R. Webster West

Interactive Demonstrations for Statistics Education on the World Wide Web

The World Wide Web (WWW) is a tool that can beused in many ways for basic statistics education. Using the latest WWW technology, educators can nowinclude interactive demonstrations in the form of J...

Modeling the impact of HIV on the spread of tuberculosis in the United States

Tuberculosis (TB) was thought to be safely in decline in the United States in the mid-1980s because the number of cases had dropped by 74% between 1953 and 1985. An increase in TB cases was reported, however, in 1986, and an upward trend in TB incidence has continued. The turnaround in TB is well correlated with the rise of the HIV (human immunodeficiency virus) epidemic. The purpose of this work is to investigate, through the use of mathematical models, the magnitude and duration of the effect that the HIV epidemic may have on TB. Models are developed which reflect the transmission dynamics of both TB and HIV, and the relative merits of these models are discussed. The models are then linked together to form a model for the combined spread of both diseases. A numerical study is performed to investigate the influence of certain key parameters. The effect that HIV will have on the general population is found to be dependent on the contact structure between the general population and the HIV risk groups, as well as a possible shift in the dynamics associated with TB transmission.

Models for the simple epidemic.

Stochastic and deterministic models for the simple epidemic are formulated and compared. Both discrete and continuous time models are considered. The conjecture of equivalence between stochastic and deterministic models for large initial susceptible populations is shown to be of limited practical importance by a simulation study, whereas the number of initial infectives is shown to dramatically affect the convergence of the two types of models. In addition, the discrete stochastic model, which is easy to formulate and simulate, is shown to converge with its continuous counterpart as the time step becomes small.

Exact one-sided simultaneous confidence bands via Uusipaikka’s method

Computation of one-sided simultaneous confidence bands is detailed for a simple linear regression under interval restrictions on the predictor variable, using a method due to Uusipaikka (1983,J. Amer. Statist. Assoc.,78, 638–644). The case of a single interval restriction is emphasized. A WWW-based applet for computing the bands is described.

Statistical Tools on the World Wide Web

Abstract The World Wide Web (WWW) represents a powerful tool for furthering the development and practice of statistics. The GASP (Globally Accessible Statistical Procedures) WWW site has been set up as a primary listing of statistical procedures which can be used over the WWW. This article highlights several possible approaches for making a procedure WWW accessible. These approaches effectively solve many of the problems typically encountered when using a new statistical procedure. Applying the methods discussed, any statistical technique can be made available to anyone with a forms- or Java-capable WWW browser. Procedures can be delivered in a virtually platform-independent manner with only minimal requirements on a users hardware or software.

Benchmark Analysis: Shopping with Proper Confidence

We discuss the issue of using benchmark doses for quantifying (excess) risk associated with exposure to environmental hazards. The paradigm of low-dose risk estimation in dose-response modeling is used as the primary application scenario. Emphasis is placed on making simultaneous inferences on benchmark doses when data are in the form of proportions, although the concepts translate easily to other forms of outcome data.

Confidence limits on one-stage model parameters in benchmark risk assessment

In modern environmental risk analysis, inferences are often desired on those low dose levels at which a fixed benchmark risk is achieved. In this paper, we study the use of confidence limits on parameters from a simple one-stage model of risk historically popular in benchmark analysis with quantal data. Based on these confidence bounds, we present methods for deriving upper confidence limits on extra risk and lower bounds on the benchmark dose. The methods are seen to extend automatically to the case where simultaneous inferences are desired at multiple doses. Monte Carlo evaluations explore characteristics of the parameter estimates and the confidence limits under this setting.

Multiplicity-adjusted inferences in risk assessment: Benchmark analysis with continuous response data

We develop and study multiplicity adjustments for low-dose inferences in environmental risk assessment. Application is intended for risk analysis studies where human, animal, or ecological data are used to set safe levels of a hazardous environmental agent. A modern method for making inferences in this setting is known as benchmark analysis, where attention centers on the dose at which a fixed benchmark level of risk is achieved. Both upper confidence limits on the risk and lower confidence limits on the “benchmark dose” are of interest. In practice, a number of possible benchmark risks may be under study; if so, corrections must be applied to adjust the limits for multiplicity. In this note, we discuss approaches for doing so with continuous, nonquantal response data.

SIMULTANEOUS CONFIDENCE BOUNDS FOR LOW-DOSE RISK ASSESSMENT WITH NONQUANTAL DATA

ABSTRACT We study the use of simultaneous confidence bounds for making low-dose inferences in quantitative risk analysis. Confidence limits are constructed for outcomes measured on a continuous scale, assuming a simple linear model for the observed response. From the simultaneous confidence bounds, simultaneous lower limits on the benchmark dose associated with a particular risk are also constructed.

Asymmetric confidence bands for simple linear regression over bounded intervals

Abstract Computation of simultaneous confidence bands is described for simple linear regressions where the band is constructed to be asymmetric about the predictor mean. Both two-sided and one-sided bands are constructed. The bands represent extensions of a class of symmetric confidence bands due to Bowden, 1970. J. Amer. Statist. Assoc. 65, 413–421. An example illustrates the computations, and a WWW-based applet for computing the bands is described.