A Comparison of Nonparametric Methods in the Graduation of Mortality: Application to Data from the Valencia Region (Spain)

Working Life Expectancy at Age 50 in the United States and the Impact of the Great Recession

A key concern about population aging is the decline in the size of the economically active population. Working longer is a potential remedy. However, little is known about the length of working life and how it relates to macroeconomic conditions. We use the U.S. Health and Retirement Study for 1992–2011 and multistate life tables to analyze working life expectancy at age 50 and study the impact of the Great Recession in 2007–2009. Despite declines of one to two years following the recession, in 2008–2011, American men aged 50 still spent 13 years, or two-fifths of their remaining life, working; American women of the same age spent 11 years, or one-third of their remaining life, in employment. Although educational differences in working life expectancy have been stable since the mid-1990s, racial differences started changing after the onset of the Great Recession. Our results show that although Americans generally work longer than people in other countries, considerable subpopulation heterogeneity exists. We also find that the time trends are fluctuating, which may prove troublesome as the population ages. Policies targeting the weakest performing groups may be needed to increase the total population trends.

Multivariable flexible modelling for estimating complete, smoothed life tables for sub-national populations

BACKGROUND

The methods currently available to estimate age- and sex-specific mortality rates for sub-populations are subject to a number of important limitations. We propose two alternative multivariable approaches: a relational model and a Poisson model both using restricted cubic splines.

METHODS

We evaluated a flexible Poisson and flexible relational model against the Elandt-Johnson approach in a simulation study using 100 random samples of population and death counts, with different sampling proportions and data arrangements. Estimated rates were compared to the original mortality rates using goodness-of-fit measures and life expectancy. We further investigated an approach for determining optimal knot locations in the Poisson model.

RESULTS

The flexible Poisson model outperformed the flexible relational and Elandt-Johnson methods with the smallest sample of data (1%). With the largest sample of data (20%), the flexible Poisson and flexible relational models performed comparably, though the flexible Poisson model displayed a slight advantage. Both approaches tended to underestimate infant mortality and thereby overestimate life expectancy at birth. The flexible Poisson model performed much better at young ages when knots were fixed a priori. For ages 30 and above, results were similar to the model with no fixed knots.

CONCLUSIONS

The flexible Poisson model is recommended because it derives robust and unbiased estimates for sub-populations without making strong assumptions about age-specific mortality profiles. Fixing knots a priori in the final model greatly improves fit at the young ages.

Bivariate discrete beta Kernel graduation of mortality data

Various parametric/nonparametric techniques have been proposed in literature to graduate mortality data as a function of age. Nonparametric approaches, as for example kernel smoothing regression, are often preferred because they do not assume any particular mortality law. Among the existing kernel smoothing approaches, the recently proposed (univariate) discrete beta kernel smoother has been shown to provide some benefits. Bivariate graduation, over age and calendar years or durations, is common practice in demography and actuarial sciences. In this paper, we generalize the discrete beta kernel smoother to the bivariate case, and we introduce an adaptive bandwidth variant that may provide additional benefits when data on exposures to the risk of death are available; furthermore, we outline a cross-validation procedure for bandwidths selection. Using simulations studies, we compare the bivariate approach proposed here with its corresponding univariate formulation and with two popular nonparametric bivariate graduation techniques, based on Epanechnikov kernels and on P-splines. To make simulations realistic, a bivariate dataset, based on probabilities of dying recorded for the US males, is used. Simulations have confirmed the gain in performance of the new bivariate approach with respect to both the univariate and the bivariate competitors.

The Age Pattern of Increases in Mortality Affected by HIV: Bayesian Fit of the Heligman-Pollard Model to Data from the Agincourt HDSS Field Site in Rural Northeast South Africa

BACKGROUND

We investigate the sex-age-specific changes in the mortality of a prospectively monitored rural population in South Africa. We quantify changes in the age pattern of mortality in a parsimonious way by estimating the eight parameters of the Heligman-Pollard (HP) model of age-specific mortality. In its traditional form this model is difficult to fit and does not account for uncertainty.

OBJECTIVE

1. To quantify changes in the sex-age pattern of mortality experienced by a population with endemic HIV. 2. To develop and demonstrate a robust Bayesian estimation method for the HP model that accounts for uncertainty.

METHODS

Bayesian estimation methods are adapted to work with the HP model. Temporal changes in parameter values are related to changes in HIV prevalence.

RESULTS

Over the period when the HIV epidemic in South Africa was growing, mortality in the population described by our data increased profoundly with losses of life expectancy of ~15 years for both males and females. The temporal changes in the HP parameters reflect in a parsimonious way the changes in the age pattern of mortality. We develop a robust Bayesian method to estimate the eight parameters of the HP model and thoroughly demonstrate it.

CONCLUSIONS

Changes in mortality in South Africa over the past fifteen years have been profound. The HP model can be fit well using Bayesian methods, and the results can be useful in developing a parsimonious description of changes in the age pattern of mortality.

COMMENTS

The motivating aim of this work is to develop new methods that can be useful in applying the HP eight-parameter model of age-specific mortality. We have done this and chosen an interesting application to demonstrate the new methods.