Age, Period, Cohort and Early Mortality: An Analysis of Adult Mortality in Italy

Graziella Caselli; Riccardo Capocaccia

Population Studies, Vol. 43, No. 1. (Mar., 1989), pp. 133-153.

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Population Studies, 43 (1989), 133-153

Printed in Great Britain

Age, Period, Cohort and Early Mortality : An Analysis of Adult Mortality in Italy

G R A Z I E L L A C A S E L L I * A N D R I C C A R D O C A P O C A C C I A t

1. I N T R O D U C T I O N

Previous analyses of Italian mortality over the last century have suggested interesting links between period and cohort mortality,l in particular the delayed effects of certain dramatic events, such as the two world wars. It has been suggested that the persistent higher mortality of the cohorts involved in the First World War was the result of a general weakening due to exposure to high health risks and to particularly unfavourable living conditions during the war.

Similarly, the events of the first years of life -which are known to have a major influence on the subsequent health and development of an individual -may be important factors in determining the level of cohort mortality. It is possible, for example, that unfavourable conditions during infancy and childhood (e.g. malnutrition, poor hygiene, etc.) are a handicap for future survival. An alternative hypothesis would be that a cohort which has lost its weakest members early in their lives has been preselected and is in a better position later.

A number of authors have considered this argument, both from an empirical and a theoretical point of view. Of particular note is the classic study by Kermack, McKendrick and McKinley in 1934,2 in which the authors suggested that the health of a cohort was determined primarily by the environment in which its members spent the first 15 years of their lives. Similarly, Preston and Van de Walle demonstrated the influence of living conditions in infancy on subsequent mortality in three French departments during the nineteenth ~ e n t u r y . ~ Mortara4 and Gini5 studied the presence of possible selection effects in infancy on mortality in old age. Somewhat more recently, Livi Bacci studied the relationship between infant mortality and mortality at advanced ages for the different regions of I t a l ~ . ~

From a methodological perspective the problem may be studied by means of models aimed at decomposing the major components of mortality - age, period, and cohort -as discussed by Hobcraft, Menken and Prestoq7 and applied by Hobcraft and

* Dipartimento di Scienze Demografiche, Universita di Roma, Rome, Italy. t Laboratorio di Epidemiologia e Biostatistica, Istituto Superiore di Sanita, Rome, Italy.

Graziella Caselli 'I1 contributo dell'analisi per generazioni a110 studio della geografia della mortalita', Genus, 39 (1983), nos 1-4; Graziella Caselli, James W. Vaupel and Anatoli I. Yashin, 'Mortality in Italy: contours of a century of evolution', Genus, 41 (1985), nos 1-2.

". 0.Kermack, A. G. McKendrick and P. L. McKinley, 'Death rates in Great Britain and Sweden: some general regularities and their significance', Lancet, March 1934.

Samuel Preston and Etienne van de Walle, 'Urban French mortality in the nineteenth century ', Population Studies, 32 (1978).

Giorgio Mortara, 'Le variazioni della mortalita da generazione a generazione in Svezia', Annuli di Statistica serie V, 4 (1912).

Corrado Gini, 'Sull'utilita delle rappresentazioni grafiche', Giornale degli Economisti e Rivista di Statistica, 48, (2), 1914.

"assimo Livi Bacci' Alcune considerazioni sulle tendenze della mortalita senile e sull'eventuale influenza selettiva della mortalita infantile', Rivista Italiana di Economia, Demogra$a e Statistica, 18 (34) , 1962. ' John Hobcraft, Jane Menken and Samuel Preston, 'Age, period and cohort effects in demography: a

review', Population Index 48 (I), 1982.

133

134 G R A Z I E L L A C A S E L L I A N D R I C C A R D O C A P O C A C C I A

G i l k ~ . ~Models of this kind have increasingly also been used in epidemiological analyses of both general and cause-specific mortality.'

The present study has a double objective. The first is to increase our understanding of the evolution of adult mortality in Italy. The second is to investigate the relationship between early and adult mortality, on the hypothesis that the life experiences which influence the former during the youngest years also affect the latter later in life.

In our study, we use mathematical models which take account of the age, period and cohort components of mortality. Two models are employed: in the first, the age-period-cohort (APC) model discussed in Section 2, we investigate adult mortality in terms of these three factors; in the second, the age-period-early mortality (APEM) model discussed in Sections 3 and 4, we analyse the relationships between mortality in infancy and childhood and mortality at later ages. Both models are applied to observed probabilities of death in the cohorts born between 1882 and 1953 in Italy.lo

2. AGE, P E R I O D A N D COHORT ANALYSIS: THE A P C M O D E L

2.1. Statistical Model

The observed probabilities of death were fitted by a logistic linear model

logit (q,,,) = log -4ijk = ai +P, +7, +constant, (1)1-9,jk

where: q,,, are the probabilities of death from cohort life tables for age i, period j, and cohort k; a, 0 < i < 54, are the age effects from 25 to 79 years; P, 0 <j < 71, are the period effects from 1907 to 1978; and, y, 0 < k < 71, are the cohort effects for cohorts born between 1882 and 1953.

The data consisted of cohort life tables for the cohorts given above, of which only those relating to the cohort of 1899 and earlier cohorts were complete (up to age 79). The estimated values for a,, P,, and yk were derived by maximizing the likelihood function, which involved calculating the number of individuals at risk for each combination of the three factors. All calculations were carried out using the BMDPLR program for logistic regression analysis.I1 In this program the parameters are estimated by means of an iteratively reweighted least-squares procedure, that is, by minimizing the expression

C wi(ei-oJ2, 2

where o, and e, are the numbers of observed and estimated cases, respectively, in the i-th cell. The weights, w,, are the reciprocal of the variance of e,.

The coefficients a,, P,, and y,, were scaled by setting the first of each group equal to zero : a, = Po = yo = 0.

John Hobcraft and Walter Gilks, 'Age, period and cohort analysis in mortality studies', in Methodologies for the Collection and Analysis of Mortality Data, ed. J . Vallin, J. H. Pollard and L. Hillingman (Liege: Ordina Editions, 1984). ' Nathan E. Breslow and Nicholas E. Day, 'Indirect standardization and multiplicative models for rates,

with reference to the age adjustment of cancer incidence and relative frequency data', Journal of Chronic Diseases, 28 (1975); Michel Gail, 'The analysis of heterogeneity for indirect standardized mortality ratios', Journal of the Royal Statistical Society, A 141 (1978); Peter Boyle, Nicholas E. Day and Knut Magnus, 'Mathematical modelling of malignant melanoma trends in Norway, 1953-1978', American Journal of Epidemiology, 118 (1982); Clive Osmond, Martin J. Gardner and E. D. Acheson, 'Analysis of trends in cancer mortality in England and Wales during 1951-80 separating changes associated with period of birth and period of death', British Medical Journal, 284 (1982).

lo Marcello Natale and Amedeo Bernassola, ' L a mortalita per causa nelle regioni italiane. Tavole per contemporanei 1965-1966 e per generazioni 1790-1964 (Istituto di Demografia, Universita di Roma, n. 25, Rome, 1973); Graziella Caselli and Bruno Greco, 'Aggiornamento alle tavole di mortalita per generazioni di Natale e Bernassola, period0 1965-1978' (Dipartimento di Scienze Demografiche, Universita di Roma 'La Sapienza', 1983). " W. J. Dixon et al. eds, BMDP Statistical Software (Berkeley: University of California Press, 1983).

a particular solution can be 2,is an arbitrary parameter. For each value of ,4 where

A D U L T M O R T A L I T Y I N I T A L Y 135

As is well known, Model (1) does not have a unique solution, since the three factors, age, period, and cohort, are constrained by the relationship:

period = age +cohort.

If a,, b,, and c,, are estimates of the parameters at, p,, and y, then the same expected probabilities are given by each transformed set of the form:

identified. The effect of a change in the parameter A determines a shift proportional to the distance from the initial point that looks like a rotation. Period values are affected by a rotation in a direction opposite to age and cohort values.

Various methods have been proposed to overcome the inconvenience posed by this identification problem, most of which have consisted of imposing some ulterior constraint on the coefficients of the logistic function.12 In this paper, however, since it is difficult (if not impossible) to find a means of constraining the solution set which is not arbitrary, we prefer a different approach. If the effects due to age, period and cohort, are decomposed into a linear trend and a higher-order residual component, it is only the former which is subject to the problem of identification. The non-linear part, on the other hand, is uniquely determined.13

For any chosen solution to Model (I), the estimated values of the coefficients a,, b,, and c,, can thus be expressed as the sums of the respective linear trends whose coefficients are indicated by rl, 6, and c", and of the residual components a), bj*,and

It is easy to show that the transformation (2) will change the linear part while leaving the residuals invariant :

S'i=(&-A)i a ) ' =a* , (4 a)

Hence, it is evident that the three linear trends due to age, period, and cohort, cannot be analysed separately and we therefore make no attempt to do so.

The fact that the three linear trends cannot be estimated comes as no surprise and is due to the nature of the data being analyzed. The linear components represent constant mortality changes over a time interval taken from the totality of the data. For example, the terms 6 and c" give the logarithm of the average change in mortality associated, respectively, with the passing of a year or with the succession of one generation. Considering that, for a given age, successive cohorts actually live in successive periods of time, the attribution of the linear trend to one of the two components is completely immaterial both from a practical point of view and for interpretation. Neither the period

l2 Clive Osmond and Martin J. Gardner, 'Age, period and cohort models applied to cancer mortality rates', Statistics in Medicine, 1 (1982); Nicholas E. Day and Bernadette Charnay, 'Time trends, cohort effects, and aging as influence on cancer disease' in Trends in Cancer Incidence (Cause and Practical Implications), ed. K . Magnus (Hemisphere Publishing Company, Washington, 1982); Shiro Horiuchi, 'The long-term impact of war on mortality: old-age mortality of First World War survivors in the Federal Republic of Germany', Population Bulletin ofthe United Nations, no. 5 (1983); William M. Mason and Herbert L. Smith, Age-Period-Cohort Analysis and the Study of Deaths from Pulmonary Tuberculosis (Research Report 81-19, Ann Arbor: The Population Studies Center of the University of Michigan, 1984).

' W f . the appendix to Hobcraft, Menken and Preston, loc. cit. in fn. 7 .

136 G R A Z I E L L A C A S E L L I A N D R I C C A R D O C A P O C A C C I A

nor the cohort is, by itself, the cause of mortality. Either can be taken to represent the pattern of constant change.

The same is not true when we consider the non-linear components. The presence of periods of high mortality, as for example during epidemics, can produce 'false' cohort effects, if explicit allowance is not made for them. Conversely, particularly high or low levels of mortality for certain cohorts can produce distortions in the period analysis if these abnormalities are not accounted for.

Model (1) can be used in the analysis of mortality change associated with each variable to control for the effects of the non-linear perturbations. Taking into account expressions (3) and (4), the estimated values of q,, can be written:

where, given the linear constraint, i+ k =j, both sides are unaffected by the value of the parameter A.

A convenient way to look at this model is obtained by setting A = C, i.e. the linear cohort component equal to zero. We then obtain the full age-period model:

Grouping homogeneous parameters together, we have

logit (q,,,) = [(Z-8 i+a*] +[(h+C)j+ b:] +c,* +constant,

logit (q,,,) = AB, +B, +c,* +constant, (6)

where the parameters AB, indicate the age effects, B, the period effects, and c,* the non- linear cohort effects.

Similarly, if we set A = -6, we obtain the three components of the full age-cohort model:

logit (q,,,) = [(Z+b) i+ a 3 +[(C+ 6)k ++,*I +bf +constant,

logit (g,,) = AC, +C, +bf +constant, (7)

where the parameters AC, indicate the age effects, C, the cohort effects, and bf the non- linear period effects.

The terms full age-period model and full age-cohort model are used to indicate two particular formulations of the general model (1) which yield equivalent estimates of the observed probabilities, and differ only on the basis of which pair of the three linear terms is included.

The parameters of Models (6) and (7) can be computed from the linear and non-linear components of each actual solution of Model (1). It is easy to verify that the expressions in brackets are independent of the value of A. The two age components AB, and AC, differ only in the linear part, the higher-order component being the same.

It is necessary now to see how the quantities B,, C,, AB,, AC, can be interpreted in terms of odds-ratios (OR). We consider the odds-ratio of expected mortality at two different points, P, = (i,, j,, k,) and P, = (i,, j,, k,), of the given data set:

OR (P,, PI) = -qi,j,k, -

-qililkl

-qi2j,k2 qililkl

First, substituting qiljlkl, qiZjskZ from (6), we have

OR (P,, PI) = exp (AB,, -ABil) exp (B,, -Bjl) exp (c: -c:~).

A D U L T M O R T A L I T Y I N I T A L Y 137

Thus, we can express the estimated mortality odds-ratios as the product of three terms. The first contains the change across ages (controlling for period and non-linear cohort effects) ; the second the change across periods (controlling for age and non-linear cohort effects); the last non-linear cohort effects (controlling for age and period).

Similarly, substituting qilllrl, qigJlkg from (7), we obtain:

OR (P,, PI) = exp (ACi2 -ACtl) exp (Ck2 -Ckl) exp (b; -bz). (9)

Hence, we can express the estimated mortality odds-ratios as the product of an age term, a cohort term and a term containing non-linear period effects, each of them controlling for the other two.

If, in the above formulae (8) and (9), we take the point PIas given by the initial values for the three covariates, so that PI = (0,0,0) and the point P2= (i,j,k), then the quantities, Bj, C,, AB,, and AC,, become simple logarithms of odds-ratios for: period (1907+j) with respect to 1907; cohort (1882+k) with respect to 1882; age (25+i) with respect to 25 from a period point of view; and age (25+ i) with respect to 25 from a cohort point of view.

Once the parameters of the model had been estimated, the analysis of residuals showed no systematic deviations of the fitted from the observed values. Standardized residuals appear to be fairly normally distributed with variance independent of the factors studied. The squared correlation coefficient between the observed and expected probabilities of dying can be taken as a global measure of the goodness of fit. The values thus obtained are R2= 0.992 for males, and R2 = 0.997 for females, indicating a satisfactory fit.

2.2. Results

By applying the model described above, we were able to calculate odds-ratios using the probabilities of dying between ages 25 and 79 for Italian cohorts whose members were born between 1882 and 1953. These are shown in Tables 1-3 and Figures 1-2, with the constraint that the initial value in each case is equal to unity.

Table 1 shows, for both men and women, the theoretical period-mortality odds-ratios by age, net of cohort perturbations, and the theoretical cohort-mortality odds-ratios by age, net of period perturbations. Clearly, these values do not represent the mortality of any particular period or cohort, but are rather a model of the average movement of mortality across age. In any case, they demonstrate certain noteworthy characteristics of changes in mortality by age. For men as well as for women, the age profile of mortality is similar for cohorts and for periods. When we compare the trends in mortality by age for the two sexes, we note important differences. In effect, the odds-ratio for men's mortality, both from a period and a cohort point of view, reaches a maximum between the ages of 30 and 40. From this point onward, the odds-ratios increase at a more or less constant ratio between one age group and the next. For females, the values do not initially show the same maximum, but their rate of increase increases with age.

Before analysing the results relating to the period and cohort components, it is necessary to recall that our approach does not make it possible to separate these two effects completely. In spite of this limitation, in Figure 1 (and Table 2) we report the period components for the two sexes. First, we can trace the evolution of adult mortality across the periods considered net of perturbations due to cohorts, i.e. from a full age and period model (see Formula 6). Secondly, we can interpret the oscillations in the odds- ratios as variations in mortality between successive periods due solely to fluctuations in the period component of mortality.

138 G R A Z I E L L A C A S E L L I A N D R I C C A R D O C A P O C A C C I A

Table 1 . APC model. Estimated mortality odds ratios by sex and age, with respect to age 25, from a longitudinal point of view (AC), and from a cross-sectional point of view ( A B )

Males Females

AC AB

139 A D U L T M O R T A L I T Y I N I T A L Y

Table 2. APC model. Estimated mortality odds ratios by sex and calendar year, with respect to 1907

Year Males Females Year Males Females

Analogously, in Figure 2 (and Table 3) we show the evolution of adult mortality across the cohorts, controlling for perturbations due to periods, that is, from a full age and cohort model (see Formula 7). Again, we can interpret oscillations in the odds-ratios as variations in mortality between consecutive cohorts due to fluctuations in the cohort component of mortality.

Thus, the general decline in period effects (B,) for adult men during the 72 years considered (see Figure 1) brings out three points of relative disadvantage. The first, and most important, is found between 1915 and 1919 and can be attributed to the negative effects of the First World War (in 1917-18 the negative effects of Spanish influenza are also evident). The years 1943-5, with the heaviest losses during World War 11, show the second most important point of disadvantage, and finally, even if less important, the years following World War I (in particular between 1920 and 1933); this third period was an extremely difficult one for Italy, reflecting the havoc wrought by the war. During this period it was particularly the men who suffered, probably because of their key role in the reconstruction and development of the country under conditions which were decidedly unfavourable.

On the other hand, periods of relatively strong decline are found during the decades

--

140 G R A Z I E L L A C A S E L L I A N D R I C C A R D O C A P O C A C C I A

Table 3. APC model. Estimated mortality odds ratios by sex and year of birth, with respect to the 1882 cohort

Cohort Males Females Cohort Males Females

1.000 0.998 0.959 0.949 0.958 0.907 0.884 0.857 0.875 0.843 0.829 0.807 0.793 0.773 0.748 0.737 0.726 0.707 0.644 0.649 0.632 0.632 0.603 0.595 0.580 0.575 0.549 0.543 0.518 0.518 0.496 0.486 0.464 0.448 0.476 0.494

just before and just after the Second World War. After 1955, the decline slowed down and the oscillations due to period fluctuations are smaller than previously.

For males, the evolution of the cohort odds-ratios clearly shows that the largest part of the decline occurred in the most recent cohorts, particularly those born after the Second World War. A detailed analysis reveals some points of interest. The odds-ratios increase progressively from the birth cohort of 1882 to that of 1900. This group includes the cohorts most directly involved in the First World War. For the birth cohorts from 1901 to 1920 there is a general drop in mortality relative to the preceding cohorts with points of relative disadvantage for the cohorts born or passing through adolescence during the war. These phenomena of excess mortality are similar to those already discussed for other countries also involved in the war.14 Beginning with the cohorts born after 1930, the risks decrease more quickly. It is useful to bear in mind, however, that

l4 Jacques Vallin, La mortalithpar ginhration en France, depuis 1899 (Travaux et Documents, Cahier n. 63, INED. Presses Universitaires de France, 1973); Horiuchi, loc. cit. in fn. 12; Robert M. Dinkel, 'The seeming paradox of increasing mortality in a highly industrialized nation : the example of the Soviet Union', Population Studies, 39 (I), 1985.

A D U L T M O R T A L I T Y I N I T A L Y

-Males .....

a.a.. -Males ............Females .... ............Females :...

I I I 4 I I I I I r 1900 1920 1940 1960 1980 1880 1900 1920 1940 1960

Year of death Year of birth

Fig. 1 Fig. 2

Figure 1. APC model. Period mortality trend in terms of odds ratios. Figure 2. APC model. Cohort mortality trend in terms of odds ratios.

the values for the latter cohorts are based on a very small number of observations and are, therefore, less reliable.

For women, the odds ratios in Figure 1 illustrate, first of all, a more accentuated decline than that observed for the men, but, as with men, the two mortality crises corresponding to the two world wars are clearly evident. Not evident, however, is the disadvantage during the years following the first conflict. In this regard we may recall that women were less heavily involved in the processes of reconstruction and industrial development. In addition, beginning with the decade of the 1920s, women were able to benefit from a decline in maternal mortality thanks to improvements in obstetrics and maternal health care. The last 20 years are characterized, as for men, by an absence of important oscillations; but, in contrast to men, by a continued relative decline. Within this period of general improvement, we can, however, note one small point of disadvantage corresponding to 1957, evident more clearly for women than for men, which could perhaps be attributed to the Asian influenza epidemic.

Figure 2, which shows the evolution of cohort mortality net of period perturbations, is rather different from that for men. In point of fact, the cohorts born between 1882 and 1900 did not suffer the relative disadvantage noted for men, which was attributed to the negative effects of the first war. This discrepancy reflects the fact that women were not directly involved in this war. Analogously to men, however, female cohorts born during the period of conflict show a similar high risk of mortality. These years are, in fact, the only ones in which the general decline of women's mortality across cohorts is marked by relevant perturbations.

3. AGE, P E R I O D A N D E A R L Y M O R T A L I T Y A N A L Y S I S : T H E A P E M M O D E L

3.1. Cohort efects and early mortality

The APC model presented in Section 2 made it possible to analyze Italian adult mortality in terms of three components : age, period and cohort. The model represented the movement of mortality in three directions - across ages, across periods and across

142 G R A Z I E L L A C A S E L L I A N D R I C C A R D O C A P O C A C C I A

cohorts - in terms of odds-ratios; it thus underlined the perturbations which were linked to peculiar periods or cohorts. We are still far, however, from a complete decomposition of the effects due to the three components. It should be noted that they cannot be considered as true risk factors, since they are not (directly or indirectly) causes of death, as has already been noted by several authors.15

Age is associated with the probability of dying since it is linked to the biological process of ageing and indicates the accumulation of harmful effects from prolonged exposure to risks in the past. In either case, age does not represent a direct measure of an individual's state of health, but a proxy for other variables that cannot be observed directly.

The period subsumes a complex set of events (wars, epidemics), environmental factors (hygiene, sanitation) or individual factors (nutrition, life-style) which influence the probability of dying of individuals, irrespective of age, but which are characterized by their short delay and reversible effects.

The cohort variable, finally, represents endogenous (e.g. genetic) and exogenous factors (e.g. malnutrition in infancy, accumulation of deleterious environmental effects) that act for an extended period from the moment of exposure. Of the three factors, it is linked least directly to the determinants of mortality. It may, therefore, be appropriate to substitute the cohort factor with more easily interpreted proxy variables.

Since adult mortality undoubtedly depends on the experience of the early years, cohort mortality during the first few years of life, which is a measure of exposure to specific endogenous and exogenous risk factors, may be a significant element in the cohort component of mortality. The relationship between early and adult mortality could arguably be one of either debilitation or selection. For example, high infant and childhood mortality may act, on one hand, as a debilitating force by weakening all members of the cohort, or, on the other, as a selection mechanism by gradually eliminating only the weakest members.

On this basis, we proceed to a formalization of a different model of the probabilities of dying for the same generations previously considered, again for ages 25-79 and years 1907-78. As a means of representing the cohort component, we relate the level of adult mortality not only to the relevant age and period, but also to the mortality experience in infancy and childhood of the cohort involved. By thus controlling for the level of early mortality, we are able to analyse the age and period factors in the evolution of adult mortality separately from the cohort component.

Clearly, such a simplification may not explain fully the mechanism which links the level of adult mortality with the history of the cohort concerned, since, in particular, it does not deal with the question how, at a given age, the level of mortality may be influenced by what has happened to members of the cohort after their fifteenth birthdays. Nevertheless, among the diverse solutions which would have been possible, this approach seems to be the one which will best facilitate an understanding of one factor which is certainly of prime importance for adult mortality, that is the experience of the earliest years of life.

3.2. Statistical model

In order to investigate possible relationships between early and adult mortality in the cohorts studied the factor 'cohort' is then replaced by the probability of dying during

l5 James W. Vaupel, Kenneth G. Manton and Eric Stallard, 'The impact of heterogeneity in individual frailty on the dynamics of mortality', Demography, 16 (1979); Hobcraft et al., loc. cit. in fn. 7; Hobcraft and Gilks, loc. cit. in fn. 8 ; James W. Vaupel and Anatoli I. Yashin, 'Death, selection and debilitation' (unpublished paper). International Institute for Applied System Analysis Laxenburg, Austria (1985).

143 A D U L T M O R T A L I T Y IN I T A L Y

the first year of life for each cohort (qc) or, alternatively, by the corresponding probability during the first fifteen years of life (,,go).

A logistic regression model is then run with age, period and Q, as dependent variables, where Q, is henceforth understood to be either go or ,,go, for the cohort k, as appropriate. The possible age dependence of the association between infant or childhood mortality and subsequent adult mortality is considered by introducing a different coefficient for each age in the term containing Q,. Symbolically, this gives:

It is important to note that there is no identification problem in this case, since independent information (carried by the variable, Q,) has been considered apart from the age and period variables.

In order to compare the results of this section with those of Section 2, we define the odds-ratio in this case, to be:

OR (P,, 4)= qi2j2(Q2) 1 -qi,j,(Ql>

1-qi2j2(Qz) qi,j,(Ql) ' where P, = (i,, j,) and P, = (i,, j,). Hence, when we consider the odds-ratio for one period and for the same level of infant/childhood mortality, that is for j, =j, and Q, = Q,, it is easy to verify that

OR (P,, Pl) = exp (at2 -a,,). (1 1)

Likewise, if we wish to calculate the odds-ratio for a given age and again the same level of Q, we have

Finally, we may consider a small change in Q, such that

without changing either age or period, so that the odds-ratio for age i becomes:

OR (AQ) = exp (6, AQ). (13)

These three formulae will allow us to interpret, unambiguously, the terms, a,,@, and 6, AQ, as age, period, and early mortality effects. 6, corresponds roughly to the logarithm of the relative risk of dying at age i linked to a unit increase in the cohort's early mortality.

After fitting the model, residual analysis indicated, as with the previous model, an approximately Gaussian error distribution, with a variance independent of the factors considered. The values of R2 for the model where Q = go were 0.995 and 0.998 for men and women, respectively; for the model where Q = ,,go, they were 0.996 and 0.999.

3.3. Results

The mortality effects associated with infant and childhood mortality, expressed as odds- ratios for different ages, are given in Table 4. The figures in columns 1 and 3 are the odds-ratios as given in Formula (13) above for a change in Q of 10 per 1000. In Columns 2 and 4 are the changes in OR associated with a change of one standard deviation in the values of Q for the appropriate sex. For the cohorts studied (1882-1953), the mean values of infant mortality per thousand (lOOOqo) were 162.8 and 146.1 for males and females, respectively, with standard deviations of 35.1 and 31.4. For ,,go the mean values were 296.2 and 282.4, and the standard deviations 79.2 and 78.2.

In order to compare the values of OR between the two sexes, but for the same model, it is best to consider a constant change in Q, which we have taken to be 10 per 1000.

144 G R A Z I E L L A C A S E L L I A N D R I C C A R D O C A P O C A C C I A

Table 4. Change in the odds ratios for each age associated with an increase in early mortality AQ

Q = so Q = 1690

A Q = A Q = A Q = A Q = Age 10/1000 so 10/1000 so

Males 1.618 1.064 1.479 1.055 1.310 1.036 1.140 1.018 1.007 1.001 0.935 0.990 0.895 0.984 0.879 0.973 0.902 0.981 0.883 0.981 0.905 0.988

Females 1.493 1.063 1.424 1.056 1.240 1.033 1.125 1.018 0.987 1.000 0.910 0.989 0.880 0.983 0.877 0.977 0.947 0.993 0.997 1.001 0.991 1.001

However, since the relative variability of q, and ,,go is different, it is best to compare the two models, for a given sex, by calculating the values of OR on the basis of a change of one standard deviation in the values of Q. In this way, we can see, by comparing Columns 2 and 4, that the two models give very similar results for males. For females, however, the coefficients for the second model appear to have a similar form but are at a generally higher level than in the other model. In this paper, considering that ,,go clearly contains more information on the history of cohort mortality than q,, we have simplified matters by examining only the results for the second model.

The results of the second model (considering now only the case where Q = ,,go) confirm the hypothesis of a relationship between early and adult mortality, as shown in Figure 3 and Table 4. For both sexes, higher mortality at early ages is associated with higher mortality up to age 45, and lower mortality a t later ages. It is noteworthy that the absolute magnitude of the influence of early on adult mortality is greater between ages 25 and 45 than at more advanced ages. One possible interpretation of this can be given in terms of debilitation and selection. That is, for the cohorts analysed, if living conditions during the early period of life are unfavourable, negative effects could continue during the first 45 years of life. The same conditions that cause high mortality at early ages would entail greater vulnerability in the survivors. Only after members had passed their 45th birthdays would the forces of selection to which the cohorts have been exposed lead to a reduction in the number of highly vulnerable individuals, so as to produce lower mortality.

This explanation is only one of the possible ways of interpreting this set of data. It does not take into account (particularly from age 45-50 onwards) the cumulative effects of unfavourable living conditions during the working ages and also, for women, during

A D U L T M O R T A L I T Y I N I T A L Y

Males -Females ........ . ...

0.9004 t I 1I I

20 30 40 50 60 70 80

Age

Figure 3. APEM model. Change in odds ratios associated with a 10/1000 increase in infant and childhood mortality (,,q,).

the reproductive ages. In fact, the observed association between early and adult mortality could be merely an example of the more general phenomenon of autocorrelation. From an epidemiological point of view, risk factors associated with mortality at a certain age could become less important throughout the life of a cohort. A complete study of this question should be considered in future research, since in this case it would be necessary to employ different statistical methods.

The trend of mortality over age will not be discussed here, since we assume that it will vary in accordance with levels of early mortality. The interrelation between these two factors may be better understood if we compare observed estimates of mortality assuming higher or lower mortality in early ages. This approach will be developed in Section 4.

For the moment it is of interest to examine the period effects in the APEM model. These effects, still expressed in terms of odds-ratios which compare each successive period to the first, are uniquely determined and independent of age and early mortality (see Formula 12, where j, now refers to 1907). Figure 4 and Table 5 illustrate the changes between 1907 and 1978. For the entire 72-year period we see a decreasing trend in mortality for both sexes, which is very slight for men but much steeper for women. Since the model controls for the level of early mortality, this sex difference in the evolution of mortality over time cannot be interpreted as a function of differential forces of debilitation and selection in infancy and childhood. That is to say, that even without the advantage of a more favourable early mortality, adult mortality would still have diminished more rapidly for women than for men.

The period effects in the APEM model (Figure 4) illustrate for both sexes the mortality crises corresponding to the two world wars which we have already noted in the APC model (Figure 1). Once again, the higher mortality of men during the decade and a half following the First World War is particularly evident. In addition, however, this time a slight negative period influence can also be noted for women.

It is instructive to consider simultaneously the changes in adult mortality in the APC and the APEM models. In the former, we recall, the movement of mortality across periods (Figure 1) combines both the period components and the linear trend of the cohort component. Additionally, the cohort effects are constrained to be equal throughout the lives of the cohorts considered. But the APEM model separates the period from the cohort components (which are, admittedly, limited to early mortality cohort effects) more completely. The APEM model also has the advantage of allowing cohort effects which are variable by age.

146 G R A Z I E L L A C A S E L L I A N D R I C C A R D O C A P O C A C C I A

0.2i-MalesI ............Females

8 -

1900 1920 1940 19k0 19'80 Year of death

Figure 4. APEM model. Period mortality effects in terms of odds ratios.

Table 5. APEM model. Estimated mortality odds ratios by sex and calendar year, with respect to 1907

Year Males Females Year Males Females

1.000 1943 1.938 1.278 1.028 1944 1.790 1.157 1.016 1945 1.475 0.975 1.052 1946 1.261 0.851 1.047 1947 1.176 0.790 1.021 1948 1.110 0.740 1.047 1949 1.076 0.698 1.162 1950 1.072 0.680

1951 0.670 1952 0.648 1953 0.616 1954 0.590 1955 0.602 1956 0.608 1957 0.577 1958 0.545 1959 0.537 1960 0.532 1961 0.535 1962 0.541 1963 0.524 1964 0.513 1965 0.488 1966 0.489 1967 0.485 1968 0.474 1969 0.483 1970 0.453 1971 0.441 1972 0.435 1973 0.422 1974 0.421 1975 0.407 1976 0.397 1977 0.394 1978 0.362

147 A D U L T M O R T A L I T Y I N I T A L Y

In comparing the results of the two models, apart from the similarity of the mortality crises, the most remarkable feature is the difference in the decline in mortality across periods, a difference which is manifest both in the speed of the decline and in its form. The difference in the rate of decrease between the two models is due to their different structures, and is consistent with the hypothesis that the largest part of the decline in adult mortality during this period is associated with the decline in infant and childhood mortality for the cohorts involved. The contrasting form of the odds-ratio curves is quite evident, especially for men: in the APC model the odds ratios decrease rapidly for the first half-century (ignoring the war years) and more slowly afterwards; in the APEM, however, the opposite is true (in fact, in the second case the odds ratios rise for some 40 years before beginning their decline).

The reasons for these contradictions are explained by the different formulations of the two models, in particular by the absence in the APC model (and the presence in the APEM model) of the possibility for age-cohort interactions. Remembering that the link between early and adult mortality is strongest between ages 25 and 45, it is clear that the decline in infant mortality should weigh most heavily in this age group. Since, during the first 30 years of our study, only the youngest age groups are present in the analysis (since we consider cohort life-tables starting with the 1882 cohort), the rapid decline in the odds-ratios in the APC model for the period 190740 reflects the rapid decrease in mortality for these ages alone. Conversely, in the APEM model, which controls for the interaction between early mortality and the age pattern of mortality, the evolution of the odds-ratio does not depend on which ages are included in the analysis for the different periods.

4. E A R L Y D E B I L I T A T I O N EFFECTS I N C O H O R T M O R T A L I T Y

Part of the mortality differentials evident in successive cohorts at adult ages may thus be linked to their different levels of mortality during the first 15 years of life. To evaluate the magnitude of this association, we choose to estimate the probability of dying after age 25, controlling for the level of early mortality by setting it equal for all, and then compare these values with the observed values. From a theoretical point of view this is equivalent to assuming similar forces of debilitation or selection for each cohort during the first 15 years of life. The results presented below for the cohorts in the study are an example of the effects of such forces. In fact, if we eliminate the effect of mortality in early life, for instance by applying an arbitrary level to all cohorts (set equal to the average value taken over all the cohorts included in the studies: 296.2 per 1000 for males and 282.4 per 1000 for females), we can evaluate the mortality differences between cohorts according to the model's other components, age and period. In this way, for all the cohorts, we have a hypothetical mortality experience for individuals between 25 and 79 years old which depends exclusively on the period component.

The analysis has been performed on a sub-set of the cohorts ;those born in 1882, 1896, 1903, 1918, 1921, and 1931. They were selected because they are representative of the entire set of cohorts. The birth cohort of 1882 was chosen because it is the oldest of those in the study. The male cohort of 1896 directly experienced the First World War. The birth cohorts of 1903 and 1918 are among those which suffered from the influenza pandemic and the deprivations of the war during their adolescence or year of birth, respectively. The cohorts of 1921 and 1931 were chosen to represent the mortality experience of more recent cohorts.

We should keep in mind that only a general agreement between the observed and estimated probabilities justifies using the latter as a means of comparing the hypothetical

148 G R A Z I E L L A C A S E L L I A N D R I C C A R D O C A P O C A C C I A

1882 / 1918

(Early mortality = 421) (Early mortality = 320)

0.1 - 1903 (Early mortality = 356)

*/.

0.1 - 1931 (Early mortality = 194)

h

d!-S8

5' 0.01- 0.01 -

..

0.001 20 30

I

40 I

50

Age

I

60 I

70 I

80 I

20 0.001 I

30 I

40 I

50

Age

I

60 I

70 I

80

Figure 5. Observed (......) and estimated (-) probabilities of death (q,) by age for selected male cohorts.

A D U L T M O R T A L I T Y I N I T A L Y

1882 (Early mortality = 406)

0.1- 1896 (Early mortality = 325) ,/

0.1- lg21 (Early mortality = 215)

./*

-8- /:

0.01 - .f '. 0.01-

s" -..-,.. :?#" / ,.**

/

.&.../" l*..

'.* 0.001- 0.001-

I I I I I 1 I I I 1 I I

20 30 40 50 60 70 80 20 30 40 50 60 70 80

- 1903 0.1- 1931 (Early mortality = 320) (Early mortality = 176)

./

- 0.01 -

..&...J."' ... /

- 0.001- ../*. I I I I I I I I c

20 30 40 50 60 70 80 20 30 40 50 60 70 80

Age Age

Figure 6. Observed (......) and estimated (-) probabilities of death (9,) by age for selected female cohorts.

G R A Z I E L L A CASELLI A N D R I C C A R D O C A P O C A C C I A

Estimated probabilities

1882 -1896 --

-1 1903 -.-\-/ 1918 .......a.

1921 -1931---

Figure 7. Estimated and hypothetical death probabilities (q,) for selected male cohorts.

0.1 - Estimated probabilities 0.1 - Hypothetical probabilities (actual early mortality) (equal early mortality)

(15% = 0.2824)

-& w q 0.01 -X

1882 -1896 -- 1896 --1903 -.- 1903 -.-1918 ......... 1918 .........

/

0.001 - L-0 /

1921 - 0.001 - 1921 -1931 --- 1931 ---

I I I I I I I I ! I I I

20 30 40 50 60 70 80 20 30 40 50 60 70 80

Age Age

Figure 8. Estimated and hypothetical death probabilities (qZ)for selected female cohorts.

mortality experience of the various cohorts. As illustrated in Figures 5 and 6, the fit is quite good: the estimated values reproduce the mortality of all the cohorts well, with some exceptions for the male birth cohorts of 1903 and 1918 and the female cohort of 1918. For the latter, the differences relate mainly to ages up to 35.

Figures 7 and 8 present the results of both estimated and hypothetical probabilities. The latter represent the theoretical mortality experience of the various cohorts, in the case where all are subject to the same already mentioned arbitrary level of mortality during the first 15 years. It is clear that the oldest cohorts, favoured in this case by a lower theoretical level of early mortality, will show hypothetical mortality rates between ages 25 and 45 that are lower than the actual ones, in contrast to the more recent cohorts for which the opposite will be true. As predicted in the model, the age-cohort interaction effects are reversed after age 45, but are then smaller.

Concerning ages 25-45, it is interesting to note the changes in the curve, especially for the male cohorts whose members were born in 1918, 1921, and 1931. Their levels of

151 A D U L T M O R T A L I T Y I N I T A L Y

mortality, so far apart in actuality up to age 45, are almost identical when early mortality is set equal for each cohort. The difference between this hypothetical and the actual mortality experience clearly shows the high price paid, for example, by the 1918 cohort born during the World War I and by the epidemic of Spanish influenza, since the hardships experienced by its members during their early years heavily affected their future health. For the same reasons, members of the 1903 cohort were also strongly affected. Members of this cohort were in their adolescence during the First World War.

The hypothetical curves for women in this same age group differ more. This confirms that period effects for women were more important than for men. In fact, in contrast to Figure 7, the curves in Figure 8 show that for the most recent female cohorts (those of 1921 and 1931), the advantage over earlier cohorts persists even if early mortality were assumed to be the same.

Between ages of 46 and 79, the observed mortality of men (except for the cohort 1882) is very similar for cohorts born a quarter-century apart (even the trend for the 1931 cohort is nearly the same). The situation is much the same for the hypothetical probabilities. The only cohorts which benefit in this case, and then only slightly, are the younger ones. It is, therefore, interesting to ask why the level of mortality in the oldest and the youngest male cohorts is more or less the same. There could be many explanations for this. For instance, it could be the case, as is suggested by a comparison of the hypothetical curves, that the low mortality at ages above 45 in the oldest cohorts was caused by their weakest members being lost through highly selective mortality in childhood and early adult life. By the same argument, the mortality of the younger cohorts could have been raised, because of their more favourable early mortality, which has resulted in a larger number of intrinsically weak survivors.

However, this explanation is questionable, particularly when we consider the differences between the observed and the hypothetical probabilities for the two sexes. Mortality of the more recent male cohorts, considered independently from forces of selection, has declined little. This must be looked at in the context of their habits and conditions of life between the ages of 15 and 45. Members of cohorts born between approximately 1920 and 1930 took part in World War 11 and were responsible for the economic reconstruction after the war. They were also exposed to the harmful effects of industrial development, without strict safeguards for health, and the incidence of smoking among them was higher than among women.

The observed and hypothetical probabilities of dying after age 45 for women are clearly lower in the more recent cohorts. Members of even more recent cohorts have beei~ less economically active than men of the same age and, therefore, less likely to have been affected by harmful influences. Their health has also benefited more from the positive aspects of development, including fewer pregnancies and births.

It is obvious that these considerations, even though they refer to the Italian situation, are based on hypotheses to be checked. However, our model retains as a cohort factor the experience of only one particular age group (the most suitable proved to be 0-14 years) and this is, in itself, rather limiting. A more realistic model would assume that mortality at each age is influenced by the events that occurred at all preceding ages.

5. C O N C L U S I O N S

In this paper we have analysed particular aspects of adult mortality in Italy. We have shown the contribution which can be made by studies which take cohort mortality into consideration, and have outlined some of the characteristics of the method.

152 G R A Z I E L L A C A S E L L I A N D R I C C A R D O C A P O C A C C I A

In Section 2 of the paper, the logistic age-period-cohort model was applied to cohort life tables for ages 25 to 79 and cohorts born between 1882 and 1953. This model made it possible to express the mortality of different ages, periods, and cohorts in terms of odds-ratios, and hence to interpret the evolution of the relative levels of mortality across these three components.

In analyzing the results of this model, the existence of a similar age-profile of mortality for both cohorts and periods was apparent, as was a difference in the age-profile for the two sexes. The odds-ratios for the different periods brought out clearly the excess mortality at the time of the two world wars as well as for the 15 years following the first conflict. An examination of the cohort factors showed, moreover, the higher levels of mortality for cohorts born between 1882 and 1900, and additionally for those born during the First World War.

In Sections 3 and 4, the relationships between cohort and early mortality were analysed. The age-period-early mortality model thus developed was employed, first, to help to interpret the results of the APC model and, secondly, to estimate the link between adult mortality and the experiences in infancy and adolescence by examining the level of early mortality. In the former case, the comparison of the results of the APC and the APEM models made it possible to stress the principal defect of the former model, that it does not allow for age-cohort interactions in considering changes in mortality; the APEM model confirmed the role of cohort component in the evolution of adult mortality and underlined an association between the probabilities of dying between ages 25 and 79 and those during the first 15 years of life.

For both sexes, higher mortality early in life is associated with higher mortality up to age 45 and lower levels at later ages. This association made it possible to evaluate the effects of changes in the levels of debilitation and selection during the first years of life on the evolution of adult mortality. The analysis of mortality differences between the birth cohorts of 1882, 1897, 1903, 1918, 1921, and 1931, stressed the importance of this association.

For males it becomes evident, on the one hand, that the mortality differences between older and the more recent cohorts between ages 25 and 45 are closely linked to the differences in vulnerability acquired on early life. The absence of differences among the various cohorts after age 45, on the other hand, may also in part be explained by the levels of early mortality.

For females mortality differences between the cohorts are very marked up to age 45. In addition to the advantage associated with a decrease in early debilitation, the decline in the mortality of adult women also appears to have been linked to the benefits accrued to the youngest cohorts during their fertile ages. In contrast to men, the differences between cohorts remain apparent after age 45.

It is clear that the characteristics of adult mortality are only partially explained by the results of the APEM model. Our speculations provide only incomplete answers to the questions raised. We managed, nevertheless, to bring out the influence of factors which affect the health of cohorts at an early age and which still manifest themselves in observed probabilities of dying in later years.

A significant limitation may have been that our hypotheses did not consider the totality of the debilitating factors operating from age 15 onwards. For example, the smaller advantages of men, compared to those of women and the relative advantages enjoyed by the more recent female cohorts over older cohorts could be related to different experiences in early adult life or in middle age.

In particular, for men born between 1920 and 1930, mortality at ages above 45 could be linked to the debilitating influence of World War 11, to the adverse influence of

153 A D U L T M O R T A L I T Y I N I T A L Y

industrial work, and to the stresses of changing life-styles. For women, the lower mortality at post-reproductive ages for the younger cohorts could be associated with lower fertility and the benefits of improved maternal health care.

In conclusion, the combined results for men and women suggest the need for further research taking into account the factors of dkbilitation after age 15 and, in particular, during the active and reproductive years. Such research could also provide a better understanding of the mortality differentials between the two sexes.

Additionally, it would be interesting to measure the association between early mortality and young adult mortality (ages 15 to 24) in men, which has not been considered in this paper. This would allow a better understanding of the causes of the peak in mortality in this age range, observed already at the end of the last century when accidents were not yet a dominant cause of death for this group.