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

By Sharrow, David J.; Clark, Samuel J. et al. | Demographic Research, July-December 2013 | Go to article overview

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


Sharrow, David J., Clark, Samuel J., Collinson, Mark A., Kahn, Kathleen, Tollman, Stephen M., Demographic Research


Abstract

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 efficiently 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 re- flect 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.

(ProQuest: ... denotes formula omitted.)

1. Introduction

This work makes two contributions. The first is a detailed description of the likely impact of HIV on period-sex-age-specific, all-cause mortality as the HIV epidemic grows in a population living in rural northeast South Africa. This task is accomplished by reinter- preting the parameters of the eight-parameter Heligman-Pollard mortality model (Helig- man and Pollard 1980; Rogers and Gard 1991; Gage and Mode 1993; Congdon 1993) and fitting it to age-specific probabilities of dying. The second is a Bayesian fitting proce- dure developed to produce robust fits of the Heligman-Pollard mortality model that yield probability distributions for the parameters, the age-specific probabilities of dying, and the other columns of the corresponding life tables.

Populations with high HIV prevalence in east and southern Africa have experienced dramatic increases in mortality (Dorrington et al. 2001; UNAIDS and WHO 2009) and corresponding declines in life expectancy (UNAIDS 2008). Because the primary modes of transmission of HIV in those populations are heterosexual sex and mother-to-child transmission at birth or through breastfeeding, the majority of HIV positive people are either very young children or sexually-active adults. Consequently there is a characteristic age pattern of deaths resulting from AIDS: very young children who progress through the disease quickly and middle-aged adults who are HIV positive for roughly ten years before dying of AIDS. Adult women living with HIV are typically several years younger than HIV positive men because women tend to have sex with slightly older men.

Using prospectively collected data from people of all ages in a population of roughly 69,000 living in rural northeast South Africa (Kahn et al. 2007, 2012), we look for these signature effects of HIV on sex-age-specific mortality through time. Because we expect to see important changes in child mortality and a well-defined 'hump' in the age pattern of mortality for adults, we summarize the age pattern of mortality using the eight-parameter Heligman-Pollard mortality model (Heligman and Pollard 1980). …

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