A life table for a West Indian slave population

This note comments briefly on the system of slave registration set up in the British colonies, and deals in particular with the data tabulated for the British Guiana slave population in the Parliamentary Papers, 1833. From the age distributions given there a life table has been constructed by a census differencing method. This life table shows the extremely high mortality then being experienced by slave populations in the West Indies.     

The Relationships Between Sense of Belonging to a Community GLB Youth Group; School,Teacher, and Peer Connectedness; and Depressive Symptoms: Testing of a Path Model

Research indicates belonging to a gay, lesbian, and bisexual (GLB) support group is indirectly associated with fewer depressive symptoms, via higher levels of sense of belonging to the general community. The current study extended this research by testing a path model to determine whether school, teacher, and peer connectedness are influenced by sense of belonging to a community GLB youth group. A sample of 82 Australian GLB adolescents aged 14 to 18 years who currently attend high school completed the Center for Epidemiologic Studies Depression Scale, the Psychological Subscale of the Sense of Belonging Instrument, and the Social Questionnaire for Secondary Students. Results indicated very good model fit. Higher levels of belonging to a community GLB youth group were associated with higher levels of school, teacher, and peer connectedness, but only peer connectedness was directly associated with depressive symptoms. Higher levels of school and teacher connectedness were associated with higher levels of peer connectedness. Interventions aimed at increasing belonging to a community GLB youth group may have indirect benefits for the mental health of GLB adolescents, via higher levels of school, teacher, and peer connectedness.     

A robust automatic clustering algorithm for probability density functions with application to categorizing color images

This study develops a robust automatic algorithm for clustering probability density functions based on the previous research. Unlike other existing methods that often pre-determine the number of clusters, this method can self-organize data groups based on the original data structure. The proposed clustering method is also robust in regards to noise. Three examples of synthetic data and a real-world COREL dataset are utilized to illustrate the accurateness and effectiveness of the proposed approach.     

Estimation of discrete survival function for error‐prone diagnostic tests

The product limit or Kaplan‐Meier (KM) estimator is commonly used to estimate the survival function in the presence of incomplete time to event. Application of this method assumes inherently that the occurrence of an event is known with certainty. However, the clinical diagnosis of an event is often subject to misclassification due to assay error or adjudication error, by which the event is assessed with some uncertainty. In the presence of such errors, the true distribution of the time to first event would not be estimated accurately using the KM method. We develop a method to estimate the true survival distribution by incorporating negative predictive values and positive predictive values, into a KM‐like method of estimation. This allows us to quantify the bias in the KM survival estimates due to the presence of misclassified events in the observed data. We present an unbiased estimator of the true survival function and its variance. Asymptotic properties of the proposed estimators are provided, and these properties are examined through simulations. We demonstrate our methods using data from the Viral Resistance to Antiviral Therapy of Hepatitis C study.     

SPC as a tool for creating a successful business measurement framework

Many companies are trying to get to the bottom of what their main objectives are and what their business should be doing. The new Six Sigma approach concentrates on clarifying business strategy and making sure that everything relates to company objectives. It is vital to clarify each part of the business in such a way that everyone can understand the causes of variation that can lead to improvements in processes and performance. This paper describes a situation where the full implementation of SPC methodology has made possible a visual and widely appreciated summary of the performance of one important aspect of the business. The major part of the work was identifying the core objectives and deciding how to encapsulate each of them in one or more suitable measurements. The next step was to review the practicalities of obtaining the measurements and their reliability and representativeness. Finally, the measurements were presented in chart form and the more traditional steps of SPC analysis were commenced. Data from fast changing business environments are prone to many different problems, such as the short previous span of typical data, strange distributions and other uncertainties. Issues surrounding these and the eventual extraction of a meaningful set of information will be discussed in the paper. The measurement framework has proved very useful and, from an initial circulation of a handful of people, it now forms an important part of an information process that provides responsible managers with valuable control information. The measurement framework is kept fresh and vital by constant review and modifications. Improved electronic data collection and dissemination of the report has proved very important.     

Diagnostic checks for discrete data regression models using posterior predictive simulations

Model checking with discrete data regressions can be difficult because the usual methods such as residual plots have complicated reference distributions that depend on the parameters in the model. Posterior predictive checks have been proposed as a Bayesian way to average the results of goodness-of-fit tests in the presence of uncertainty in estimation of the parameters. We try this approach using a variety of discrepancy variables for generalized linear models fitted to a historical data set on behavioural learning. We then discuss the general applicability of our findings in the context of a recent applied example on which we have worked. We find that the following discrepancy variables work well, in the sense of being easy to interpret and sensitive to important model failures: structured displays of the entire data set, general discrepancy variables based on plots of binned or smoothed residuals versus predictors and specific discrepancy variables created on the basis of the particular concerns arising in an application. Plots of binned residuals are especially easy to use because their predictive distributions under the model are sufficiently simple that model checks can often be made implicitly. The following discrepancy variables did not work well: scatterplots of latent residuals defined from an underlying continuous model and quantile–quantile plots of these residuals.     

Two ways of modelling overdispersion in non-normal data

For non-normal data assumed to have distributions, such as the Poisson distribution, which have an a priori dispersion parameter, there are two ways of modelling overdispersion: by a quasi-likelihood approach or with a random-effect model. The two approaches yield different variance functions for the response, which may be distinguishable if adequate data are available. The epilepsy data of Thall and Vail and the fabric data of Bissell are used to exemplify the ideas.     

Adaptive interval estimation in one-way random effects models

Two-stage procedures are introduced to control the width and coverage (validity) of confidence intervals for the estimation of the mean, the between groups variance component and certain ratios of the variance components in one-way random effects models. The procedures use the pilot sample data to estimate an “optimal” group size and then proceed to determine the number of groups by a stopping rule. Such sampling plans give rise to unbalanced data, which are consequently analyzed by the harmonic mean method. Several asymptotic results concerning the proposed procedures are given along with simulation results to assess their performance in moderate sample size situations. The proposed procedures were found to effectively control the width and probability of coverage of the resulting confidence intervals in all cases and were also found to be robust in the presence of missing observations. From a practical point of view, the procedures are illustrated using a real data set and it is shown that the resulting unbalanced designs tend to require smaller sample sizes than is needed in a corresponding balanced design where the group size is arbitrarily pre-specified.