THE USE OF AGGREGATE DATA TO ESTIMATE GOMPERTZ‐TYPE OLD‐AGE MORTALITY IN HETEROGENEOUS POPULATIONS

We consider two related aspects of the study of old‐age mortality. One is the estimation of a parameterized hazard function from grouped data, and the other is its possible deceleration at extreme old age owing to heterogeneity described by a mixture of distinct sub‐populations. The first is treated by half of a logistic transform, which is known to be free of discretization bias at older ages, and also preserves the increasing slope of the log hazard in the Gompertz case. It is assumed that data are available in the form published by official statistical agencies, that is, as aggregated frequencies in discrete time. Local polynomial modelling and weighted least squares are applied to cause‐of‐death mortality counts. The second, related, problem is to discover what conditions are necessary for population mortality to exhibit deceleration for a mixture of Gompertz sub‐populations. The general problem remains open but, in the case of three groups, we demonstrate that heterogeneity may be such that it is possible for a population to show decelerating mortality and then return to a Gompertz‐like increase at a later age. This implies that there are situations, depending on the extent of heterogeneity, in which there is at least one age interval in which the hazard function decreases before increasing again.     

Genetic algorithms for numerical optimization

Genetic algorithms (GAs) are stochastic adaptive algorithms whose search method is based on simulation of natural genetic inheritance and Darwinian striving for survival. They can be used to find approximate solutions to numerical optimization problems in cases where finding the exact optimum is prohibitively expensive, or where no algorithm is known. However, such applications can encounter problems that sometimes delay, if not prevent, finding the optimal solutions with desired precision. In this paper we describe applications of GAs to numerical optimization, present three novel ways to handle such problems, and give some experimental results.     

The health expectancies of older Australians

Health expectancies of the states ‘Disability-free’ and ‘Disabled’ are estimated for Australian females and males aged 60 and over, both by cohort from 1980 and current for survey years 1981, 1988, 1993 and 1998. Modifications of recently developed logistic regression techniques are used rather than the standard 1971 method due to Sullivan. Results from the three later surveys are broadly similar and differ in important respects from those of the 1981 survey. Based on the last three surveys our estimates support the view that, depending on age, two-thirds or more of the increase in female life expectancy over the decade 1988–1998 is spent in the Disabled state. The situation is worse for elderly men, for whom all of the increased years of expected life are estimated to be spent in the Disabled state. The findings do not support rectangularization of the survival curve or Disability-free survival curve.     

A comparison between genetic algorithms and the RAND method for solving the joint replenishment problem

The purpose of this paper is to compare the performance of genetic algorithms (GAs) and the best available heuristic, known as the RAND, for solving the joint replenishment problem (JRP). An important feature of the JRP which makes it suitable for GAs is that it can be formulated as a problem having one continuous decision variable and a number of integer decision variables equal to the number of products being produced or ordered. Experiments on randomly generated problems indicate that GAs can provide better solutions to the JRP than the RAND for some problems, and at worst can almost match the performance of the RAND from a practical point of view for the rest of the problems. GAs never converged to solution with a total cost of more than 0.08% of the total cost of the RAND for 1600 randomly generated problems. In addition, GAs have the advantages of: (i) being easy to implement (e.g. less than 200 lines of code); (ii) having a code which is easy to understand and modify; and (iii) dealing easily with constrained JRPs which are neglected by most of the available methods including the RAND, in spite of their importance in practice.     

ESTIMATING PROCESSES OF COUNTS FROM CROSS-SECTIONAL AGGREGATE DATA, WITH AN APPLICATION TO MULTISTATE LIFE TABLES AND HEALTH EXPECTANCIES

This paper discusses the estimation of time‐dependent probabilities of a finite state‐space discrete‐time process using aggregate cross‐sectional data. A large‐sample version of multistate logistic regression is described and shown to be useful for analysing multistate life tables. The technique is applied to the estimation of disability‐free, severely disabled and other disabled survival curves and health expectancies in Australia, based on data from national health surveys in 1988, 1993 and 1998. A conclusion is that there has been a general upward trend in the future time expected to be spent in a state of disability, the picture being more pessimistic for males than females. For example, during 1988‐1998 the estimated increase in male life expectancy at birth of 2.7 years is decomposed as a decrease of 1.2 years in disability‐free health (life) expectancy and increases of 1.3 and 2.6 years, respectively, in states of severe disability and other disability.     

Non-standard methods in evolutionary computation

The paper presents non-standard methods in evolutionary computation and discusses their applicability to various optimization problems. These methods maintain populations of individuals with nonlinear chromosomal structure and use genetic operators enhanced by the problem specific knowledge.     

Policy Climates and Reductions in Automobile Use*

Objectives. This study examines how national environmental policy influences individual car‐driving behavior in the European Union. Methods. Using the International Social Survey: Environment II in conjunction with the 2001 and 2002 Environmental Sustainability Indices, we analyze the relationship between macro‐level policy indicators and the reported reduction of individual car driving for environmental reasons, controlling for meso‐ and micro‐level factors. Results. Our results show that individuals report a greater likelihood of driving less for environmental reasons when they live in nations that adopt strong pro‐environmental policies, even when such policies are not directly related to car use. Conclusions. Our finding that a national policy climate focused on environmental sustainability is associated with pro‐environmental behaviors among individuals in that nation encourages us to believe that greater international cooperation on environmental issues (such as the Kyoto Protocol) and increased strength of domestic environmental policies will positively change individual behavior.     

The Downfall of Gomułka

Marina Tsvetaeva’s 1934 “Chërt” (The Devil) forms a central part of the cycle of autobiographical prose she wrote in emigration. This article assembles clues to the hidden origins of the Devil she describes in prose about her grandfathers, some of it censored in pre-1990 editions of her works. Tsvetaeva’s Devil is not simply metaphysical: it has the unusual appearance of a Great Dane. Though she goes on to trace its appearances in the literature and culture of her childhood, some of its physical features (eyes, nose, colour and posture) link it with other people in her life. The vivid details of the Devil suggest relationships, though peculiarly mediated ones, to members of her own family, especially her maternal grandfather, Aleksandr Danilovich Mein. The poet describes herself using Pushkin’s poem “Utoplennik” to camouflage her own sense of self from her mother. Much of the rest of “The Devil” describes her recognition of the Devil in varying symbolic or even phonetic guises, tracing how the poet stayed faithful to him even after he ceased to appear visibly, how she found and read his symbols in surrounding reality—e.g., card games, toys, rituals for finding lost objects—and in unexpected, otherwise respectable, parts of society, including her own grandfather. As always, Tsvetaeva creates a story that affirms her identity as a poet and illustrates the work she had to do to achieve that identity.     

Change-point detection in a shape-restricted regression model

A regression model with a possible structural change and with a small number of measurements is considered. A priori information about the shape of the regression function is used to formulate the model as a linear regression model with inequality constraints and a likelihood ratio test for the presence of a change-point is constructed. The exact null distribution of the test statistic is given. Consistency of the test is proved when the noise level goes to zero. Numerical approximations to the powers against various alternatives are given and compared with the powers of the k-linear-r-ahead recursive residuals tests and CUSUM tests. Performance of four different estimators of the change-point is studied in a Monte Carlo experiment. An application of the procedures to some real data is also presented.     

Intake Fraction Variability Between Air Pollution Emission Sources Inside an Urban Area

The cost‐effective mitigation of adverse health effects caused by air pollution requires information on the contribution of different emission sources to exposure. In urban areas the exposure potential of different sources may vary significantly depending on emission height, population density, and other factors. In this study, we quantified this intraurban variability by predicting intake fraction (iF) for 3,066 emission sources in Warsaw, Poland. iF describes the fraction of the pollutant that is inhaled by people in the study area. We considered the following seven pollutants: particulate matter (PM), nitrogen oxides (NO_x), sulfur dioxide (SO₂), benzo[a] pyrene (BaP), nickel (Ni), cadmium (Cd), and lead (Pb). Emissions for these pollutants were grouped into four emission source categories (Mobile, Area, High Point, and Other Point sources). The dispersion of the pollutants was predicted with the CALPUFF dispersion model using the year 2005 emission rate data and meteorological records. The resulting annual average concentrations were combined with population data to predict the contribution of each individual source to population exposure. The iFs for different pollutant‐source category combinations varied between 51 per million (PM from Mobile sources) and 0.013 per million (sulfate PM from High Point sources). The intraurban iF variability for Mobile sources primary PM emission was from 4 per million to 100 per million with the emission‐weighted iF of 44 per million. These results propose that exposure due to intraurban air pollution emissions could be decreased more effectively by specifically targeting sources with high exposure potency rather than all sources.