Model life table fitting by maximum likelihood estimation: a procedure to reconstruct paleodemographic characteristics from skeletal age distributions

A procedure is presented that uses the regression coefficients for the Coale and Demeny west model life tables to model selected demographic characteristics from skeletal age-at-death distributions. Model death distributions were constructed and compared to a given skeletal distribution, using methods of maximum likelihood estimation to determine the best fit. Two chi-square tests are employed to evaluate the degree of fit. The resulting model includes estimates of demographic characteristics including gross reproductive rate, crude birth rate and life expectancy. The procedure is applied to three archaeological skeletal samples as test cases: two from eastern North America and one from Mexico. These display a range of correspondence (between the best fitting model and the data) from good to poor. The proposed procedure is a potentially powerful tool for both reconstructing paleodemographic rates and illuminating differences between typical human patterns and those found in archaeological populations.     

Anatomical, physiological, and epidemiological correlates of the aging process: a confirmation of multifactorial age determination in the Libben skeletal population

Paleodemographic analyses based on estimates of skeletal age at death consistently report high levels of young adult mortality with few individuals living in excess of 50 years. Critics assert these data indicate systematic underaging of adults and justifiably remark that criteria for estimating skeletal age at death may be unreliable, age determinations are too frequently based on one or two criteria alone, and adult paleodemographic age profiles often mimic the age distribution of the modern population from which an age indicator's standards were originally derived. This study reports a series of tests based on well-documented biological aging phenomena that can be used to investigate potential effects of systematic underaging in adults, assuming the skeletal population is of sufficient size to permit such tests. These include patterns of third decade sternal clavicular epiphyseal fusion, multiple age and sex criteria associated with cortical bone dynamics, and fractures known to occur throughout the entire adult ages range. These phenomena are examined here for the Libben site skeletal population where adult age at death was determined by the multifactorial summary age technique. None of the biological criteria reported here were used in the Libben summary age analysis and thus serve as an independent test of accuracy in age determination. In addition, the summary age method has recently been applied to a series of modern skeletons of known age (Todd samples 1 and 2). Age standards for criteria employed with Libben and Todd 1 were identical. Since Todd 1 displayed underaging in older adults, a second Libben age distribution adjusted for Todd 1 bias was generated for comparison. A third Libben adult survivorship profile based on a Coale and Demeny West level 3 mortality experience, considered by some to be a more realistic model for skeletal populations, was produced for comparison. For all criteria examined, original Libben summary ages provided superior concordance with known patterns of biological aging in human populations. While Libben ages adjusted for Todd 1 bias were slightly better in the third decade, both Todd 1 adjusted and Coale and Demeny West level 3 age distributions produced unrealistic patterns of biological aging for individuals greater than 35 years. Implications of these results are discussed.     

Child Mortality Estimation: A Global Overview of Infant and Child Mortality Age Patterns in Light of New Empirical Data

Background

The under-five mortality rate (the probability of dying between birth and age 5 y, also denoted in the literature as U5MR and ₅ q ₀) is a key indicator of child health, but it conceals important information about how this mortality is distributed by age. One important distinction is what amount of the under-five mortality occurs below age 1 y (₁ q ₀) versus at age 1 y and above (₄ q ₁). However, in many country settings, this distinction is often difficult to establish because of various types of data errors. As a result, it is common practice to resort to model age patterns to estimate ₁ q ₀ and ₄ q ₁ on the basis of an observed value of ₅ q ₀. The most commonly used model age patterns for this purpose are the Coale and Demeny and the United Nations systems. Since the development of these models, many additional sources of data for under-five mortality have become available, making possible a general evaluation of age patterns of infant and child mortality. In this paper, we do a systematic comparison of empirical values of ₁ q ₀ and ₄ q ₁ against model age patterns, and discuss whether observed deviations are due to data errors, or whether they reflect true epidemiological patterns not addressed in existing model life tables.

Methods and Findings

We used vital registration data from the Human Mortality Database, sample survey data from the World Fertility Survey and Demographic and Health Surveys programs, and data from Demographic Surveillance Systems. For each of these data sources, we compared empirical combinations of ₁ q ₀ and ₄ q ₁ against combinations provided by Coale and Demeny and United Nations model age patterns. We found that, on the whole, empirical values fall relatively well within the range provided by these models, but we also found important exceptions. Sub-Saharan African countries have a tendency to exhibit high values of ₄ q ₁ relative to ₁ q ₀, a pattern that appears to arise for the most part from true epidemiological causes. While this pattern is well known in the case of western Africa, we observed that it is more widespread than commonly thought. We also found that the emergence of HIV/AIDS, while perhaps contributing to high relative values of ₄ q ₁, does not appear to have substantially modified preexisting patterns. We also identified a small number of countries scattered in different parts of the world that exhibit unusually low values of ₄ q ₁ relative to ₁ q ₀, a pattern that is not likely to arise merely from data errors. Finally, we illustrate that it is relatively common for populations to experience changes in age patterns of infant and child mortality as they experience a decline in mortality.

Conclusions

Existing models do not appear to cover the entire range of epidemiological situations and trajectories. Therefore, model life tables should be used with caution for estimating ₁ q ₀ and ₄ q ₁ on the basis of ₅ q ₀. Moreover, this model-based estimation procedure assumes that the input value of ₅ q ₀ is correct, which may not always be warranted, especially in the case of survey data. A systematic evaluation of data errors in sample surveys and their impact on age patterns of ₁ q ₀ and ₄ q ₁ is urgently needed, along with the development of model age patterns of under-five mortality that would cover a wider range of epidemiological situations and trajectories. Please see later in the article for the Editors'' Summary.     

Mathematical hazard models of mortality: an alternative to model life tables

A five-parameter competing hazard model of the age pattern of mortality is described, and methods of fitting it to survivorship, death rate, and age structure data are developed and presented. The methods are then applied to published life table and census data to construct life tables for a Late Woodland population, a Christian period Nubian population, and the Yanomama. The advantage of this approach over the use of model life tables is that the hazard model facilitates life-table construction without imposing a particular age pattern of mortality on the data. This development makes it possible to use anthropological data to extend the study of human variation in mortality patterns to small populations.     

Sex differentials in infant and child mortality in Korea

Abstract

This paper reports on a study of infant and child mortality in the Republic of Korea, a country known for a strong son preference, using the 1974 World Fertility Survey data. When the age‐specific probabilities of dying for ages zero to five are compared for male and female children, an unusual pattern of relatively high female mortality is observed. The higher female mortality is more pronounced during childhood than during infancy. Multivariate analysis of life tables, using a hazard model, shows that covariates influencing the mortality at young ages differ for male and female children and suggests that male and female children receive unequal care by their parents. The analysis also reveals different patterns of interaction between infant and child mortality and mother's fertility control behavior depending on the sex of the child.     

MODELING AGE-SPECIFIC MORTALITY FOR MARINE MAMMAL POPULATIONS

A method is presented for estimating age-specific mortality based on minimal information: a model life table and an estimate of longevity. This approach uses expected patterns of mammalian survivorship to define a general model of age-specific mortality rates. One such model life table is based on data for northern fur seals (Callorhinus ursinus) using Siler's (1979) 5-parameter competing risk model. Alternative model life tables are based on historical data for human females and on a published model for Old World monkeys. Survival rates for a marine mammal species are then calculated by scaling these models by the longevity of that species. By using a realistic model (instead of assuming constant mortality), one can see more easily the real biological limits to population growth. The mortality estimation procedure is illustrated with examples of spotted dolphins (Stenella attenuata) and harbor porpoise (Phocoena phocoena).     

Book Reviews

Book reviewed in this article:
The Demography of Tropical Africa. William Brass, Ansley J. Coale, Paul Demeny, Don F. Heisel, Frank Lorimer, Anatole Romaniuk, and Etienne Van De Walle.
The Population of Tropical Africa. John C. Caldwell and Chukuka Okonjo, eds.     

Models for estimating empirical Gompertz mortality: With an application to evolution of the Gompertzian slope

Using data from the human mortality database (HMD), and five different modeling approaches, we estimate Gompertz mortality parameters for 7,704 life tables. To gauge model fit, we predict life expectancy at age 40 from these parameters, and compare predicted to empirical values. Across a diversity of human populations, and both sexes, the overall best way to estimate Gompertz parameters is weighted least squares, although Poisson regression performs better in 996 cases for males and 1,027 cases for females, out of 3,852 populations per sex. We recommend against using unweighted least squares unless death counts (to use as weights or to allow Poisson estimation) are unavailable. We also recommend fitting to logged death rates. Over time in human populations, the Gompertz slope parameter has increased, indicating a more severe increase in mortality rates as age goes up. However, it is well-known that the two parameters of the Gompertz model are very tightly (and negatively) correlated. When the slope goes up, the level goes down, and, overall, mortality rates are decreasing over time. An analysis of Gompertz parameters for all of the HMD countries shows a distinct pattern for males in the formerly socialist economies of Europe.     

Construction of expanded continuous life tables--a generalization of abridged and complete life tables.

This article extends the recent abridged life-table method of Hsieh. It generalizes the conventional discrete (abridged and complete) life tables into a continuous life table that can produce life-table functions at any age and develops a unified method of life-table construction that simplifies the disparate laborious procedures used in the traditional approach of constructing abridged and complete life tables. A set of precise procedures based on the complete cubic spline for the main body of the table and a mortality law for advanced ages is developed for estimating the basic and nonbasic life-table functions from a given mortality schedule. The proposed method can also produce more life-table functions than other existing methods. The method is illustrated with Canadian data.     

A censored quantile regression approach for relative survival analysis: Relative survival quantile regression

We propose a censored quantile regression model for the analysis of relative survival data. We create a hybrid data set consisting of the study observations and counterpart randomly sampled pseudopopulation observations imputed from population life tables that adjust for expected mortality. We then fit a censored quantile regression model to the hybrid data incorporating demographic variables (e.g., age, biologic sex, calendar time) corresponding to the population life tables of demographically-similar individuals, a population versus study covariate, and its interactions with the variables of interest. These latter variables can be interpreted as relative survival parameters that depict the differences in failure quantiles between the study participants and their population counterparts.     

Sex differentials in infant and child mortality in Korea

This paper reports on a study of infant and child mortality in the Republic of Korea, a country known for a strong son preference, using the 1974 World Fertility Survey data. When the age-specific probabilities of dying for ages 0 to 5 are compared for male and female children, an unusual pattern of relatively high female mortality is observed. The higher female mortality is more pronounced during childhood than during infancy. Multivariate analysis of life tables, using a hazard model, shows that covariates influencing the mortality at young ages differ for male and female children and suggests that male and female children receive unequal care by their parents. The analysis also reveals different patterns of interaction between infant and child mortality and mother's fertility control behavior depending on the sex of the child.     

The effect of retrospective sampling on binary regression models for clustered data

Recently a great deal of attention has been given to binary regression models for clustered or correlated observations. The data of interest are of the form of a binary dependent or response variable, together with independent variables X1,...., Xk, where sets of observations are grouped together into clusters. A number of models and methods of analysis have been suggested to study such data. Many of these are extensions in some way of the familiar logistic regression model for binary data that are not grouped (i.e., each cluster is of size 1). In general, the analyses of these clustered data models proceed by assuming that the observed clusters are a simple random sample of clusters selected from a population of clusters. In this paper, we consider the application of these procedures to the case where the clusters are selected randomly in a manner that depends on the pattern of responses in the cluster. For example, we show that ignoring the retrospective nature of the sample design, by fitting standard logistic regression models for clustered binary data, may result in misleading estimates of the effects of covariates and the precision of estimated regression coefficients.     

Age‐specific mortality analysis of the dry forest kissing bug,Rhodnius neglectus

Age‐specific mortality patterns can be very different across insects with different life histories. Some holometabolous insects (like mosquitoes, fruit flies) show a pattern where mortality rate decelerates at older ages, whereas other holometabolous insects (bruchid beetles) and hemimetabolous insects (cotton stainers, milkweed bugs, and kissing bugs) show an age‐specific mortality pattern that increases through all ages. Kissing bugs are strictly hematophagous and are vectors of Trypanosoma cruzi Chagas, the etiologic agent of Chagas disease. Here, we tested whether cohort data from the dry forest kissing bug, Rhodnius neglectus Lent (Hemiptera: Reduviidae), supports an increase of mortality rate that decelerates with age. We analyzed the age‐specific mortality pattern of a cohort of 250 individuals of R. neglectus. We used a suite of seven models with different degrees of complexity, to model age‐dependent forms of change in mortality rate increase in R. neglectus in the laboratory. We used the Akaike model selection criterion to choose between models that consider absence or presence of mortality deceleration. Five of the seven models (logistic, Gavrilovs, Gompertz, DeMoivre, and exponential) showed a statistically significant fit to the mortality rate. Weak late‐age mortality deceleration in R. neglectus was supported by the best fit (logistic model), and this result is consistent with predictions of the disposable soma theory of senescence.     

Model life tables for the larger old world monkeys

Mortality statistics for 25 populations of the larger Old World monkeys (members of the subfamily Cercopithecinae) were evaluated with a competing hazard model of mortality. The best eight of these life tables were combined to generate a standard model life table representative of the mortality patterns of these primates. Two applications of the standard model to smooth, graduate, and compare life tables based on limited and defective data are presented.     

Worldwide variation in life-span sexual dimorphism and sex-specific environmental mortality rates

In all human populations mean life span of women generally exceeds that of men, but the extent of this sexual dimorphism varies across different regions of the world. Our purpose here is to study, using global demographic and environmental data, the general tendency of this variation and local deviations from it. We used data on male and female life history traits and environmental conditions for 227 countries and autonomous territories; for each country or territory the life-span dimorphism was defined as the difference between mean life spans of women and men. The general tendency is an increase of life-span dimorphism with increasing average male-female life span; this tendency can be explained using a demographic model based on the Makeham-Gompertz equation. Roughly, the life-span dimorphism increases with the average life span because of an increase in the duration of expressing sex- and age-dependent mortality described by the second (exponential) term of the Makeham-Gompertz equation. Thus we investigated the differences in male and female environmental mortality described by the first term of the Makeham-Gompertz equation fitted to the data. The general pattern that resulted was an increase in male mortality at the highest and lowest latitudes. One plausible explanation is that specific factors tied to extreme latitudes influence males more strongly than females. In particular, alcohol consumption increases with increasing latitude and, on the contrary, infection pressures increase with decreasing latitude. This finding agrees with other observations, such as an increase in male mortality excess in Europe and Christian countries and an increase in female mortality excess in Asia and Muslim countries. An increase in the excess of female mortality may also be due to increased maternal mortality caused by an increase in fertility. However, this relation is not linear: In regions with the highest fertility (e.g., in Africa) the excess of female mortality is smaller than in regions with relatively lower fertility (e.g., in Asia). A possible explanation of this phenomenon is an evolutionary adaptation of women to the pressures of extremely high fertility by means of some reduction of their maternal mortality.     

Mortality and Life Expectancy in Homeless Men and Women in Rotterdam: 2001–2010

Background

Data on mortality among homeless people are limited. Therefore, this study aimed to describe mortality patterns within a cohort of homeless adults in Rotterdam (the Netherlands) and to assess excess mortality as compared to the general population in that city.

Methods

Based on 10-year follow-up of homeless adults aged ≥ 20 years who visited services for homeless people in Rotterdam in 2001, and on vital statistics, we assessed the association of mortality with age, sex and type of service used (e.g. only day care, convalescence care, other) within the homeless cohort, and also compared mortality between the homeless and general population using Poisson regression. Life tables and decomposition methods were used to examine differences in life expectancy.

Results

During follow-up, of the 2096 adult homeless 265 died. Among the homeless, at age 30 years no significant sex differences were found in overall mortality rates and life expectancy. Compared with the general Rotterdam population, mortality rates were 3.5 times higher in the homeless cohort. Excess mortality was larger in women (rate ratio [RR] RR 5.56, 95% CI 3.95–7.82) as compared to men (RR 3.31, 95% CI 2.91–3.77), and decreased with age (RR 7.67, 95% CI 6.87–8.56 for the age group 20–44 and RR 1.63, 95% CI 1.41–1.88 for the age group 60+ years). Life expectancy at age 30 years was 11.0 (95% CI 9.1–12.9) and 15.9 (95% CI 10.3–21.5) years lower for homeless men and women compared to men and women in the general population respectively.

Conclusion

Homeless adults face excessive losses in life expectancy, with greatest disadvantages among homeless women and the younger age groups.     

鄂西南不同区域亮叶桦种群结构与动态特征

对鄂西南木林子、七姊妹山、金子山3个区域亮叶桦种群进行调查,划分种群龄级和高度级,绘制种群结构图。采用空间代替时间的方法,编制各区域亮叶桦种群的静态生命表,绘制存活曲线、死亡率曲线和消失率曲线,应用4个生存分析函数分析不同区域亮叶桦种群动态。结果表明: 3个区域的亮叶桦种群均属增长型,高度级结构较为完整,七姊妹山和金子山种群龄级结构有不同程度的缺失;数量变化动态指数V_pi＞0,但对外界干扰比较敏感。静态生命表表明,亮叶桦种群不同龄级的存活量差别较大,随龄级增加而逐渐减少;存活曲线趋近于Deevey-Ⅱ型;死亡率和消失率曲线变化趋势基本一致,但存在不同程度的波动。不同区域亮叶桦种群均具有前期锐减、中后期动态稳定的特征。     

Micrococcal nuclease as a DNA structural probe: its recognition sequences, their genomic distribution and correlation with DNA structure determinants

We have analyzed micrococcal nuclease (MNase) DNA cleavage patterns at the sequence level by examining 2.3 X 10(3) base-pairs of data derived from the Drosophila melanogaster 44D larval cuticle locus. Within this region, MNase preferentially cleaved 140 sites. Clusters of these sites appear to generate the preferential MNase eukaryotic DNA cleavage sites seen on agarose gels at roughly 100 to 300 base-pair intervals. These clusters of preferential cleavage sites rarely occur within gene coding regions. The analysis revealed that duplex DNA sequences preferentially cleaved by MNase are generally determined by a single strand sequence: d(A-T)n, where n greater than or equal to 1, flanked by a 5' dC or dG. Cleavage of the other strand is generally staggered 5' by several nucleotides and occurs even if such sequences are absent on that strand. An empirical predictive DNA cleavage model derived from a statistical analysis of the sequence level data was applied to seven eukaryotic gene loci of known sequence. The predicted patterns were in good general agreement with the previously observed eukaryotic gene/spacer cleavage pattern. Statistical analysis also revealed that sites of predicted preferential DNA cleavage occur less frequently in protein coding regions than for randomized sequences of the same length and nucleotide content. Comparison of the MNase cleavage patterns to the sequence-dependent pattern of binding energies between duplex DNA strands indicates that MNase preferentially cleaves sequences with low helix stability.     

“区域模型生命表”在古人口学研究中的应用

作为普通生命表的归纳总结,"模型生命表"反映了人口发展的普遍现象和内在规律。本文将"区域模型生命表"引入古人口学研究,以大甸子墓地为例对婴幼儿组和高龄组死亡人数进行了调整。根据校正后数据所编制的简略生命表,该遗址人口平均预期寿命下降为24.12岁,年龄别死亡率曲线呈更加合理的"U"型。鉴于古人口学中样本容量和代表性往往较差,引入"区域模型生命表"对偏差数据校正后再进行人口研究将使所得结论更加合理可靠。