case, it is common that the process characteristics become dependent as items produced one after another are inspected. In this paper, we study the problem of process monitoring when the process is of high quality and measurement values possess a certain serial dependence. The problem of assuming independence is examined and a Markov model for this type of process is studied, upon which suitable control procedures can be developed.     

Shrinkage Structure of Partial Least Squares

Partial least squares regression (PLS) is one method to estimate parameters in a linear model when predictor variables are nearly collinear. One way to characterize PLS is in terms of the scaling (shrinkage or expansion) along each eigenvector of the predictor correlation matrix. This characterization is useful in providing a link between PLS and other shrinkage estimators, such as principal components regression (PCR) and ridge regression (RR), thus facilitating a direct comparison of PLS with these methods. This paper gives a detailed analysis of the shrinkage structure of PLS, and several new results are presented regarding the nature and extent of shrinkage.     

Estimation of long-run inefficiency levels: a dynamic frontier approach

Cornwell, Schmidt, and Sickles (1990) and Kumbhakar (1990), among others, developed stochasticfrontier production models which allow firm specific inefficiency levels to change over time. These studies assumed arbitrary restrictions on the short-run dynamics of efficiency levels which have little theoretical justification. Further, the models are inappropriate for estimation of long-run efficiencies. We consider estimation of an alternative frontier model in which firmspecific technical inefficiency levels are autoregressive. This model is particularly useful to examine a potential dynamic link between technical innovations and production inefficiency levels. We apply our methodology to a panel of US airlines.     

The peculiar shrinkage properties of partial least squares regression

Partial least squares regression has been widely adopted within some areas as a useful alternative to ordinary least squares regression in the manner of other shrinkage methods such as principal components regression and ridge regression. In this paper we examine the nature of this shrinkage and demonstrate that partial least squares regression exhibits some undesirable properties.     

Detecting active effects in unreplicated designs

Unreplicated factorial designs pose a difficult problem in analysis because there are no degrees of freedom left to estimate the error. Daniel [Technometrics 1 (1959), pp. 311-341] proposed an ingenious graphical method that does not require σ to be estimated. Here we try to put Daniel's method into a formal framework and lift the subjectiveness that carries. A simulation study has been conducted that shows that the proposed method behaves better than Lenth's [Technometrics 31 (1989), pp. 469-473] popular method.     

Predicting body fat using weight–height indices

While body fat is the most accurate measure of obesity, its measurement requires special equipment that can be costly and time consuming to operate. Attention has thus typically focused on the easier to calculate body mass index (BMI). However, the ability of BMI to accurately identify obesity has been increasingly questioned. This paper focuses attention on whether more general body mass indices are appropriate measures of body fat. Using a data set of body fat, height, and weight measurements, general models are estimated which nest a wide variety of weight–height indices as special cases. In the absence of a race and gender categorisation, the conventional BMI was found to be the appropriate index with which to predict body fat. When such a categorisation was made, however, the BMI was never selected as the appropriate index. In general, predicted female body fat was some 10 kg higher than that of a male of identical build and predicted % body fat was over 11 percentage points higher, but age effects were smaller for females. Considerable racial differences in predicted body fat were found for males, but such differences were less marked for females. The implications of this finding for interpreting recent research on the effect of obesity on health, society, and economic factors are considered.