CC BY
51
UDC 314.48
B. A. Korobitsyn, A. A. Kuklin, I. L. Manzhurov, N. L. Nikulina
ASSESSMENT OF DAMAGE FROM REDUCTiON OF EXPECTED LiFESPAN DUE TO CANCER
This paper presents the theoretical and methodological approaches to the assessment of damage from premature mortality and reduction of life expectancy due to various reasons. The concepts measuring the price of a human life are analyzed: the evaluation from the standpoint of the theory of human capital; indirect estimation taking into account non-monetary social costs; evaluation of individuals' willingness to pay for the elimination of the risk of death; estimation based on the determination of insurance premiums and compensations under court decision; evaluation of the social investments, aimed to reduce the risk of premature mortality of the individual. The following indexes were calculated for all subordinate entities of the Russian Federation: reduction of life expectancy, lost years of potential life in the working age, and gross regional product lost due to the reduction of years of potential life in the working-age population as a result of cancer.
Keywords: economic evaluation of a human life, damage from premature mortality, life expectancy, lost years of potential life
A high death rate is one of the most difficult medical and demographic problems of the social development in modern Russia. One of the aspects of this problem is a high level of premature mortality in the working age. To improve the effectiveness of the risk management for the life of the population instruments of the economic analysis of the premature mortality consequences are necessary. That's why many attempts are taken to estimate the value of a human life or the damage from the early death due to various reasons.
General probability-theoretical basis for the assessment of the death risk
In accordance with established terminology, death risk from a negative factor is a death probability as a result of exposure to such factors. An age-specific death rate m(a) is a basic health and demographic index used for assessing the death risk. It is defined as the probability density of death at the age of a, on condition of surviving up to this age. The classical definition of theoretical probability is given as follows:
p,(a) = lim Pr(x | y) / Aa.
Aa-»0
x — a man died in the interval (a, a + Aa), y — a man lived up to age a, Pr (x | y) — is a probability of event x under condition y.
Survivorship function P(a) is defined as the unconditional probability of leaving up from birth to the age of a. If N0 — is a number of people who were born, and N(a) — is the same number of people surviving to age a, then
1 tflV(fl).
H(a) = -
N(a) da
(1)
P(a) = N4
JV
These equations show that
P(a)—exp
a
-f Ka)da
(2)
(3)
Let us set P(e, a) as a conditional probability for the person at the age e to survive till the age a
P(e,a) = P(a)/ P(e).
(4)
Full (from birth) life expectancy Q(0) can be calculated as
oo
6(0) = f P(a)da.
(5)
Life expectancy for a man at the age of e is calculated similarly:
&(e) = fP(e,a)da.
(6)
The lifelong death risk Ri(e) for a man at the age of e is defined as a probability to die from the i source of risk throughout the expected lifetime
oo
Ri(e) = fP(e,ay(a)da. (7)
e
The condition of normalization is feasible
£>!(e) = 1. (8)
i
The intensity of the death risk from the i source of risk ri(e, a) for a man at the age of e
г'(е,а) = Р(е,аУ(а).
(9)
In practice, the mortality rates are usually calculated separately for each age group. In this case,
the formulas (1-9) are converted to the discrete form.
If is a probability to die during the j year of life, on condition to survive up to this age, i. e. | — is a probability of dying from the date of birth to exact age of 1 year, and m70 — is probability of dying from the exact age of 69 till the exact age 70.
Then the probability of survival from birth to the moment of reaching the exact age a P 0a = Pa equals
P0,a= fla-Mv)- (10)
/=1
Pea is a probability of surviving till the age a for a man, who reached the age of e, is calculated similarly to the formula (4):
Pe,a=Pa/Pe- (11)
Full (from birth) life expectancy equals to Q0:
k=oo i=k
0o = Ell(1-^)- (12) k=1 ;'=1
For a man, who reached the age of e, life expectancy Qe is calculated as
k=co i=k
0e=ErK1-^)- (13)
k=e+1 j=e+1
Full (from birth) the lifetime death risk from the i source of risk Rj equals
k=co i=k-l
K = ^k n fl-Mv). (14)
k=l /=0
Where m0 = 0.
R' — the lifetime death risk from the i source
e
of risk for a man, who reached the age of e, equals
k=oo ;=fc—1
(15)
/c=e+l j=e
If a man survived till the age of e, the probability of dying from all causes during the age interval from e to a equals R
e,a
k=a j=k-l
Ka = Х>*П fl-M"
lc=e+l j=e
(16)
k—oc )=k k-oc j=k
AB-' =©-'-©„ = En(1-h!)-Eri(1-^). (18) k=1 ;'=1 k=l j=1
Where is a full (from birth) life expectancy under eliminating the i cause of death, p,T' — the probability of dying during the j year of life, on condition of survival up to this age under eliminating the i cause of death.
While calculating assessments of the impact of the different death causes on life expectancy for the population of the subordinate entities of the Russian Federation a problem arises. The scientists have to face the lack of published statistical reports on age-specific mortality in the regions. In this case, as a first approximation we can assume that
vT
MReg
M
SF '
(19)
Where MReg and MRF are standardized death rates for the population of the region under examination and for the Russian Federation. Similarly, a quantity |xT'. can be estimated. These standardized indexes are regularly published in the cancer and demographic statistics digests.
To characterize the mortality at the population level, the index «lost years of potential life» — PYLL (potential years of life lost) is used. It is a number of years, which were not lived by a population up to the normative age, usually 70. It is assumed that each individual can live for 70 years. It is called a «productive» life and therefore death at the age of a results in a loss of 70 — a, if a < 70. It is assumed that all deaths occur in the middle of the age interval (including usage of 5-year intervals). A so-called unlived years are calculated for each age interval X:
X. = T - a,, (20)
Where T — is an upper age limit (usually 70 years), a — is a middle of the proper age interval. Years of potential life lost are calculated as the sum of productions of the total number of dead in each age group for the years they unlived
R'e a the death risk from the i source of the risk during the arbitrary age interval from e to a, on a condition that a man, survived till the age of e, is calculated similarly
Ka= S^'ffa-M- (17)
k=e+1 j=e
To assess the impact of specific causes of death on life expectancy the index of the increase in life expectancy under eliminating the i cause of death is used A©o! :
(21)
Where D, — is a number of people who died during the year in the age group . Similarly, the years of potential life lost because of the i cause of death can be calculated — PYLL.
PYUl =J2D)Xi'
(22)
Where Dj — is a number of people who died in the age group from the i cause during the year. According to this analysis, «weight» of each per-
son, who died from a specific cause, is the number of years unlived by them to a specified age limit, so the «weight» of an older man is smaller than the «weight» of a newborn. Causes of death, which lead to the biggest losses in a man-year, are considered to be a priority. The absolute number of the potential life years lost gives the opportunity to measure the scale of the problems associated with premature mortality of the population.
Similarly, an index of «years of potential life lost in the working-age» PYLLWork can be introduced. In this case the age limit T is assumed to be 60 years for men and 55 — for women. For individuals who died at the age of 16, PYLLWork is calculated according to the formulas similar to (20)-(22). For individuals who died before the age of 16, PYLLWork is assumed to be 44 years for men and 39 years for women.
Table 1
The expected reduction in life expectancy at birth as a result of malignant neoplasms, years
Subject of Federation Sex Subject of Federation Sex
male female male fem.
Belgorod region 2.10 1.88 Republic of Bashkortostan 1.48 1.57
Bryansk region 2.09 1.61 Republic of Mari El 1.75 1.52
Vladimir region 1.99 1.92 Republic of Mordovia 1.99 1.74
Voronezh region 1.87 1.70 Republic of Tatarstan 1.87 1.77
Ivanovo region 1.82 1.83 Udmurt Republic 1.81 1.61
Kaluga region 1.99 1.93 Chuvash Republic 1.62 1.47
Kostroma region 1.75 1.79 Perm Krai 1.77 1.79
Kursk region 2.20 1.78 Kirov region 1.79 1.68
Lipetsk region 1.79 1.51 Nizhny Novgorod region 1.78 1.84
Moscow region 2.09 2.26 Orenburg region 2.10 1.97
Oryol region 2.15 1.79 Penza region 1.97 1.71
Ryazan region 2.08 1.90 Samara region 1.82 1.91
Smolensk region 1.64 1.71 Saratov region 1.78 1.76
Tambov region 2.19 1.78 Ulyanovsk region 2.03 1.81
Tver region 1.74 1.84 Kurgan region 2.20 2.01
Tula region 2.02 1.97 Sverdlovsk region 2.20 2.03
Yaroslavl region 2.09 1.93 The Tyumen region (without Autonomous Area) 1.60 1.69
Moscow city 2.22 2.66 Khanty-Mansi Autonomous Area 2.15 2.11
Republic of Karelia 1.95 1.98 Yamalo-Nenets Autonomous Area 2.27 2.09
Komi Republic 1.91 1.74 Chelyabinsk region 2.18 2.16
Arkhangelsk region 1.98 1.86 Altai Republic 1.78 1.82
Vologda region 1.80 1.68 Republic of Buryatia 1.76 1.90
Kaliningrad region 1.79 1.98 Republic of Tyva 1.31 1.65
Leningrad region 2.01 1.94 Republic of Khakassia 1.90 2.00
Murmansk region 1.90 1.87 Altai Territory 2.19 1.99
Novgorod region 1.60 1.63 Zabaykalsky Krai 1.56 1.90
Pskov region 1.65 1.69 Krasnoyarsk Krai 2.21 2.11
St. Petersburg 2.41 2.81 Irkutsk region 1.80 1.94
Republic of Adygea 2.11 2.10 Kemerovo region 1.82 1.96
Republic of Kalmykia 1.76 1.82 Novosibirsk region 2.30 2.06
Krasnodar Krai 2.13 2.11 Omsk region 2.04 2.01
Astrakhan region 2.00 1.96 Tomsk region 2.39 2.26
Volgograd region 2.05 2.01 Republic of Sakha (Yakutia) 1.52 1.84
Rostov region 1.93 2.04 Kamchatka Krai 1.77 1.92
Republic of Dagestan 1.76 1.63 Primorsky Krai 1.89 2.08
Republic of Ingushetia 1.49 1.40 Khabarovsk Krai 1.83 1.84
Kabardino-Balkar Republic 1.88 1.87 Amur region 1.48 1.60
Karachay-Cherkess Republic 1.97 1.93 Magadan region 1.74 2.08
Republic Northern Ossetia — Alania 1.99 1.84 Sakhalin region 2.01 2.04
Chechen Republic 1.90 1.77 Jewish Autonomous Province 1.61 1.73
Stavropol Krai 1.93 1.89 Chukot Autonomous Area 1.12 1.94
Table 2
The years of potential life lost in the working age due to malignant neoplasms, years
Subject of Federation Sex Sex Sex
male female male female
Belgorod region 4451 2409 Republic of Bashkortostan 9735 5811
Bryansk region 4377 1900 Republic of Mari El 2297 1054
Vladimir region 5131 2672 Republic of Mordovia 2759 1334
Voronezh region 6983 3518 Republic of Tatarstan 10096 5796
Ivanovo region 3356 1846 Udmurt Republic 4494 2308
Kaluga region 3348 1776 Chuvash Republic 3382 1717
Kostroma region 2098 1137 Perm Krai 8150 4581
Kursk region 4104 1843 Kirov region 4195 2064
Lipetsk region 3567 1649 Nizhny Novgorod region 10333 5804
Moscow region 24290 14948 Orenburg region 6969 3704
Oryol region 2698 1269 Penza region 4228 2079
Ryazan region 3904 1945 Samara region 9724 5804
Smolensk region 3103 1673 Saratov region 7097 4052
Tambov region 3878 1710 Ulyanovsk region 4406 2199
Tver region 4519 2441 Kurgan region 3201 1617
Tula region 5366 2820 Sverdlovsk region 14064 7741
Yaroslavl region 4126 2213 The Tyumen region (without Autonomous Area) 9025 5554
Moscow city 28684 23411 Khanty-Mansi Autonomous Area 5366 3145
Republic of Karelia 2277 1251 Yamalo-Nenets Autonomous Area 1707 1015
Komi Republic 3341 1629 Chelyabinsk region 11366 6681
Arkhangelsk region 4393 2209 Altai Republic 667 374
Vologda region 4000 1964 Republic of Buryatia 3099 1821
Kaliningrad region 2750 1684 Republic of Tyva 884 625
Leningrad region 5934 3062 Republic of Khakassia 1718 1014
Murmansk region 2857 1499 Altai Krai 8446 4330
Novgorod region 2042 1053 Zabaykalsky Krai 3465 2140
Pskov region 2304 1145 Krasnoyarsk Krai 10397 5683
St. Petersburg 14419 11149 Irkutsk region 7769 4621
Republic of Adygea 1287 767 Kemerovo region 9255 5362
Republic of Kalmykia 875 491 Novosibirsk region 9135 4802
Krasnodar Krai 14927 9086 Omsk region 6399 3661
Astrakhan region 3281 1801 Tomsk region 3889 2138
Volgograd region 7752 4454 Republic of Sakha (Yakutia) 2669 1741
Rostov region 12114 7513 Kamchatka Krai 1238 641
Republic of Dagestan 4975 3537 Primorsky Krai 6708 3857
Republic of Ingushetia 387 366 Khabarovsk Krai 4556 2441
Kabardino-Balkar Republic 1849 1292 Amur region 2643 1417
Karachay-Cherkess Republic 1159 774 Magadan region 644 355
Republic of North Ossetia — Alania 1523 1008 Sakhalin region 2196 1067
Chechen Republic 2439 1645 Jewish Autonomous Province 597 319
Stavropol Krai 7063 4305 Chukotka Autonomous Area 240 149
Table 1 shows results of calculation of the expected reduction in life expectancy at birth as a result of malignant neoplasms (as on 2010). Calculations were executed by formula (19) using the statistics [3].
Table 2 shows results of calculation of years of potential life lost in the working age due to malignant neoplasms (as on 2010). Calculations were executed formulas (20) and (22) using a statistics [3].
Damage from mortality due to malignant neoplasms
In order to assess the damage from mortality due to malignant neoplasms it is necessary to get a monetary evaluation of a human life or years of the potential years of life lost.
The problem of the monetary expression of the price of a human life is extremely difficult. Many philosophical and ethical doctrines are based
on the principle that «human life is priceless», thereby eliminating any possibility to discuss this matter. However, in a market economy, it is a very pressing problem.
Analysis of the literature allows us to say that the following concepts, measuring the price of a human life were formed [1, 6]:
— evaluation from the standpoint of the theory of human capital;
— indirect estimation taking into account non-monetary social costs;
— evaluation of individuals' willingness to pay for the elimination of the death risk;
— estimation based on the determination of insurance premiums and compensations under court decision;
— evaluation of the social investments, aimed to reduce the risk of premature mortality of the individual.
Evaluation according to the theory of human capital is based on the assumption that the utility of the individual to society depends primarily on his productivity, because in the theory of human capital, every individual is considered from the point of view of his ability to participate in social production and to earn money at the same time. A life loss, according to this theory, leads to a decrease in the productive capacity of society. A total salary of an individual couldn't earn due to premature death is proposed to be a measure of value of a human live [2, 4, 5]. But this concept has several serious disadvantages. The theory of human capital has a discrimination against employee's age. This concept gives more weight to an accident at work that caused death of a young worker, than to incurable occupational disease of an older one.
Secondly, the approach under consideration creates unequal conditions for individuals who receive different payment for their work, which leads to an underestimation of the poor segments of society. Thirdly, it is unclear how to evaluate the life of individuals who are not involved in the process of production, for example receive a pension or live on welfare. One of the variant of this approach is the estimation of human life on the basis of the gross domestic product, per capita, this method is characterized by similar shortcoming to those listed above.
Indirect estimation taking into account non-monetary social costs is based on the analysis of the political decisions aimed at reducing the number of fatal accidents and the following comparison of the achieved effect with the society's costs and received damage. A good illustration of the practical use of this concept is the history and consequences of enacting of the speed limits in the
U.S. after an embargo on oil exports to the United States, established by a number of Arab countries in 1973. [3] This concept does not require neither information on the salary of individuals, nor data about themselves (for example, their age doesn't matter), and thus it is free from a number of shortcomings listed above. It can be used in cases related to the actual number of deaths, which have already occurred. It can help to make decisions about voluntary risk-taking or, conversely, to prevent it. The possibilities of indirect estimation attracted attention of the scientists, but it didn't receive practical application so far. The probable reason for that is the fact that the indirect estimate of the preservation of life does not always coincide with the assets established by the direct estimation. A discrepancy can be big.
Evaluation of individuals' willingness to pay for the elimination of the death risk, based on public opinion polls. Respondents were asked about the sum of money they were willing to pay for elimination of the death risk, caused by participation in a particular hazardous activity. The main drawback of this method is that a perception of individual risk is subjective and inadequate. Specifics of the risk perception by individuals and by social groups, is the subject of numerous psychological and socio-psychological researches. The main factors that influence the process of risk perception and the mechanisms, controlling it are revealed. A nature of risk, the form of its display, a degree of awareness (ignorance) about it, the ability to understand, the significance of the positive effects associated with the risk, media coverage, the degree of controllability, voluntary assumption, reversibility (irreversibility), the impact on children and future generations, etc., are among these factors. It is known that people tend to underestimate the risk they take voluntarily; voluntary risks include the usage of a car, smoking, extreme sports such as mountain climbing, etc. Another psychological effect is the high probability of underestimation of the risk, caused by hazardous events and overestimation of highly unlikely events. That's why people tend to underestimate the death risk of a car accident and at the same time, fear to fly by planes, even though the probabilities vary greatly. Thus, the subjective underestimation (overestimation) of the death risk leads to an underestimation (overestimation) of the life value. The concept of the individuals' willingness to pay for the elimination of the death risk can't be considered as correct, due to inadequate risk perception.
Estimation based on the determination of insurance premiums and compensations for the rel-
Table 3
Short-received Gross Regional Product because of the years of potential life lost in the working age due to malignant neoplasms, million rub. and % out of available Gross Regional Product
Subject of Federation GRP reduction % out of GRP Subject of Federation GRP reduction % out of GRP
Belgorod region 2916 0.73 Republic of Bashkortostan 4693 0.62
Bryansk region 1173 0.81 Republic of Mari El 631 0.77
Vladimir region 1975 0.90 Republic of Mordovia 823 0.79
Voronezh region 2458 0.75 Republic of Tatarstan 6811 0.68
Ivanovo region 804 0.82 Udmurt Republic 1909 0.72
Kaluga region 1540 0.83 Chuvash Republic 1001 0.66
Kostroma region 746 0.81 Perm Krai 4999 0.79
Kursk region 1703 0.89 Kirov region 1283 0.77
Lipetsk region 1882 0.74 Nizhny Novgorod Region 5203 0.80
Moscow region 16012 0.89 Orenburg region 3897 0.86
Oryol region 865 0.84 Penza region 1197 0.76
Ryazan region 1487 0.86 Samara region 5438 0.78
Smolensk region 1176 0.79 Saratov region 2701 0.73
Tambov region 1196 0.86 Ulyanovsk region 1451 0.83
Tver region 1901 0.87 Kurgan region 1034 0.90
Tula region 2112 0.89 Sverdlovsk region 8587 0.93
Yaroslavl region 1972 0.84 The Tyumen region (without Autonomous Area) 3497 0.64
Moscow city 59928 0.71 Khanty-Mansi Autonomous Area 15900 0.80
Republic of Karelia 1144 0.90 Yamalo-Nenets Autonomous Area 5727 0.74
Komi Republic 3005 0.85 Chelyabinsk region 5512 0.85
Arkhangelsk region 3002 0.84 Altai Republic 182 0.84
Vologda region 2048 0.81 Republic of Buryatia 1112 0.82
Kaliningrad region 1469 0.75 Republic of Tyva 251 0.82
Leningrad region 4266 0.85 Republic of Khakassia 779 0.83
Murmansk region 1963 0.84 Altai territory 2605 0.87
Novgorod region 1050 0.83 Zabaykalsky Krai 1318 0.81
Pskov region 729 0.86 Krasnoyarsk Krai 9463 0.90
St. Petersburg 14050 0.84 Irkutsk region 4474 0.83
Republic of Adygea 366 0.79 Kemerovo region 5382 0.86
Republic of Kalmykia 181 0.74 Novosibirsk region 4037 0.84
Krasnodar Krai 7748 0.77 Omsk region 3019 0.81
Astrakhan region 1188 0.82 Tomsk region 2571 0.90
Volgograd region 3383 0.77 Republic of Sakha (Yakutia) 2768 0.72
Rostov region 4771 0.75 Kamchatka Krai 905 0.89
Republic of Dagestan 1341 0.47 Primorsky Krai 3974 0.86
Republic of Ingushetia 66 0.31 Khabarovsk Krai 2873 0.82
Kabardino-Balkar Republic 442 0.58 Amur region 1407 0.78
Karachay-Cherkess Republic 285 0.66 Magadan region 557 0.96
Republic of North Ossetia — Alania 446 0.60 Sakhalin region 5068 1.03
Chechen Republic 387 0.56 Jewish Autonomous Province 272 0.83
Stavropol Krai 2112 0.67 Chukotka Autonomous Area 481 1.15
atives proceeding from common insurance practice, assuming that the life insurance is connected with two main factors — the value of the client's life from his own point of view and the probability of a life loss due to any activity. The weak points of this approach are as following reasons. First of all, the insurance premium, no matter how
big it is, can't reduce the death risk (as shown below, this reduction takes place in the concept of life assessment based on investments aimed at reducing the risk of premature death). Secondly, a client of the insurance company does not protect his own life, he acts in favor of the family members or other dear people. Civil suit in the courts
about premature death, and insurance activities, can't reduce the probability of fatal accidents. And the compensational payments by the court are going to the victim's family. In addition, such claims are often based on the theory of human capital, they are enacted for the recovery of the total payroll lost, due to premature death. Therefore, these assessments have the same shortcomings as the concept of the human capital.
The concept of evaluation, based on the social investments, aimed to reduce the risk of premature mortality of the individual, gives an assessment to a so-called statistical life. A statistical life is considered to be saved, if the risk for the whole society was reduced so much that unidentifiable individual escaped death. Reduction of the death risk is connected with certain steps for decrease of threats (for example, universal vaccination). Such steps have a precise monetary value, which makes
the estimation procedure easier. However, despite the remarkable progress in the development of the concept of life assessment, based on evaluation of the social investments, aimed to reduce the risk of premature mortality of the individual, it is still far from being perfect.
In this research we used index of reduction of the gross regional product due to the loss of potential life years in the working-age population because of malignant neoplasms (as on 2010). The results are presented in Table 3.
This analysis shows that none of the formed concepts of human life estimation can serve as an operating tool. All existing concept of life estimation are simplified or incorrect. This is a complex issue and it requires a new study approach. That lives a wide field for the new interdisciplinary researches.
The research was supported by the Ural Branch of the Russian Academy of Sciences, an interdisciplinary project 12-27-M-2053.
References
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Information about the authors
Korobitsyn Boris Alengordovich (Yekaterinburg, Russia) — Ph. D. in Physics and Mathematics, Leading Research Scientist, the Institute of Industrial Ecology, Ural Branch of Russian Academy of Sciences (20 Sophya Kovalevskaya St., Yekaterinburg, 620990, Russia, e-mail: [email protected]).
Kuklin Aleksandr Anatolevich (Yekaterinburg, Russia) — Doctor of Economics, Professor, Head of the Center for Economic Security, Institute of Economics, Ural Branch of Russian Academy of Sciences (29 Moskovskaya Str., Yekaterinburg, 620014, Russia, e-mail: [email protected]).
Manzhurov Igor Leonidovich (Yekaterinburg, Russia) — Ph. D. in Physics and Mathematics, Head of the Laboratory, the Institute of Industrial Ecology, Ural Branch of Russian Academy of Sciences (20 Sophya Kovalevskaya Str., Yekaterinburg, 620990, Russia, e-mail: [email protected]).
Nikulina Natalya Leonidovna (Yekaterinburg, Russia) — Ph. D. in Economics, Acting Head of the Sector, Institute of Economics, Ural Branch of Russian Academy of Sciences (29 Moskovskaya Str., Yekaterinburg, 620014, Russia, e-mail: nikulinanl@ mail.ru).
