A Simple Data Transformation for Estimating Benchmark Doses in Developmental Toxicity Experiments

Developmental anomalies induced by toxic chemicals may be identified using laboratory experiments with rats, mice or rabbits. Multinomial responses of fetuses from the same mother are often positively correlated, resulting in overdispersion relative to multinomial variation. In this article, a simple data transformation based on the concept of generalized design effects due to Rao-Scott is proposed for dose-response modeling of developmental toxicity. After scaling the original multinomial data using the average design effect, standard methods for analysis of uncorrected multinomial data can be applied. Benchmark doses derived using this approach are comparable to those obtained using generalized estimating equations with an extended Dirichlet-trinomial covariance function to describe the dispersion of the original data. This empirical agreement, coupled with a large sample theoretical justification of the Rao-Scott transformation, confirms the applicability of the statistical methods proposed in this article for developmental toxicity risk assessment.     

A multivariate extension of poisson's theorem

For n ≥ 1, let X_nl,…, X_nn be independent integer-valued random variables, and define S_n = X_nl+···+X_nn. In a recent paper, we obtained a simple proof for the convergence of the distribution of S_n to a Poisson distribution under very general conditions. In this paper, we extend that result to the multidimensional case.     

Judaism and homosexuality: the traditionalist/progressive debate

This article critically reviews modern Jewish teaching on Judaism and homosexuality. The historical prohibition of homosexual acts is grounded in a world-view that views heterosexuality as natural and heterosexual marriage as the only route to religious and personal fulfillment. Progressive Jews have begun in recent years to question the underlying premises of traditional Jewish teaching on sexuality. Employing the categories of covenant theology and applying the interpretative methodology of liberal Judaism, the author argues for the valuation of the person as homosexual as a legitimate expression of human and Jewish covenantal obligation.     

Generalized Quantification of Risk Associated with Extreme Events1

In the partitioned multiobjective risk method (PMRM) the probability axis is typically partitioned into three regimes: high-exceedance low-consequence, intermediate-exceedance intermediate-consequence, and low-exceedance high-consequence (LE/HC). For each regime, the PMRM generates a conditional expected risk-function given that the damage lies within the regime. The theme of this paper is the conditional expected-risk function for the LE/HC regime. This function, denoted by f₄(.), captures the behavior of the “extreme events” of an underlying decision-making problem. The PMRM offers two advantages: (a) it isolates LE/HC events, allowing the decision-maker(s) to focus on the impacts of catastrophies; and (b) it generates more valuable information than that obtained from the common unconditional expected-risk function. Theoretical problems may arise from uncertainty about the behavior of the tail of the risk curve describing the underlying frequency of damages. When the number of physical observations in small (e.g., in flood frequency analysis), the analyst is forced to make assumptions about the density of damages. Each succeeding distributional assumption will generate a different value of f₄(.). An added dimension of difficulty is also created by the sensitivity of f₄(.) to the choice of the boundary of the LE/HC regime. This paper has two overall objectives: (a) to present distribution-free results concerning the magnitude of f₄(.); and (b) to use those results to obtain a distribution-free estimate of the sensitivity of f₄(.) to the choice of the boundary of the LE/HC regime. The above objectives are realized by extending, and further developing, existing inequalities for continuously distributed random variables.     

Stone's Hypothesis of “Personalizing” Shopping as Compensation for Urban Depersonalization: A Reconsideration*

Critics of Wirth's theory of urban life suggest that he underemphasized the extent of urban social networks that counteract trends toward depersonalization. One argument, by Stone. claims that persons who lack social ties at the neighborhood level compensate by establishing personal relationships in shopping, an activity normally considered highly pecuniary in orientation. A replication of Stone's theory for grocery shoppers shows just the opposite. If anything, persons who lack social ties at the neighborhood level also minimize “personalizing” in their grocery shopping.     

Population and family planning of minority groups]

The population of minority groups has been increasing rapidly in recent years, but the rate of increase is different depending on the region, for various reasons: 1) Population increase rates are high in flat, low regions with warm weather, a good natural environment, and good transportation systems. Productivity is beginning to lag behind population growth (population increased by 90% from 1953 to 1982). 2) Population is increasing at a slower rate in high regions with cool weather and an average natural environment. The productivity growth rate in these regions is about the same (the population increased by 37.5% from 1949 to 1980). 3) Population is increasing at a lower, or even negative, rate in mountainous regions with little flat land and poor transportation service. 4) In some regions, large families are predominant because of tradition and/or religion. In some minority groups, where large extended families are the rule, increases are low because of health problems. People in minority groups are willing to practice family planning, but it is impossible to make one general family planning policy because people in different regions face different problems.     

Mortality levels and family fertility goals

The relationship between mortality levels and family fertility goals is a fundamental problem in the theory of the demographic transition. This paper deals with the logical problems of estimating family fertility rates from the expected probability of a child surviving to a given age of a parent. The possibility of committing the ecological fallacy makes precise prediction difficult. We critically analyze an existing mathematical model of family fertility decisions. We show that, by incorporating more data (here, on birth order) in a more comprehensive model capable of using those data, then the predictability of fertility rates over time can be significantly improved.