The population of the USSR

Official population data for the USSR for 1986 and 1987 are presented. Tables are included on age and sex distribution; rural and urban population; birth, death, and natural increase rates, 1970-1986; fertility and mortality by sex, 1970-1986; birth order; age-specific birth rates by rural and urban area and Union republic; age-specific death rates, 1970-1986; infant mortality, 1970-1986; life expectancy, 1926-1986; life tables; marriage and age at marriage; and divorce.     

Reference priors for constrained rate models of count data

We derive reference priors for constrained rate models of count data using the sequential algorithm of Berger and Bernardo (1992b). The event counts for various groups of subjects are modeled as discrete random variables (Poisson, binomial, or negative binomial) with group specific rates. We consider situations in which the groups can be completely ordered according to one covariate. The priors enforce monotonicity (or monotonicity and convexity) of the rates with respect to the ordering. We use the priors to model a data set on mortality rates for men in different age groups assuming that the mortality rates increase with respect to age. We also consider the situation in which the parameter space is augmented to include rates corresponding to unobserved age groups, and the case of a random upper bound on the mortality rates. In addition, we provide an evaluation of the out-of-sample predictive performance of the proposed methods.     

A tilting algorithm for the estimation of fractional age survival probabilities

Life tables used in life insurance determine the age of death distribution only at integer ages. Therefore, actuaries make fractional age assumptions to interpolate between integer age values when they have to value payments that are not restricted to integer ages. Traditional fractional age assumptions as well as the fractional independence assumption are easy to apply but result in a non-intuitive overall shape of the force of mortality. Other approaches proposed either require expensive optimization procedures or produce many discontinuities. We suggest a new, computationally inexpensive algorithm to select the parameters within the LFM-family introduced by Jones and Mereu (Insur Math Econ 27:261–276, 2000). In contrast to previously suggested methods, our algorithm enforces a monotone force of mortality between integer ages if the mortality rates are monotone and keeps the number of discontinuities small.     

A comparison of models for dynamic life tables. Application to mortality data from the Valencia Region (Spain)

The graduation of mortality data aims to estimate the probabilities of death at age x, q ( x ), by means of an age-dependent function, whose parameters are adjusted from the crude probabilities that are directly obtainable from the data. However, current life tables have a problem, the need for periodic updates due to changes in mortality over short periods of time. The table containing mortality rates for different ages in different years, q ( xt ), is called a dynamic life table, which captures mortality variation over time. This paper proposes a review of the most commonly used dynamic models and compares the results obtained by each of them when applied to mortality data from the Valencia Region (Spain). The result of the comparison leads us to the conclusion that the Lee-Carter method offers the best results for both sexes, while that based on Heligman and Pollard functions provides the best fit for men alone. Our working method is of additional interest as it may be applied to mortality data for a wide range of ages in any geographical location, allowing the most appropriate dynamic life table to be selected for the case at hand.     

Assessing Differential Area Mortality Trends via Bayesian Random Effects

Changes in area mortality are important for assessing spatial health inequality. They are likely to be differentiated by age as well as spatially and may vary by demographic strata (e.g., gender, ethnic group). A simple approach assumes linear improvement in log mortality risks, with noninteracting area and age coefficients. By contrast, this article considers parsimonious models for mortality change allowing nonlinear trends and interactions between ages and areas in mortality levels and trends. A case study considers trends in mortality in 32 London boroughs over the 8-year period 1999–2006 for deaths data disaggregated by age, sex, and area.     

Estimation of actuarial quantities at fractional ages with Kriging

ABSTRACT

Life tables used in life insurance are often calibrated to show the survival function of the age of death distribution at exact integer ages. Actuaries usually make fractional age assumptions (FAAs) when having to value payments that are not restricted to integer ages. Traditional FAAs have the advantage of simplicity but cannot guarantee to capture precisely the real trends of the survival functions and sometimes even result in a non intuitive overall shape of the force of mortality. In fact, an FAA is an interpolation between integer age values which are accepted as given. In this article, we introduce Kriging model, which is widely used as a metamodel for expensive simulations, to fit the survival function at integer ages, and furthermore use the precisely constructed survival function to build the force of mortality and the life expectancy. The experimental results obtained from a simulated life table (Makehamized life table) and two “real” life tables (the Chinese and US life tables) show that these actuarial quantities (survival function, force of mortality, and life expectancy) presented by Kriging model are much more accurate than those presented by commonly-used FAAs: the uniform distribution of death (UDD) assumption, the constant force assumption, and the Balducci assumption.     

A progressive rise in stomach cancer-related mortality rate during 1970–1995 in Japanese individuals over 85 years of age

A large number of studies have shown a gradual fall in stomach cancer-related mortality rate during the last decade. Here we analyzed the pattern of stomach cancer-related mortality rates in Japanese aged>85 years from 1970 to 1995. We used data for the entire population of Japan. The magnitude of change was measured by relative risk and cause-elimination life tables to distinguish time trends in mortality rates of stomach cancer for individuals over 85 years of age compared with other age groups (55–84 years). In the over-85 age group, stomach cancer mortality increased from 374 in 1970 to 662 in 1995 per 100,000 (77%) for males and from 232 to 296 per 100,000 (27%) for females. Using the 55–59 years group as the reference category, the relative risk increased from 2.3 to 9.9 and from 2.8 to 11.1 in men and women, respectively. The effects of mortality on life expectancy also increased 1.5 times and 1.1 times, respectively. Our results showed a rise of stomach cancer mortality in Japanese aged over 85 years, which paralleled the increase in relative risk and negative contribution to life expectancy. While the mortality of younger age groups is decreasing, the change over from increase to decrease in the over-85 age group is only just beginning.     

Assessment of vague and noninformative priors for Bayesian estimation of the realized random effects in random-effects meta-analysis

Random-effects meta-analysis has become a well-established tool applied in many areas, for example, when combining the results of several clinical studies on a treatment effect. Typically, the inference aims at the common mean and the amount of heterogeneity. In some applications, the laboratory effects are of interest, for example, when assessing uncertainties quoted by laboratories participating in an interlaboratory comparison in metrology. We consider the Bayesian estimation of the realized random effects in random-effects meta-analysis. Several vague and noninformative priors are examined as well as a proposed novel one. Conditions are established that ensure propriety of the posteriors for the realized random effects. We present extensive simulation results that assess the inference in dependence on the choice of prior as well as mis-specifications in the statistical model. Overall good performance is observed for all priors with the novel prior showing the most promising results. Finally, the uncertainties reported by eleven national metrology institutes and universities for their measurements on the Newtonian constant of gravitation are assessed.     

Quadratic fractional age assumption revisited

This paper introduces a quadratic fractional age assumption which makes the force of mortality and survival function continuous at all ages. The necessary and sufficient condition for the assumption to be valid is derived. Important life table parameters are estimated and applications are shown using several life table data.     

The Impact of Ovarian Cancer on Life Expectancy in Japan

The purpose of this study was to determine how life expectancy is modified by ovarian cancer from 1950-2000. The contributions of ovarian cancer to life expectancy were estimated. The age characteristics of ovarian cancer were detected using the Gompertz relational mortality model. The patterns between years of potential life lost (YPLL) and mortality were obtained by fitting a linear regression equation to the natural logarithm of their ratios. YPLLs are substantially higher in Ireland than in Japan. However, the rates of change were much higher in Japan than in Ireland. YPLLs changed from 0.02 year in 1950 to 0.12 year in 2000. In Japan, there was a sixfold increase in the proportion of YPLLs for death from ovarian cancer relative to those for death from gynaecological cancers during the last half century. The impact of ovarian cancer on life expectancy clearly increased and the age-specific mortality tend to ageing.     

Mortality in the years 1950-1990

"The author of the paper has attempted to show...trends in...mortality by sex, age, place of residence and [the] selected most important death causes in Poland. The crude and the specific as well as standardized death rates and life expectancy have been analyzed for the period...1950-1990." (SUMMARY IN ENG)     

Linear regression analysis of survival data with missing censoring indicators

Linear regression analysis has been studied extensively in a random censorship setting, but typically all of the censoring indicators are assumed to be observed. In this paper, we develop synthetic data methods for estimating regression parameters in a linear model when some censoring indicators are missing. We define estimators based on regression calibration, imputation, and inverse probability weighting techniques, and we prove all three estimators are asymptotically normal. The finite-sample performance of each estimator is evaluated via simulation. We illustrate our methods by assessing the effects of sex and age on the time to non-ambulatory progression for patients in a brain cancer clinical trial.     

Bayesian analysis of multivariate mortality data with large families

This paper presents a Bayesian method for the analysis of toxicological multivariate mortality data when the discrete mortality rate for each family of subjects at a given time depends on familial random effects and the toxicity level experienced by the family. Our aim is to model and analyse one set of such multivariate mortality data with large family sizes: the potassium thiocyanate (KSCN) tainted fish tank data of O'Hara Hines. The model used is based on a discretized hazard with additional time-varying familial random effects. A similar previous study (using sodium thiocyanate (NaSCN)) is used to construct a prior for the parameters in the current study. A simulation-based approach is used to compute posterior estimates of the model parameters and mortality rates and several other quantities of interest. Recent tools in Bayesian model diagnostics and variable subset selection have been incorporated to verify important modelling assumptions regarding the effects of time and heterogeneity among the families on the mortality rate. Further, Bayesian methods using predictive distributions are used for comparing several plausible models.     

Nonparametric forecasting: a comparison of three kernel-based methods

In this paper the use of three kernel-based nonparametric forecasting methods - the conditional mean, the conditional median, and the conditional mode -is explored in detail. Several issues related to the estimation of these methods are discussed, including the choice of the bandwidth and the type of kernel function. The out-of-sample forecasting performance of the three nonparametric methods is investigated using 60 real time series. We find that there is no superior forecast method for series having approximately less than 100 observations. However, when a time series is long or when its conditional density is bimodal there is quite a difference between the forecasting performance of the three kernel-based forecasting methods.     

Probabilistic approaches to current life table estimation

"Two simple current life table estimators of conditional probabilities of death result from making either a uniform or exponential distributional assumption of time at death in the age interval. Each is compared with Chiang's estimator based on the concept of fraction of the last age interval of life. Graphical and numerical results are presented to assess the magnitude and direction of differences between estimators when the true value of Chiang's fraction takes on specific values."     

Small area estimation using reduced rank regression models

Abstract

Small area estimation techniques have got a lot of attention during the last decades due to their important applications in survey studies. Mixed linear models and reduced rank regression analysis are jointly used when considering small area estimation. Estimates of parameters are presented as well as prediction of random effects and unobserved area measurements.     

Probabilistic Approaches to Current Life Table Estimation

Two simple current life table estimators of conditional probabilities of death result from making either a uniform or exponential distributional assumption of time at death in the age interval. Each is compared with Chiang's estimator based on the concept of fraction of the last age interval of life. Graphical and numerical results are presented to assess the magnitude and direction of differences between estimators when the true value of Chiang's fraction takes on specific values.     

Likelihood analysis for a class of beta mixed models

Beta regression is a suitable choice for modelling continuous response variables taking values on the unit interval. Data structures such as hierarchical, repeated measures and longitudinal typically induce extra variability and/or dependence and can be accounted for by the inclusion of random effects. In this sense, Statistical inference typically requires numerical methods, possibly combined with sampling algorithms. A class of Beta mixed models is adopted for the analysis of two real problems with grouped data structures. We focus on likelihood inference and describe the implemented algorithms. The first is a study on the life quality index of industry workers with data collected according to an hierarchical sampling scheme. The second is a study assessing the impact of hydroelectric power plants upon measures of water quality indexes up, downstream and at the reservoirs of the dammed rivers, with a nested and longitudinal data structure. Results from different algorithms are reported for comparison including from data-cloning, an alternative to numerical approximations which also allows assessing identifiability. Confidence intervals based on profiled likelihoods are compared with those obtained by asymptotic quadratic approximations, showing relevant differences for parameters related to the random effects. In both cases, the scientific hypothesis of interest was investigated by comparing alternative models, leading to relevant interpretations of the results within each context.