Original articleMortality inequality in populations with equal life expectancy: Arriaga's decomposition method in SAS, Stata, and Excel
Introduction
Life expectancy is a useful measure of population health for its capacity to summarize mortality in a single measure. Life expectancy has unique mathematical properties that often go unrecognized which can be tapped to facilitate population comparisons by epidemiologists. The difference in life expectancy between two groups is an algebraic function of underlying age and cause-specific mortality rates [1], [2], [3], [4], [5], [6]. Recent methods proposed in demography have taken advantage of these relationships to show that life expectancy gaps can be partitioned into age and cause-specific components. Such methods have successfully identified the age groups and causes of death resulting in socioeconomic [7], [8], [9], [10], [11], ethnocultural [8], [12], [13], [14], [15], and temporal [7], [8], [10], [11], [13], [14], [15], [16] inequalities in life expectancy in several countries.
Although there is an abundance of decomposition analyses in the literature, such studies are rarely performed in the absence of a life expectancy gap. Populations can have large inequalities in age or cause-specific mortality, yet very similar life expectancy—in such settings, decompositions can still be undertaken to determine the reason for the absence of a gap. No matter how small, the difference in life expectancy between two populations is the sum of positive and negative contributions of age and cause-specific mortality rates [2], [3], [4], [5]. Contributions can be quite large, yet be in opposite directions that cancel each other when summed, potentially yielding little or no life expectancy gap (i.e., equal life expectancy in both groups). For example, life expectancy in a population with mortality that is high at younger and low at older ages could be very similar to another with mortality low at younger and high at older ages, despite the large inequality in age-specific mortality. Decomposition methods are ideal for determining whether life expectancy gaps that appear negligible are in fact associated with large differences in mortality. If the ages or causes of death are sensitive to preventive interventions, such as tobacco cessation, decomposition approaches can provide public policy initiatives with evidence on which age groups or causes of death to target for reducing mortality.
Our primary objective was to demonstrate the utility of decomposition methods for unmasking potentially hidden mortality inequalities among populations with similar life expectancies. Doing so could provide evidence on whether specific age groups or causes of death could be targeted to increase life expectancy. We analyzed mortality data from Canada. Life expectancy of Canadians is high at 79 years for men and 83 years for women, and gaps between provinces are negligible [17]. Yet the province of Quebec has an exceptionally high prevalence of tobacco consumption [17], and higher smoking-related mortality should intuitively lead to lower life expectancy in this province. Decomposition analysis can determine whether tobacco-related mortality indeed affects life expectancy between Quebec and the rest of Canada. Our secondary objective was to encourage similar analyses by researchers and policy makers in other milieus through readily adaptable syntax and an easy-to-use spreadsheet containing formulae for the decomposition of a life expectancy gap.
Section snippets
Data and variables
We obtained data on all deaths in men and women in Quebec and the rest of Canada (hereafter, Canada) for 2005 through 2009 from the Quebec Health and Social Services Ministry and Statistics Canada. Death counts were available in 5-year age blocks (<1, 1–4, 5–9, …, 85–89, and ≥90 years). Population counts were obtained from the Census of Canada (administered in 2006, with estimates for 2005 and 2007–2009) for ages 1 year or more, and birth registration certificates for infants younger than 1
Results
There was essentially no gap in life expectancy between Quebec and Canada (Table 1). The difference was only 0.1 years, for both men and women. There were differences in age and tobacco-related mortality between Quebec and Canada, but the reason why life expectancy was similar between the two areas was not readily apparent from the rates alone (Table 2).
There was no clear pattern in age-specific contributions to the life expectancy gap between Quebec and Canada for women, although higher
Discussion
In this study, we decomposed the life expectancy gap between Quebec and Canada into age and tobacco-related causes of deaths. We selected these two populations for their similar life expectancy, despite differences in prevalence of major risk factors for mortality including tobacco [17]. We aimed to demonstrate that, no matter how small, life expectancy gaps can be partitioned to determine whether risk factors such as tobacco indeed influence life expectancy. Using Quebec and Canada as an
Acknowledgment
This work was supported by a grant from the Research Center of the University of Montreal Hospital Center. N.A. and S.H. acknowledge career awards from the Fonds de recherche du Québec. The authors thank Karine Garneau for programming the Arriaga formulae in Excel.
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