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Alves LC and Arruda NM

quintiles. We categorized the first quintile as low income and the fifth quintile as high
income.
We estimated the life expectancy with and without chronic diseases for the Brazilian
elderly population in 1998 and 2008 based on the construction of life tables, which
combined mortality information and prevalence of chronic diseases, as proposed by
the method used by Sullivan (1971). The Sullivan method is the most widely used
to estimate healthy life expectancy or disease-free life expectancy (Imai and Soneji,
2007). The most important figures for calculation of life (and therefore health)
expectancy are the person-years lived in each age group by a future cohort assuming
that the same age-specific mortality rates apply. To calculate these, we need to know
the total time spent in each age group by each member of the cohort. Such data are not
available at the individual level. Instead, we can do the estimation using the population
in each age group and the number of deaths in the age group (Jagger, Hauet and
Brouard, 2001).
The age-specific prevalence with and without chronic disease, and age-specific
mortality rates in the population, are estimates. The expected years with and without
chronic disease are calculated by applying the age- and sex- specific cross-sectional
prevalence rates of these two states to the person-years lived in different age categories
derived from period life tables (Andrade, Corona, Lebrão et al., 2014). So,
∑ 1 [ − π ] L x (1)
DFLE = n l x xi n
x
and

∑ [ π ] L x (2)
LED = n xi n
x
l x
where DFLE x is the average number of years that an individual will live without
chronic disease, starting from exact age x whereas life expectancy with chronic disease
(LED x ) is the average number of years that an individual will live with any disease,
starting from exact age x. n π xi is the proportion of age group x to x+n with a chronic
disease i, which is the disease prevalence based on the PNAD. n L x is a person years
lived in the age interval and l x is the total number of people who have already survived
to age x. Both are obtained from the life table generated based on estimates provided
by the Mortality Reporting System. 1 – n π xi is the proportion of age group x to x+n
without chronic disease i. [1– n π x ]* n L x is a person years lived in an age interval without
chronic disease. [ n π x ]* n L x is a person years lived with chronic disease in age interval x
to x+n. Σ[1 – n π x ]* n L x is a total years lived without chronic disease from age x. It was
obtained as the sum of the all [1– n π x ]* n L x from age x up to the final age group (85+).
Σ[ n π x ]* n L x is total years lived with at least one chronic disease from age x.
The total life expectancy (TLE) at each age, e x , is found by dividing the total number
of years lived beyond that age by the total number of individuals who have already
survived to age x. Life expectancy with and without chronic disease was estimated
by sex, education and income. All statistical analyses were performed with the aid of
using the software R version 3.2.2 and Microsoft Excel 2010.

3 Results

This section presents the results of chronic disease prevalence and disease-free life
expectancy by age (60 or 80), education (high or low) and income (high or low) for
four conditions: hypertension, diabetes, bronchitis/asthma, and heart disease.
Table 1 shows the prevalence of chronic diseases among elderly Brazilians in
1998 and 2008. This data reveal that the prevalence of diabetes and hypertension has
increased among the elderly and for both sexes during the period. In turn, there has
been a reduction in cardiac and respiratory diseases for both sexes. Hypertension is

International Journal of Population Studies 2017, Volume 3, Issue 1 67