Keywords

1 Introduction

The period 1961–2013 is characterized by enormous developments in the economic, political and social characteristics of Greece. After the political instability in the 1960s and the dictatorship of the Colonels (1967–1974), the country progressively underwent a rapid democratization process; thus the progressive political stability and the social and economic growth which occurred caused the rapid modernization of Greece. During that course, the country rejoined NATO and became a full member of the European Union at the beginning of the 1980s. In 2001 the Euro was adopted as a national currency and the country organized the Olympic Games in 2004. However, after 2008 a vast economic crisis afflicted Greece and all the socioeconomic indicators were burdened. Several austerity programs and cuts of the social and health expenses as well as the downgrading of personal income and the GDP of the country, left their clear marks on everyday life (see also Clogg 2002, pp. 166–238 and Eurostat http://ec.europa.eu/eurostat/data/database).

The scope of this paper is to analyze the health trends of the Greek population, separately for each gender during that period. The main question which arises deals with the method which is suitable for that reason.

Of the several methods which have been proposed in the literature the most well-known is that of the World Health Organization. In this method, the results of the Global Burden of Disease Study are combined with mortality data (see Murray et al. 2012, 2015) in order to calculate the number of years lost because of disability and consequently the healthy life expectancy (see Vos et al. 2012; WHO 2013, 2014). However, several limitations emanate from this method, among them its extremely high complexity. Others are related to the lack of reliable data on mortality and morbidity for several countries and the lack of comparability of self-reported data from health interviews, which are included in the Global Burden of Disease Study (see also Das and Smarasekera 2013).

Besides this method, Jansen and Skiadas (1995) applied the general theory of dynamic models to life table data in order to evaluate human health. This kind of process is defined by a parent stochastic process, which is the human health being unpredictable, and a boundary, denoted by death (for the first exit time theory see also Ting Lee and Whitmore 2006). Death comes when the human health falls below that boundary. Based on that notion Skiadas and Skiadas (2010, 2012, 2014) and Skiadas (2012a, b) were able to calculate the human health function and based on that, to calculate the years lost either because of severe or because of severe and moderate disabilities using only life table data. The relevant life expectancies were calculated as the difference of life expectancy at birth with the years lost because of the afore mentioned diseases. This method is based on less demanding data than the previous one, though a shortcoming maybe the complexity of the calculations. For that Skiadas has created an EXCEL sheet in order to facilitate the calculations (see http://www.cmsim.net/id31.html).

However, a more parsimonious and less demanding solution was developed quite recently which is based on the force of mortality (Skiadas and Zafeiris 2015). The aim of the method is to express the health state of the population with one main parameter. Thus, a model was proposed containing two parameters with one crucial health parameter and with similar properties of the Gompertz. This model was tested for several European countries against the two previous methods and gave very good results (see Zafeiris and Skiadas 2015), and because of that it will be used in this paper using the mortality data of Greece (1961–2013). If μ x is the force of mortality in age x, then it comes that:

$$ {\mu}_x={\left(\frac{x}{T}\right)}^b $$
(6.1)

where T is the age at which μ x  = 1 and b is a parameter expressing the curvature of μ x .

The main task is to calculate the healthy life years as a fraction of surfaces in a mortality diagram (see Fig. 6.1). This idea, which originates from the First Exit Time Theory and the Health State Function approach, is to estimate the area E x under the curve OCABO:

$$ {E}_x={\int}_0^T{\left(\frac{x}{T}\right)}^b{d}_x=\frac{T}{\left(b+1\right)}{\left(\frac{x}{T}\right)}^b $$

where d x represents the life table’s death distribution. The resulting value for E x in the interval [0, T] is given by:

$$ {E}_{mortality}=\frac{T}{\left(b+1\right)} $$
Fig. 6.1
figure 1

The mortality diagram used in the μ x based method. \( {\mu}_x^{\ast } \) values correspond to the fitted ones of μ x according to formula (6.1)

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It is also clear that the total area E total for the healthy and mortality part of the life is the area included into the rectangle of length T and height 1, thus E Total  = T. Then, the healthy area is given by:

$$ {E}_{healthy}=T-{E}_{mortality}=T-\frac{T}{\left(b+1\right)}=\frac{bT}{\left(b+1\right)} $$

Obviously:

$$ \frac{E_{health}}{E_{mortality}}=b $$

and

$$ \frac{E_{total}}{E_{mortality}}=b+1 $$

These two indicators can describe the health status of the population, the second one being compatible with the severe and moderate causes indicator of the health state approach and thus it can be used as an estimator of the loss of healthy life years (LHLY) in the form of:

$$ LHLY=\lambda\ \left(b+1\right) $$

where λ is a correction multiplier, which for multiple comparisons can be set to be one year. In that way similar results with the World Health Organization approach are found.

2 Data and Methods

Data come from the Human Mortality Database (www.mortality.org) for the years 1981–2013. Before 1981, they come from the Eurostat database (http://ec.europa.eu/eurostat/data/database), because the Human Mortality Database has not uploaded any data due to quality reasons (see also Agorastakis et al. 2015). In any case, mortality data of the Greek population become of lower quality towards the past; nevertheless, it should be used in order to examine any long or short term trends. For that reason the Life Tables of males and females were used for the years 1961–1980. However, because the open-ended open interval of the published Life Tables is the 85+ μ x values were extrapolated until the age of 110 years by applying a cubic spline to the ages 70–84 of the form (see also http://mathworld.wolfram.com/CubicSpline.html):

$$ {\widehat{q}}_i={q}_x+a\left({x}_i-x\right)+b{\left({x}_i-x\right)}^2+c{\left({x}_i-x\right)}^3 $$

where x = 70 and x i is each age until the 84th year of human life.

Afterwards, the μx based method as described in the previous session was applied. All the calculations were carried out in an EXCEL sheet.

3 Results

The results of the analysis indicate that a continuous and rather linear increase of life expectancy at birth is observed in both genders between 1961 and 2014 (Fig. 6.2).

Fig. 6.2
figure 2

Life expectancy at birth (LE) and healthy life expectancy (HLE). Greece 1961–2013

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The healthy life expectancy (HLE) increases too, though the fluctuations which are observed before 1981 must be mainly attributed to the quality of data, especially for the older ages. In any case, females live longer and healthier lives than males; however, for the last years of the study any improvements are halted. This could be attributed to the effects of the economic crisis, though it must be stressed that longer times series are needed in order for any effects to be accurately found and evaluated.

Additionally, the gap of both life expectancy and healthy life expectancy is, with one exception, positive, which means that the relevant values are higher in females (Fig. 6.3). These gaps, despite the large fluctuations observed mainly in HLE until 1981, which have been discussed in the previous paragraph, tend to increase until the onset of the economic crisis. Later on, in both indicators the among the two genders differences tend to become lower. Of course, the gap of life expectancy is always higher than the gap of healthy life expectancy.

Fig. 6.3
figure 3

The between the two genders gap (females-males) in life expectancy at birth (LE) and healthy life expectancy (HLE). Greece 1961–2013

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Another important finding is seen in the scatter plots of Fig. 6.4. If the period 1961–1980, where several outliers are observed because of the quality of data is omitted, it seems that as life expectancy increases the loss of healthy life years increases too. It is quite obvious then that as long as mortality transition goes on and the longevity of the people becomes higher, the number of years in which these people live in burdened health increases too, a fact which must be taken into consideration in the planning of social and pension systems in the country. It must also be taken into consideration that the relationship between healthy life expectancy and life expectancy at birth is not necessarily linear as is seen in Fig. 6.5, especially in males. In female, after 1981 a more linear trend occurs.

Fig. 6.4
figure 4

The lost healthy life years (LHLY) and the life expectancy at birth (LE). Greece 1961–2013

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Fig. 6.5
figure 5

The healthy life expectancy (HLE) and the life expectancy at birth (LE). Greece 1961–2013

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Another, but still open question, is if these results are in accordance with analogous results of other approaches. In Table 6.1 the findings of Murray et al. (2015) concerning Greece are cited in comparison to the results of the analysis undertaken in this paper.

Table 6.1 The healthy life expectancy at birth according to Murray et al. (2015) and to the method used in this paper
Full size table

A first observation concerning Murray et al. (2015) analysis is that the published confidence intervals are high concerning the healthy life expectancy (HALE), about 5 years for males and 6 years for females, a fact which indicates the existing high degree of uncertainty. The results of the analysis cited in this paper are within the confidence intervals of Murray et al. (2015), especially the upper one in males while in females they overtook them slightly. However, the temporal trends of healthy life expectancy indentified by the two methods are almost identical. In males, according to Murray et al. (2015) HALE increases between 1990 and 2005 by 1.48 years and 1.1 years between 2005 and 2013. HLE, according to the method used in this paper increased by 1.38 and 1.77 years respectively. In females the analogous figures are +1.8 and +0.53 years according to Murray et al. (2015) and +1.88 and +0.77 years according to the method used in this paper. It seems then that the two methods are in accordance with each other in describing the temporal trends of the healthy life expectancy. The differences they have for each year of study, seem to be acceptable giving the high degree of uncertainty of Murray et al. (2015) method.

4 Conclusions

The findings of the study can be summarized as follows:

  • The loss of healthy life years (LHLY) is always higher for females than for males thus compensating for the extra years for females measured in life expectancy. As we live longer the healthy life years lost are increasing: along with expanding the life span we have to find ways to reduce the number of the healthy life years lost. Also, the simple measures of the social security systems based on the life expectancy should be improved taking the LHLY into serious consideration in the related plans and programs.

  • The healthy life expectancy (HLE) is also higher for females than for males and in general in increasing order except for the last years in females. The gap of life expectancy at birth between the two sexes is larger than the gap for the healthy life expectancy.

  • It is a challenge for health systems to adapt their support to the growing segment of society which lives above the HLE age.

  • By comparing the method of WHO as cited by Murray et al. (2015) with the one cited in this paper similar results are found concerning the temporal trends of healthy life expectancy.

  • The method cited here is easier to apply as it is based only on mortality data, thus it can serve positively in the understanding of past and contemporary trends of the health level of a population and in fact in the evaluation of its demographic and epidemiological transition.