J Epidemiol Community Health 1998;52:259–261 259 J Epidemiol Community Health: first published as 10.1136/jech.52.4.259 on 1 April 1998. Downloaded from Age diVerential mortality in Spain, 1900–1991 Javier Llorca, M Dolores Prieto, C Fariñas Alvarez, Miguel Delgado-Rodriguez Abstract the evolution of age diVerential mortality in a Study objective—To analyse the interindi- country through time. vidual inequalities in mortality in Spain In this paper, we analyse the mortality diVer- through the 20th century using the Gini ences according to age in Spain through the coeYcient, widely used as an income con- 20th century using the Gini index. centration index. Design—Age mortality data were ob- tained from oYcial publications of vital statistics and age and sex compositions Methods Age mortality data were obtained from Spain’s were obtained from population census. 4 The Gini coeYcient was estimated. It can National Institute for Statistics (SNIS), for each year from 1900 to 1991. Population data take values between 0 and 1. Zero repre- were obtained from decennial (1900, 1910, sents the situation in which all subjects die 1920, 1930, 1940, 1950, 1960, 1970, 1981, at the same age, whereas when all but one 1991) census population figures.5 Death rates subject dies at 25 the index reaches a per 100 000 person years were calculated using figure of 1. intercensal populations estimated by exponen- Main results—In both men and women tial interpolation. V there was a trend to decrease age di eren- To calculate the Gini coeYcient we need to tial mortality (from 0.26 to 0.16 for men know the age specific death rates for each year. and from 0.26 to 0.12 for women). Never- They are obtained using the Gompertz theless, transitory increases were pro- 6 áx function, Rx =R0 e , where Rx is the specific duced in 1918 (influenza epidemic), and in mortality rate at age x. Several authors have the period of the Civil War of Spain, show- proved the current mortality data fit the Gom- ing a more important increase in the mor- pertz function and they have discussed its tality of young people than that of the consequences.7–9 In a previous paper we have elderly. A new increase was observed proved the Gompertz function works well in through the second half of eighties; it Spain for age 25 and over,10 therefore, we use resulted from an AIDS epidemic and only the mortality data for 25 years and over in motor vehicle injuries. this paper. The number of expected deaths at Conclusion—Inequalities in mortality in each age (until 100 years) is obtained applying Spain have decreased through the 20th the Gompertz function for each year to a century. cohort of 100 000 people aged 25 years. Figure 1 shows a graph of the errors of the model for http://jech.bmj.com/ (J Epidemiol Community Health 1998;52:259–261) 1991 in Spain. Let Mi be the number of deaths at age i, and T the number of person years lived by those Premature mortality is one of the major conse- i who die at age i. Mi can be derived from Gom- quences of inequality in health, independently pertz function as R N (where N is the number of its origin (inequality in health services i i i of persons aged i years. In analogous form, Ti = accessibility, life style, socioeconomic class, R N (i-25). As the Gompertz function is a i i on September 26, 2021 by guest. Protected copyright. etc). Age adjusted death rates and life expect- monotonous and increasing function, it verifies ancy are not good measures to assess age that if i > j then Mi > Mj. diVerential mortality because both of them can For each age, we calculate: increase if the whole mortality curve moves x towards the right, although diVerential mortal- ∑ Mi ity remains constant. i=25 Mx = ––––– (I) Our aim is to use the Gini coeYcient as a 100 Division of Preventive ∑ measure of diVerential mortality. The Gini Mi Medicine and Public i=25 Health, University of coeYcient was first used as an income concen- tration index.1 It can take values between 0 and x Cantabria, School of ∑ Medicine, Santander, Ti 1. Zero represents the situation in which all i=25 Spain Tx = ––––– (II) incomes are equally distributed, whereas when 100 all the incomes are concentrated in only one ∑ Correspondence to: Ti Dr J Llorca, Division of subject the index reaches a figure of 1. The i=25 Preventive Medicine and Gini coeYcient can be generalised as a where Mx is the number of accumulated deaths Public Health, University of measure of concentration degree of any Cantabria School of from age 25 to age x divided by all the deaths Medicine, Av Cardenal variable (for example, health service use or life accumulated between age 25 and age 100; and Herrera Oria s/n, years). The Gini index has been used as an Tx is the quotient of the number of person years 39011-Santander, Spain. individually based inequality measure in mor- yielded by people dying between age 25 and x Accepted for publication tality between countries using actuarial death years divided by the total number of person 5 June 1997 rates,23but it has never been used to measure years. 260 Llorca, Prieto, Alvarez, et al J Epidemiol Community Health: first published as 10.1136/jech.52.4.259 on 1 April 1998. Downloaded from 0.3 tion (equation III); it is multiplied to two and substracted to 1. 99 0.2 ∫Tx dMx = ∑ (Mx+1 -Mx)(Tx+1 -Tx)/2 (III) x=25 If there are not inequalities in the mortality, 0.1 all the points would be on the diagonal line, the graph would be a straight line and the Gini coeYcient would be zero. If all the people 0 except one person die at age 25, the line would coincide with the x axis and the Gini coefficient –0.1 would be equal to one. The Gini coeYcient is a normalised adimen- Ln (mortality rate) – (Rx) sional index. It is robust because it is not –0.2 aVected by uniform increases/decreases in mortality of all age groups. –0.3 25 45 65 85 Results Age (y) Figure 3 displays the evolution of the Gini index in the Spanish men and women between Figure 1 Errors of the Gompertz model for mortality data for the year 1991, Spain. 1900 and 1991. Throughout the period the 1.0 diVerences among men have been greater than among women. In both men and women there is a trend to decrease age diVerential mortality 0.8 (from 0.26 to 0.16 for men and from 0.26 to 0.12 for women). In the evolution of the index 0.6 several segments can be observed: (a) from Tx 1900 to 1917 the Gini coefficient decreased 0.4 slowly (between 0.26 and 0.24) in both men and women; (b) in 1918 (year of the pandemic 0.2 influenza), both sexes presented a great in- crease until 0.34; (c) from 1919 on the evolution is very diVerent for men and women. 0 0 0.2 0.4 0.6 0.8 1 In women the Gini coeYcient decreased stead- Mx ily until 1991, apart from a very slight increase during the Spanish Civil War (1936–1939) and Figure 2 Construction of the Gini coeYcient, Spain, 1980. a levelling oV in the last four years of the period. In contrast, in men a slow decrease can Both Mx and Tx range between 0 and 1 and be seen until 1935, a great increase between they can be represented in a plot (fig 2) with Mx 1936 and 1941, a great decrease from 1942 to in the x axis and Tx in the y axis. A line through 1960, a very mild decrease from 1960 to 1987, all the points can be drawn. This line is always and a slight increase from 1988 on. http://jech.bmj.com/ below the diagonal line. The double of the area between the diagonal and the line obtained is Discussion called the Gini coeYcient. Increase in life expectancy is believed to be a To estimate the Gini coefficient, the shape is consequence of improvement in health status. integrated using the compound trapeze equa- However, life expectancy does not oVer any 0.40 on September 26, 2021 by guest. Protected copyright. 0.35 Women 0.30 Men 0.25 0.20 0.15 Gini coefficient 0.10 0.05 0.00 1900 1920 1940 1960 1980 Year Figure 3 Gini coeYcient, Spain, 1900–1991. Age diVerential mortality in Spain 261 J Epidemiol Community Health: first published as 10.1136/jech.52.4.259 on 1 April 1998. Downloaded from information about whether this improvement is equal for diVerent age groups. For example, the KEY POINTS following can produce an increase in life + The Gini index allows the analysis of age expectancy: (a) a constant decrease in all age diVerental mortality through time. specific death rates; (b) a decrease in the death + The age diVerential mortality has been rates of the elderly only; and (c) a decrease in reduced more in women than in men in the death rates of young people only. In (a) Spain. interindividual diVerences remain constant, + The Gini index is not appropriate for the whereas in (b) the diVerences increase, and analysis of specific causes of death. they decrease in (c) because more people live for longer; however, these three situations are recognised as a population improvement.