Optimal designs for generalized linear models

Summary This paper solves some D-optimal design problems for certain Generalized Linear Models where the mean depends on two parameters and two explanatory variables. In all of the cases considered the support point of the optimal designs are found to be independent of the unknown parameters. While in some cases the optimal design measures are given by two points with equal weights, in others the support is given by three point with weights depending on the unknown parameters, hence the designs are locally optimal in general. Empirical results on the efficiency of the locally optimal designs are also given. Some of the designs found can also be used for planning D-optimal experiments for the normal linear model, where the mean must be positive. This research was carried out in part at University College, London as an M.Sc. project. Thanks are due to Prof. I. Ford (University of Glasgow) and Prof. A. Giovagnoli (University of Perugia) for their valuable suggestions and critical observations.     

Liability in child welfare

Child welfare workers and agencies are vulnerable to lawsuits. Recent court rulings have more clearly defined the liability of workers. The distinguishing variable is custody. Children injured while in the custody of the state are entitled to sue for damages. Children injured by their parent, even if under the supervision of a child welfare agency, are not entitled to claim a violation of their 14th Amendment rights. These cases are reviewed and strategies designed to minimize vulnerability are offered.     

A measure of slope-rotatability for second order response surface experimental designs

In the design of experiments for estimating the slope of a response surface, slope-rotatability is a desirable property. In this paper, a measure is introduced that enables us to assess the degree of slope-rotatability for a given response surface design. The measure takes the value zero if and only if the design is slope-rotatable, and becomes larger as the design deviates from a slope-rotatable design. Examples of applying this measure to some response surface designs are also given.     

Analytical approximations for iterated bootstrap confidence intervals

Standard algorithms for the construction of iterated bootstrap confidence intervals are computationally very demanding, requiring nested levels of bootstrap resampling. We propose an alternative approach to constructing double bootstrap confidence intervals that involves replacing the inner level of resampling by an analytical approximation. This approximation is based on saddlepoint methods and a tail probability approximation of DiCiccio and Martin (1991). Our technique significantly reduces the computational expense of iterated bootstrap calculations. A formal algorithm for the construction of our approximate iterated bootstrap confidence intervals is presented, and some crucial practical issues arising in its implementation are discussed. Our procedure is illustrated in the case of constructing confidence intervals for ratios of means using both real and simulated data. We repeat an experiment of Schenker (1985) involving the construction of bootstrap confidence intervals for a variance and demonstrate that our technique makes feasible the construction of accurate bootstrap confidence intervals in that context. Finally, we investigate the use of our technique in a more complex setting, that of constructing confidence intervals for a correlation coefficient.     

Defining the linear portion of a sigmoid‐shaped curve: bend points

Formulae are provided that define the ‘bend points’, the beginning and end of the essentially linear dose–response region, for the four‐parameter logistic model. The formulae are expressed in both response and dose units. The derivation of the formulae is shown in order to illustrate the general nature of the methodology. Examples are given that describe how the formulae may be used while planning and conducting bioassays. Copyright © 2003 John Wiley & Sons, Ltd.     

Exposure Reconstruction for the TCDD-Exposed NIOSH Cohort Using a Concentration- and Age-Dependent Model of Elimination

Recent studies demonstrating a concentration dependence of elimination of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) suggest that previous estimates of exposure for occupationally exposed cohorts may have underestimated actual exposure, resulting in a potential overestimate of the carcinogenic potency of TCDD in humans based on the mortality data for these cohorts. Using a database on U.S. chemical manufacturing workers potentially exposed to TCDD compiled by the National Institute for Occupational Safety and Health (NIOSH), we evaluated the impact of using a concentration- and age-dependent elimination model (CADM) (Aylward et al., 2005) on estimates of serum lipid area under the curve (AUC) for the NIOSH cohort. These data were used previously by Steenland et al. (2001) in combination with a first-order elimination model with an 8.7-year half-life to estimate cumulative serum lipid concentration (equivalent to AUC) for these workers for use in cancer dose-response assessment. Serum lipid TCDD measurements taken in 1988 for a subset of the cohort were combined with the NIOSH job exposure matrix and work histories to estimate dose rates per unit of exposure score. We evaluated the effect of choices in regression model (regression on untransformed vs. ln-transformed data and inclusion of a nonzero regression intercept) as well as the impact of choices of elimination models and parameters on estimated AUCs for the cohort. Central estimates for dose rate parameters derived from the serum-sampled subcohort were applied with the elimination models to time-specific exposure scores for the entire cohort to generate AUC estimates for all cohort members. Use of the CADM resulted in improved model fits to the serum sampling data compared to the first-order models. Dose rates varied by a factor of 50 among different combinations of elimination model, parameter sets, and regression models. Use of a CADM results in increases of up to five-fold in AUC estimates for the more highly exposed members of the cohort compared to estimates obtained using the first-order model with 8.7-year half-life. This degree of variation in the AUC estimates for this cohort would affect substantially the cancer potency estimates derived from the mortality data from this cohort. Such variability and uncertainty in the reconstructed serum lipid AUC estimates for this cohort, depending on elimination model, parameter set, and regression model, have not been described previously and are critical components in evaluating the dose-response data from the occupationally exposed populations.     

International Humanitarian Law and Combat Casualties

The purpose of the article is to provide an overview of the law regulating combat in order to assist in determining whether casualties inflicted in combat should be classified as victims of war or victims of war crimes. The boundaries and the content of International Humanitarian Law are indicated. A brief statement of the law regulating combat is given. The concepts of military objective and of proportionality are analyzed. The scope of an unlawful attack is addressed as is the relationship between unlawful attack offences and other offences in International Humanitarian Law. The article concludes with a discussion of when combat casualties are war crimes victims.     

Professional Perspectives on Decision Making about the Long-term Care of Older People

With the increasing pressure on social and health care resources,professionals have to be more explicit in their decision makingregarding the long-term care of older people. This groundedtheory study used 19 focus groups and nine semi-structured interviews(99 staff in total) to explore professional perspectives onthis decision making. Focus group participants and intervieweescomprised care managers, social workers, consultant geriatricians,general medical practitioners, community nurses, home care managers,occupational therapists and hospital discharge support staff.The emerging themes spanned context, clients, families and services.Decisions were often prompted by a crisis, hindering professionalsseeking to make a measured assessment. Fear of burglary andassault, and the willingness and availability of family to helpwere major factors in decisions about living at home. Serviceavailability in terms of public funding for community care,the availability of home care workers and workload pressureson primary care services influenced decision ‘thresholds’regarding admission to institutional care. Assessment toolsdesigned to assist decision making about the long-term careof older people need to take into account the critical aspectsof individual fears and motivation, family support and the availabilityof publicly funded services as well as functional and medicalneeds.