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.     

Confidence Intervals for Current Status Data

Abstract.  The likelihood ratio statistic for testing pointwise hypotheses about the survival time distribution in the current status model can be inverted to yield confidence intervals (CIs). One advantage of this procedure is that CIs can be formed without estimating the unknown parameters that figure in the asymptotic distribution of the maximum likelihood estimator (MLE) of the distribution function. We discuss the likelihood ratio-based CIs for the distribution function and the quantile function and compare these intervals to several different intervals based on the MLE. The quantiles of the limiting distribution of the MLE are estimated using various methods including parametric fitting, kernel smoothing and subsampling techniques. Comparisons are carried out both for simulated data and on a data set involving time to immunization against rubella. The comparisons indicate that the likelihood ratio-based intervals are preferable from several perspectives.     

Four‐Month‐Olds' Discrimination of Voice Changes in Multimodal Displays as a Function of Discrimination Protocol

Past studies have found equivocal support for the ability of young infants to discriminate infant‐directed (ID) speech information in the presence of auditory‐only versus auditory + visual displays (faces + voices). Generally, younger infants appear to have more difficulty discriminating a change in the vocal properties of ID speech when they are accompanied by faces. Forty 4‐month‐old infants were tested using either an infant‐controlled habituation procedure (Experiment 1) or a fixed‐trial habituation procedure (Experiment 2). The prediction was that the infant‐controlled habituation procedure would be a more sensitive measure of infant attention to complex displays. The results indicated that 4‐month‐old infants discriminated voice changes in dynamic face + voice displays depending on the order in which they were viewed during the infant‐controlled habituation procedure. In contrast, no evidence of discrimination was found in the fixed‐trial procedure. The findings suggest that the selection of experimental methodology plays a significant role in the empirical observations of infant perceptual abilities.     

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.     

A Numerical Solution to the Nonhomogeneous Two-Stage MVK Model of Cancer

In this article, we describe a straightforward method for solving the probability of at least one malignant cell by time t, and the associated hazard function, in the general (i.e., nonhomogeneous) two-stage Moolgavkar-Venzon-Knudson (MVK) model of cancer. The method consists of solving four coupled ordinary differential equations derived from the Kolmogorov backward equations for this process. The relationship of this method to previously proposed solutions is discussed.     

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.