Radiol Oncol 2006; 40(2): 115-24. Complete yearly life tables by sex for Slovenia, 1982-2004, and their use in public health Tina Žagar1, Vesna Zadnik1, Maja Pohar2, Maja Primic Žakelj1 1 Epidemiology and Cancer Registries, Institute of Oncology Ljubljana, 2 Institute of Biomedical In-formatics, Faculty of Medicine, Ljubljana, Slovenia Life tables are an important tool in statistical analysis in many branches of science including public health and epidemiology. In Slovenia, they are recently mostly used in relative survival analyses. For this purpose, we need complete period life tables for each calendar year. Since such life tables have not been available for Slovenia, we calculated our own life tables for years in 1982-2004, stratified by sex. In the article we de-scribe the methodology used for calculation and present some examples on the use of these life tables. The complete life tables are freely available by contacting register@onko-i.si or through the international Human Life-Table Database (http://www.lifetable.de/). We intend to produce life tables for following years as so-on the necessary data will be available. Key words: public health; life tables; survival analysis Introduction Life tables are the oldest demographic tool and still among the most important instruments for mortality analysis and other investigations concerning the length of li-fe.1 As suggested by some classical papers, already in Babylonian civilization individu-als understood the idea of likelihood of de-ath assessment.2 First simple life tables we-re composed by the roman perfect Domiti-us Ulpianus in the third century. His techni-Received 25 April 2006 Accepted 30 May 2006 Correspondence to: Tina Žagar, B.Sc., Epidemiology and Cancer Registries, Institute of Oncology Ljubljana, Zaloška 2, SI-1000 Ljubljana, Slovenia. Tel.: +386 1 5879 562; Fax: +386 1 5879 400; E-mail: tzagar@onko-i.si que of life table calculation was in use in the northern Italy till 1814.2 English insurer Milne computed first totally regular life ta-bles for the period 1779-1787.3 In Slovenia this spadework was performed by dr. Ivo Lah who computed the life tables for Drava province for the years 1931-1933.4 After the Second World War, life tables were produ-ced by Yugoslavian and Slovenian statisti-cal office. Today the life tables are used for statistical analysis in numerous branches of science as: demography, insurance, judici-ary, public administration, public health, epidemiology, biology and other.5 Various forms of life tables are known. According to the age groups used they are divided into complete and abridged life ta-bles.6 The first are calculated for one-year age groups, from the age of zero to the last 116 Žagar T et al. / Complete life tables for Slovenia, 1982-2004 defined age. On the contrary, the abbrevia-ted life table combines several years, as they presume the mortality rates in adjacent age groups are similar.7 The second classificati-on is distinguishing between cohort and period life table.6 During the preparation of co-hort life table a selected cohort is followed from its first birth till its last death. The procedure is very time consuming, and on the other hand, such data are rarely available, so cohort life tables are mostly produced for hi-storical purposes. Instead of following one cohort life-long, we model what would happen to a hypothetical cohort if a certain set of mortality conditions pertained througho-ut its life in period life table. There are many additional forms of life tables, as exact and approximate life tables, adjusted and una-djusted life tables or life tables for population and subpopulations (by gender, occupa-tion, social status etc.).6 This paper is focusing on the complete period life tables for the population of the Republic of Slovenia for each year from 1982 to 2004. Currently, the complete period life tables are available for four three-ye-ar periods only: 1980-1982, 1990-1992, 1993-1995 5 and 2000-2002.8 In addition, there are abbreviated life tables (five-year age groups) for all two-year periods betwe-en 1981 and 2001.5,9 All these life tables we-re prepared by the Statistical Office of the Republic of Slovenia (SORS). They combine several years, as the Slovenian population is rather small, hence the probability of dying in certain age group tends to fluctuate. For the same reason SORS’s life tables are adju-sted as well.5 Further on, World Health Or-ganization published the abbreviated gen-der stratified life tables for Slovenia for ye-ars 2000 and 2001 separately.10 In public health, especially for the purpose of relative survival analysis, complete, unadjusted and gender specific life tables for single year are needed. These life tables cannot be used to evaluate the demogra-Radiol Oncol 2006; 40(2): 115-24. phic attributes of Slovenian population, but only to compare a group of patients with their origin population. Therefore the exact probability of dying is required in relative survival analysis. For this purpose the complete, unadjusted and gender speci-fic period life tables for Slovenia for each year in the period 1982-2004 were prepared in our study. The methodology applied is identical for all the tables provided, which makes them intercomparable. Material and methods The data needed for calculating the life ta-bles were obtained from SORS: • aggregated number of deaths by age, sex, year of birth and year of death for deaths in period 1982-2004 and • aggregated number of residents by age and sex at the beginning of each year in period 1982-2004. Information regarding data collection and population definition is published in Statistical Yearbook of the Republic of Slo-venia by SORS.11 Probability of dying (qx) is the basic indi-cator for mortality of population. This is conditional probability for person aged x ye-ars at the beginning of the year to die during the year conditionally on surviving x years in the first place. Probability of dying for age x is calculated as the ratio between the num-ber of people that died during the observed calendar year and were aged x at the begin-ning of the year and the number of all living aged x at the beginning of the same calendar year.7,12 Probability of dying is always one for selected highest age interval, which is hundred years and more in our case. All the other variables in life tables are calculated from the probability of dying. Standard methods and notations were used Žagar T et al. / Complete life tables for Slovenia, 1982-2004 117 that are well known and easily found in literature 2,6,7,13, so they will not be explai-ned here, but listed only. The notations used in life tables are given in brackets after the name of the variable. Probability of surviving (px) is the pro-bability of a person aged x years to survive exact age x+1. The number of persons sur-viving (lx) is the number of persons who re-ach age x out of 100,000 live births. The number of deaths (dx) is the annual num-ber of deaths between ages x and x+1. The number of person–years (Lx) is the number of persons alive at any point in time betwe-en ages x and x+1. The total number of per-son–years (Tx) is the total number of years lived from age x to death. Life expectancy (ex) is the average number of years a person aged x years can expect to live assuming that mortality rates by age will remain un-changed since the year of observation. Life expectancy at birth (e0) is the mean age at death for persons dying in any particular year and is the most important indicator for population mortality.1 Probability of dying, probability of sur-viving, number of persons surviving and number of deaths are frequency (or inten-sity) measures since they show frequencies of events (deaths or survival). They are all defined within elementary age interval [x, x+1). Number of person–years, total num-ber of person–years and life expectancy at birth are duration measures since they show amounts of lifetime and are measu-red in person-years.13 Results The results of our calculations are complete, unadjusted and gender specific period life tables for Slovenia for each calendar year in the period 1982-2004. We calculated life ta-bles separately for men and women, as ge-nerally there is significant difference in mor- tality by sex.7 As an example, there are life tables for men and women for calendar year 2004 in Appendix. The life tables for all ca-lendar years are freely available by contac-ting register@onko-i.si. Since our methodo-logy is consistent with the methodology of Human Life-Table Database13, our life tables are also included in their database available on Internet (http://www.lifetable.de/). We intend to produce life tables for following years as soon as we get the necessary data. When calculating life table, special cauti-on should be given to the age group zero ye-ars. In order to illustrate this problem we take a closer look at the year 2004. As there are no data on the number of residents at the beginning of 2004 available, we use in-stead the number of residents on December 31, 2003, published in the Statistical Yearbo-ok of the Republic of Slovenia 2004.11 Ho-wever, newborns born for example in April 2004 and died in May 2004 are not accoun-ted for in this report and have to be added extra in the denominator when calculating probability of dying for age group zero ye-ars. Data on newborns provided by Institute of Public Health of the Republic of Slovenia (IPH) cannot be applied in life table analysis since IPH has different population definition - only the number of babies born to Slo-venian mothers in the territory of the Repu-blic of Slovenia is reported by IPH. 14 Howe-ver, in the SORS database the number of children aged zero to one year also includes all emigrant newborn babies and those who were born to Slovenian mothers abroad.11 The difference is about 300 (or about two percent) newborn children each year. Demographic data by age, year of birth and year of death are properly presented on Lexis diagram 15. A cut out from Lexis diagram for males in 2004 is presented on Figure 1. We can see that there were 8909 males aged less than one year out of which 30 newborns were born in 2004 and also di-ed in 2004. Additionally, 2 children were Radiol Oncol 2006; 40(2): 115-24. 118 Žagar T et al. / Complete life tables for Slovenia, 1982-2004 2003 20OI Your 2 X 5 Figure 1. Lexis diagram with data on alive and decea-sed for males by age, year of birth and year of death. born in 2003 and died in 2004 still aged ze-ro years. However, 2 children of those born in 2003 had a birthday before their death. From this data we can calculate probability of dying for 2004 for children aged zero ye-ars as q0 = (30+2+2)/8909 = 0.003816. From data on Figure 1 we can also calculate pro-bability of dying for children aged one year as q1 = (0+1)/9134 = 0.000109. For general public, the most interesting function is life expectancy. It is also the most important indicator for population mortality1 and is consequently the population health estimation. On Figure 2, one can observe how life expectancy is impro-ving with time in Slovenia. Moreover, one can observe how the difference between men and women gets smaller with age. Discussion The methodology of life tables computation and their reliability The important advantage of our life tables is the precision of data applied in their cal-culation. In the Republic of Slovenia birth and death certificates are automatically ga-thered in the Government Centre for Infor-matics database in digital form, so comple-te and updated birth and death dates are available for every period.16 Figure 2. Life expectancy in years for selected age groups by sex (M stands for men and W stands for women), Slo-venia 1982-2004. Radiol Oncol 2006; 40(2): 115-24. Žagar T et al. / Complete life tables for Slovenia, 1982-2004 119 It is of special importance to pay attenti-on on population definitions, which are not consistent in Slovenian official statistics over different databases or time periods. By comparing the IPH and SORS population definitions, one of such inconsistencies has already been mentioned regarding new-borns. Moreover, the SORS population definition by itself is inconsistent across dif-ferent time periods. It was changed after the Republic of Slovenia’s independence; since June 30, 1995 population data are re-ported according to the new definition.11 Data quality and complete understan-ding of their definitions are of major impor-tance in all medical investigations. One of the essentials is to assure maximal feasible coherency among medical (patients) and official (population) data. Errors or discor-dances of official data cannot be abolished, however it is possible to adjust the analysis and minimize the possible biases by ap-plying the adequate methodology. The application of life tables in public health From public health point of view life tables are basic tool for population health estimati-on. World Health Organization is preparing life tables for each of its state members and uses them for the major health indicator com-putation (e.g. health life expectancy – HALE). Life tables are indispensable also in most cost-benefit analyses, as the assessment of the effectiveness of screening programmes or some other public health interventions. In addition to above mentioned fundamental public health research, life tables are an essential component in relative survival analysis. The relative survival analysis is not applied frequently in Slovenia. The una-vailability of life tables in a proper format is certainly one of the main reasons for that. Only SORS’s life tables were available until now for calculation of relative survival of cancer patients in Slovenia.17,18 In these analyses the same life tables were used for several years. Data on Slovenian cancer pa-tients are included in the second and in the third European study of cancer patient’s survival EUROCARE.19,20 In the EUROCA-RE project some census data were used for the interpolation of SORS’s abbreviated life tables. Moreover, in the field of relative sur-vival methodology, Slovenian authors re-cently developed a unique statistical appro-ach and illustrated it by the investigation of survival in a myocardial infarction patient cohort.21,22 Life tables are also required in public health studies evaluating years of potential life lost. Such studies gained on its applicability in Slovenia recently.23,24 We believe that annual releases of life tables in applicable format will smooth the way for public health investigations in the future. Cancer survival data provide comprehen-sive and complex measure of cancer burden in the observed population. They reflect the impact of all measures in cancer control programmes, from mass screening to trea-tment, follow-up and rehabilitation of can-cer patients. There are several options and methods of the survival rates calculation. Observed and relative survival rates are the two fundamental forms. The observed sur-vival indicates the actual mortality in a patient group. The causes of death other than cancer may differ from group to group and depend on cancer site, patient’s age, sex, so-cio-economic position and the health care provided. Thus younger patients usually live longer in comparison with older patients with the same cancer or on the contrary sur-vival of patients with certain cancers is short regardless of their age at diagnosis.18 Death notification in Slovenia is preci-sely prescribed. Rule of the coroner’s inqu-ests (Official Gazette of RS, No. 56/93 - 25) strictly defines among other also coroner’s duties with documentation structure and its arrangement. Data protection laws are Radiol Oncol 2006; 40(2): 115-24. 120 Žagar T et al. / Complete life tables for Slovenia, 1982-2004 implemented in the rule as well. In spite of all the efforts, death certificate data are of-ten inaccurate as the primary cause of de-ath is often indeterminable. Primic Žakelj with co-authors investigated the accuracy of official causes of death in a cohort of cer-vical cancer patients between 1985 and 1999. They concluded that the official Slo-venian mortality rate of cervical cancer is underestimated for more than 25%.26 Obvi-ously the cause specific observed survival rate would be underestimated in that example as well. In this case, the relative survival analysis, which takes into account only dates of death and no causes of death, will lead us to more adequate result. Because of strict personal data protec-tion laws, collection of vital status or date of death data is very limited for individual investigators in Slovenia. Consequently, a simultaneous linkage between population diseases registries and Central Population Registry of Slovenia for patient’s vital status update is of special importance and is protected by law.27 Relative survival analysis provides rather unbiased estimation of population di-sease burden even if the cause of death is unavailable. Anyway, relative survival is not applicable in all occasions. Observed survival should still be used as a golden standard in all clinical studies as they deal with selected population which characteri-stics are not necessary in accordance with general population attributes. An application of population life tables would in such a case bias the results. That is why relative survival analyses are limited to population studies and apply data from population ba-sed disease registries. In relative survival analysis the disease unrelated death risks are removed by the usage of population life tables.28 These ta-bles are based on official mortality data stra-tified by age and sex, so only these two dise-ases unrelated death risks can be omitted by Radiol Oncol 2006; 40(2): 115-24. the relative survival analysis in Slovenia. If the influence of some other demographic characteristic on survival rates is supposed to be of practical importance, the life tables applied in relative survival analysis should be stratified by this attribute. Life tables stratified by socio-economic status are avai-lable in Finland.29 A relative survival analy-sis was performed by Finish investigators to examine the influence of social class on the survival of cancer patient cohort. In compa-rison with observed or cause specific survi-val, relative survival adjusted to social class gave the most adequate results. Laura M. Woods with co-authors 30 con-firmed that geographical patterns of life ex-pectancy identified for England and Wales in 1998 are mainly attributable to variati-ons in deprivation status. Life expectancy is highest in most affluent groups with cle-ar north-south gradient. For conducting this analysis they first had to construct life tables describing age specific mortality rates and life expectancy at birth for (a) quin-tiles if income deprivation, (b) each government office region and (c) every combina-tion of deprivation index and geography. Medical example To understand the implications of relative survival techniques we look at the results of a study of survival of patients after myo-cardial infarction.21 Having taken into account the age and calendar year, the obser-ved survival after infarction does not differ significantly (p = 0.15) with respect to sex (Figure 3). However, the problem of this study is that we do not have information on cause of death (a common situation in all the long term studies) and we are forced to consider all deaths as events. But as the observed group was on average 62 years old at diagnosis, we can expect that many of these deaths we- Žagar T et al. / Complete life tables for Slovenia, 1982-2004 121 Figure 3. Observed survival by sex, adjusted for age and calendar year (age 62, year 1984). re not necessarily due to infarction. When considering all deaths as events, we will thus always notice a strong effect of age, re-gardless whether the age is connected with the disease in question or not. The same is true for the year of diagnosis. As the population survival is constantly improving, this will be reflected in any long term study that doesn’t have information on cause of death. The relative survival comes as a solution whenever we wish to get information on the specific disease risk of a variable that has a known effect on the population risks. In our myocardial infarction study, sex is such an example. While men and women have an equal observed survival, the population hazards tell us that the women of this age should actually do much better, and we can therefore conclude that the mortality after infarction is connected with sex. The results of the relative survival are shown on Figure 4. We can see that sex (ta-king into account age and year) is strongly significant (p < 0,001). We can conclude that the hazard of dying of infarction rela-ted causes are much larger for women than for men (the hazard ratio is 1.77). Conclusion Slovenia is comparable to Scandinavian co-untries by its register orientation.16 Population and mortality data are up to date LI* LLZ M U U Figure 4. Relative survival by sex, adjusted for age and calendar year (age 62, year 1984) thanks to its electronical collection in Central Register of Population so we don’t ha-ve to wait for yearbooks to obtain neces-sary data for calculating life tables. We calculated life tables presented ex-clusively for needs of relative survival analyses. In order to promote this and oth-er already mentioned statistical analyses in public health where life tables are an essen-tial tool, we have presented them in this ar-ticle and put them available for public use. The warning should be given at this point for all potential users of our life tables. They contain crude probability of dying and so they require some adjustment regar-ding the purpose of use. For example smo-othing of crude probability of dying is nee-ded for demographic use.5,6 If needed, one can also calculate abbreviated life tables or tables for several years combined from our exact life tables. In very specific medical research separate life tables for occupational (social status, religious etc.) groups would be useful. Ho-wever, such data are not collected at population level, as registering them is very cost-ly and laborious. References 1. Detels R, McEwen J, Beaglehole R, Tanaka H, editors. Oxford textbook of public health, the methods of public health. Volume 2. 4th ed. New York: Oxford University Press; 2002: 807-17. Radiol Oncol 2006; 40(2): 115-24. 122 Žagar T et al. / Complete life tables for Slovenia, 1982-2004 2. Chiang CL. The life table and its applications. Mala-bar (Florida): Robert E Krieger Publ Co;1984: 113. 3. Milne J. A treatise on the valuation of annuities and assurances on lives and survivors. 1815. In: Smith D, Keyfitz eds. Mathematical demography. Berlin: Springer; 1977. 4. Lah I. Prva tablica umrljivosti slovenskega naroda. Ljubljana: Slovenčev koledar; 1942. 5. Šircelj M. Life tables for the population of Slove-nia 1980-1982 – 1994-1995. Ljubljana: Statistical Office of the Republic of Slovenia; 1997. 6. Malačič J. Demografija: teorija, analiza, metode in modeli. 5th ed. Ljubljana: Ekonomska fakulteta; 2003: 128-43. 7. Mathers CD, Vos T, Lopez AD, Salomon J, Ezzati M, editors. National Burden of Disease Studies: A Practical Guide. Edition 2.0. Global Program on Evidence for Health Policy. Geneva: World Health Organization; 2001. 8. Šircelj M, Ilić M. Rapid reports No. 169/2004: Population. Ljubljana: Statistical Office of the Repu-blic of Slovenia; 2004. 9. Abridged life table by sex, Slovenia. From internet page (April 30, 2006): http://www.stat.si/doc/pub/ rr798-2003/10/TABEL10.htm. 10. Life tables for 191 countries. WHO Statistical Information System (WHOSIS). Geneva: World Health Organization, 1999-2005. From internet page (April 30, 2006): http://www3.who.int/whosis/me-nu.cfm?path=whosis,life. 11. Statistical yearbook of the Republic of Slovenia, 1982-2004. Ljubljana: Statistical Office of the Republic of Slovenia; 1982–2004. 12. Preston SH, Heuveline P, Guillot M. Demography: Measuring and modelling population process. Oxford, Malden, Massachusetts: Blackwell Publishers; 2001. 13. Shkolnikov VM. Methodology note on the human li-fe-table database (HLD). From internet page (April 30, 2006): http://www.lifetable.de. 14. Zdravstveni statistični letopis, Slovenija 2001. Zdrav Var 2002; 41: 43-51. 15. Lexis W. Einleitung in die Theorie der BevölkerungsStatistik. Strasburg: Trubner; 1875. 16. Tršinar I. Centralni register prebivalstva. Zbirka pravo in politika. Ljubljana: Uradni list Republike Slovenije; 1999. 17. Pompe-Kirn V, Zakotnik B, Volk N, Benulič T, Škrk J. Cancer patients survival in Slovenia 1963-1990. Ljubljana: Onkološki inštitut; 1995. 18. Pompe-Kirn V, Zakotnik B, Zadnik V. Cancer pati-ents survival in Slovenia 1983-1997. Ljubljana: Onkološki inštitut; 2003. 19. Berrino F, Capocaccia R, Esteve J, Gatta G, Hakuli-nen T, Micheli A, et al, editors. Survival of cancer pa-tients in Europe: the EUROCARE-2 Study. Lyon: International Agency for Research on Cancer; 1999. 20. Berrino F, Capocaccia R, Coleman MP, Esteve J, Gatta G, Hakulinen T, et al, editors. Survival of cancer patients in Europe: the EUROCARE-3 Study. Ann Oncol 2003; 14. 21. Stare J, Henderson R, Pohar M. An individual me-asure of relative survival. J Roy Stat Soc C - APP 2005; 54: 115-26. 22. Stare J, Pohar M, Henderson R. Goodness of fit of relative survival models. Stat Med 2005; 24: 3911-25. 23. Šelb Šemerl J, Šešok J. Years of potential life lost and valued years of potential life lost in assessing premature mortality in Slovenia. Croat Med J 2002; 43 439-45. 24. Artnik B, Vidmar G, Javornik J, Laaser U. Prema-ture mortality in Slovenia in relation to selected bi-ological, socioeconomic, and geographical deter-minants. Croat Med J 2006; 47: 103-13. 25. Pravilnik o pogojih in načinu opravljanja mrliško pregledne službe (Ur.l. RS, No. 56/1993). 26. Primic Žakelj M, Pompe Kirn V, Škrlec F, Šelb J. Can we rely on caner mortality data? Checking the validity of cervical cancer mortality data for Slove-nia. Radiol Oncol 2001; 35: 243-47. 27. Žagar T, Primic Žakelj M, Zadnik V. The cancer registry of Slovenia and linking with related state data bases. In: Tkačik B, Urbas M, eds. Communi-cation with Statistical Data Providers and Users and Support for the EMU and Lisbon Strategy – Statistical days ‘05; 2005 Nov 7-9. Ljubljana: Statistical Office of the Republic of Slovenia, Statistial Society of Slovenia; 2005: 268-77. 28. Ederer F, Axtell LM, Cutler SJ. The relative survi-val rate. A statistical methodology. National Cancer Institute Monograph 1961; 6: 101-21. 29. Dickman PW, Auvinen A, Voutilainen ET, Hakuli-nen T. Measuring social class differences in cancer patient survival: Is it necessary to control for soci-al class differences in general population morta-lity? A Finnish population-based study. J Epidemiol Community Health 1998; 52: 727-34. 30. Woods LM, Rachet B, Riga MStone N, Shah A, Co-leman MP. Geographical variation in life expec-tancy at birth in england and wales is largely ex-plained by eprivation. J Epidemiol Commun H 2005; 59: 114-20. Radiol Oncol 2006; 40(2): 115-24. Žagar T et al. / Complete life tables for Slovenia, 1982-2004 123 Appendix Table 1. Complete life table for men, Slovenia 2004 X qx lx dx Lx T ex X qx lx dx Lx T 1x ex 0 0,003816 100000, 0 381,6 99675, 6 7302946, 1 73,03 50 0,005466 92486, 2 505,6 92233, 5 2409431, 6 26,05 1 0,000109 99618, 4 10,9 99612, 9 7203270, 5 72,31 51 0,006952 91980, 7 639,4 91661, 0 2317198, 1 25,19 2 0,000544 99607, 5 54,2 99580, 4 7103657, 6 71,32 52 0,009189 91341, 3 839,4 90921, 6 2225537, 2 24,37 3 0,000315 99553, 3 31,3 99537, 6 7004077, 2 70,36 53 0,008580 90501, 9 776,5 90113, 6 2134615, 6 23,59 4 0,000109 99521, 9 10,9 99516, 5 6904539, 7 69,38 54 0,008780 89725, 4 787,8 89331,5 2044502, 0 22,79 5 0,000213 99511,0 21,2 99500, 4 6805023, 2 68,38 55 0,010874 88937, 6 967,1 88454, 0 1955170, 5 21,98 6 0,000211 99489, 9 21,0 99479, 3 6705522, 7 67,40 56 0,011733 87970, 5 1032,2 87454, 4 1866716, 4 21,22 7 0,000101 99468, 8 10,1 99463, 8 6606043, 4 66,41 57 0,012437 86938, 3 1081,2 86397, 7 1779262, 0 20,47 8 0,000102 99458, 8 10,1 99453, 7 6506579, 6 65,42 58 0,013764 85857,1 1181,8 85266, 2 1692864, 3 19,72 9 0,000099 99448, 6 9,9 99443, 7 6407125, 9 64,43 59 0,014149 84675, 3 1198,0 84076, 3 1607598, 1 18,99 10 0,000097 99438, 8 9,7 99433, 9 6307682, 2 63,43 60 0,012695 83477, 3 1059,7 82947, 4 1523521, 8 18,25 11 0,000096 99429,1 9,5 99424, 3 6208248, 3 62,44 61 0,016026 82417, 6 1320,8 81757,1 1440574, 4 17,48 12 0,000000 99419, 6 0,0 99419, 6 6108823, 9 61,44 62 0,018685 81096, 7 1515,3 80339,1 1358817, 2 16,76 13 0,000349 99419, 6 34,7 99402, 2 6009404, 3 60,44 63 0,020545 79581, 4 1635,0 78763, 9 1278478, 1 16,07 14 0,000580 99384, 9 57,7 99356, 0 5910002, 1 59,47 64 0,020086 77946, 5 1565,7 77163, 6 1199714, 2 15,39 15 0,000230 99327, 2 22,9 99315, 8 5810646, 1 58,50 65 0,022566 76380, 8 1723,6 75519, 0 1122550, 6 14,70 16 0,000383 99304, 4 38,1 99285, 3 5711330, 3 57,51 66 0,026644 74657, 2 1989,2 73662, 6 1047031, 6 14,02 17 0,001092 99266,3 108,4 99212,1 5612045, 0 56,54 67 0,026450 72668,1 1922,1 71707, 0 973368, 9 13,39 18 0,001049 99157, 8 104,0 99105, 8 5512832, 9 55,60 68 0,029052 70746, 0 2055,3 69718, 3 901661, 9 12,75 19 0,001036 99053, 8 102,6 99002, 5 5413727, 1 54,65 69 0,031774 68690, 7 2182,6 67599, 4 831943, 6 12,11 20 0,000647 98951,2 64,0 98919, 2 5314724, 6 53,71 70 0,039502 66508,1 2627,2 65194, 5 764344, 2 11,49 21 0,001365 98887, 2 135,0 98819, 6 5215805, 4 52,75 71 0,040692 63880, 9 2599,4 62581, 2 699149, 7 10,94 22 0,001368 98752,1 135,1 98684, 6 5116985, 8 51,82 72 0,047181 61281, 4 2891,3 59835, 8 636568, 5 10,39 23 0,001417 98617, 0 139,7 98547, 2 5018301, 2 50,89 73 0,044080 58390,1 2573,8 57103, 2 576732, 7 9,88 24 0,000875 98477, 3 86,2 98434,2 4919754, 0 49,96 74 0,053367 55816, 3 2978,8 54326, 9 519629, 5 9,31 25 0,000997 98391,1 98,1 98342,1 4821319, 8 49,00 75 0,057874 52837, 5 3057,9 51308, 6 465302, 6 8,81 26 0,000765 98293, 0 75,2 98255, 4 4722977, 7 48,05 76 0,065789 49779, 6 3275,0 48142,1 413994, 0 8,32 27 0,001263 98217, 8 124,0 98155, 8 4624722, 3 47,09 77 0,076589 46504, 6 3561,8 44723, 8 365851, 9 7,87 28 0,001298 98093, 8 127,3 98030, 2 4526566, 5 46,15 78 0,071369 42942, 9 3064,8 41410, 5 321128,1 7,48 29 0,000787 97966,5 77,1 97928, 0 4428536, 4 45,20 79 0,087725 39878,1 3498,3 38128, 9 279717, 6 7,01 30 0,001054 97889, 4 103,2 97837, 8 4330608, 4 44,24 BO 0,090664 36379, 8 3298,3 34730, 6 241588, 7 6,64 31 0,000931 97786, 2 91,1 97740, 7 4232770, 6 43,29 81 0,102819 33081, 5 3401,4 31380, 7 206858, 1 6,25 32 0,001154 97695, 2 112,8 97638, 8 4135029, 9 42,33 82 0,100904 29680, 0 2994,8 28182, 6 175477, 3 5,91 33 0,001143 97582, 4 111,5 97526, 6 4037391, 1 41,37 B3 0,125664 26685, 2 3353,4 25008, 5 147294, 7 5,52 34 0,000826 97470, 9 80,5 97430, 6 3939864, 5 40,42 S4 0,128308 23331, 9 2993,7 21835,0 122286, 2 5,24 35 0,000937 97390, 3 91,3 97344, 7 3842433, 9 39,45 85 0,122419 20338, 2 2489,8 19093, 3 100451,1 4,94 36 0,001588 97299,1 154,5 97221, 8 3745089, 2 38,49 86 0,153310 17848, 4 2736,3 16480, 2 81357, 8 4,56 37 0,001985 97144, 5 192,9 97048,1 3647867, 4 37,55 87 0,135827 15112,1 2052,6 14085, 8 64877, 6 4,29 38 0,002633 96951,7 255,3 96824,1 3550819, 3 36,62 B8 0,161417 13059, 4 2108,0 12005, 4 50791,8 3,89 39 0,002317 96696, 4 224,0 96584, 4 3453995, 2 35,72 89 0,202786 10951, 4 2220,8 9841,0 38786,4 3,54 40 0,002168 96472, 4 209,2 96367, 8 3357410, 8 34,80 90 0,216891 8730, 6 1893,6 7783,8 28945,4 3,32 41 D,002697 96263, 2 259,6 96133, 5 3261043, 0 33,88 91 0,257732 6837, 0 1762,1 5956,0 21161, 5 3,10 42 0,003833 96003, 7 368,0 95819, 7 3164909, 5 32,97 92 0,238411 5074, 9 1209,9 4470,0 15205, 6 3,00 43 0,003811 95635,6 364,5 95453, 4 3069089, 9 32,09 93 0,289340 3865, 0 1118,3 3305,9 10735, 6 2,78 44 0,003573 95271, 2 340,4 95101, 0 2973636, 5 31,21 94 0,262411 2746, 7 720,8 2386,3 7429,8 2,70 45 0,003497 94930, 8 332,0 94764, 8 2878535, 5 30,32 95 0,276316 2025, 9 559,8 1746,0 5043,4 2,49 46 0,005372 94598, 8 508,2 94344, 7 2783770, 7 29,43 96 0,254545 1466,1 373,2 1279,5 3297,4 2,25 47 0,005003 94090, 6 470,8 93855, 2 2689426, 0 28,58 97 0,343750 1092, 9 375,7 905,1 2017,9 1,85 48 0,005701 93619, 9 533,8 93353, 0 2595570, 7 27,72 98 0,411765 717,2 295,3 569,6 1112,8 1,55 49 0,006444 93086,1 599,9 92786, 2 2502217, 8 26,88 99 0,437500 421,9 184,6 329,6 543,2 1,29 100+ 1,000000 237,3 237,3 213,6 213,6 0,90 Radiol Oncol 2006; 40(2): 115-24. 124 Žagar T et al. / Complete life tables for Slovenia, 1982-2004 Table 2. Complete life table for women, Slovenia 2004 X qx «X dx Lx T xx ex X qx «X dx Lx T xx ex 0 0,004193 100000, 0 419,3 99643,6 8026359, 0 80,26 50 0,003577 96460, 6 345,0 96288,1 3083520, 7 31,97 1 0,000116 99580, 7 11,5 99574, 9 7926715, 4 79,60 51 D, 003979 96115, 6 382,4 95924, 3 2987232, 6 31,08 2 0,000233 99569, 2 23,2 99557, 6 7827140, 5 78,61 52 0,003785 95733,1 362,4 95551, 9 2891308, 3 30,20 3 0,000112 99546, 0 11,1 99540,4 7727583, 0 77,63 53 0,004388 95370, 7 418,5 95161, 5 2795756, 4 29,31 4 0,000000 99534, 9 0,0 99534,9 7628042, 5 76,64 54 0,004619 94952, 3 438,6 94733, 0 2700594, 8 28,44 5 0,000000 99534, 9 0,0 99534, 9 7528507, 7 75,64 55 D, 004199 94513, 7 396,9 94315, 2 2605861, 9 27,57 6 0,000223 99534, 9 22,2 99523, 8 7428972, 8 74,64 56 0,004746 94116, 8 446,7 93893, 5 2511546, 6 26,69 7 0,000108 99512, 7 10,7 99507, 3 7329449, 1 73,65 57 0,005811 93670,1 544,4 93397, 9 2417653, 2 25,81 8 0,000107 99501, 9 10,7 99496, 6 7229941, 7 72,66 58 0,004805 93125, 7 447,5 92902, 0 2324255, 3 24,96 9 0,000000 99491, 3 0,0 99491, 3 7130445, 1 71,67 59 D, 006698 92678, 3 620,8 92367, 9 2231353,2 24,08 10 0,000307 99491, 3 30,6 99476, 0 7030953, 8 70,67 60 D, 005727 92057, 5 527,3 91793, 9 2138985, 3 23,24 11 0,000000 99460, 7 0,0 99460, 7 6931477, 8 69,69 61 0,006248 91530, 2 571,9 91244, 3 2047191, 5 22,37 12 0,000189 99460, 7 18,8 99451, 3 6832017, 1 68,69 62 0,006914 90958, 4 628,9 90643, 9 1955947, 2 21,50 13 0,000091 99441, 9 9,1 99437,4 6732565, 8 67,70 63 D, 008027 90329, 5 725,1 89966, 9 1865303, 3 20,65 14 0,000441 99432, 9 43,8 99410,9 6633128, 4 66,71 64 0,008423 89604, 4 754,7 89227, 0 1775336, 3 19,81 IS 0,000081 99389, 0 8,1 99385,0 6533717, 5 65,74 65 0,009713 88849, 7 863,0 88418,1 1686109, 3 18,98 16 0,000159 99380, 9 15,8 99373, 0 6434332, 5 64,74 66 0,010050 87986, 6 884,3 87544, 5 1597691, 2 18,16 17 0,000244 99365,1 24,2 99353,0 6334959, 5 63,75 67 D,010566 87102, 3 920,3 86642, 2 1510146, 7 17,34 18 0,000394 99340, 9 39,1 99321, 3 6235606, 5 62,77 68 0,012647 86182, 0 1090,0 85637, 0 1423504, 5 16,52 19 0,000307 99301, 7 30,5 99286,5 6136285, 1 61,79 69 0,013750 85092,1 1170,0 84507,1 1337867, 5 15,72 20 0,000300 99271, 3 29,7 99256,4 6036998, 6 60,81 70 0,017896 83922,1 1501,9 83171,1 1253360, 4 14,93 21 0,000290 99241, 5 28,8 99227,1 5937742, 2 59,83 71 D,017768 82420, 2 1464,4 81688, 0 1170189, 3 14,20 22 0,000630 99212, 7 62,5 99181, 5 5838515, 1 58,85 72 0,022632 80955, 8 1832,2 80039, 7 1088501, 3 13,45 23 0,000134 99150, 2 13,3 99143, 6 5739333, 6 57,89 73 0,022714 79123, 6 1797,2 78225, 0 1008461, 6 12,75 24 0,000408 99136, 9 40,5 99116,7 5640190, 1 56,89 74 0,023985 77326, 4 1854,7 76399, 0 930236, 6 12,03 25 0,000273 99096, 5 27,1 99082, 9 5541073, 3 55,92 75 D,031729 75471, 7 2394,6 74274, 3 853837, 6 11,31 26 0,000274 99069, 4 27,1 99055, 8 5441990, 4 54,93 76 0,032563 73077, 0 2379,6 71887, 2 779563, 3 10,67 27 0,000268 99042, 3 26,5 99029, 0 5342934, 6 53,95 77 0,039727 70697, 4 2808,6 69293,1 707676, 1 10,01 28 0,000544 99015, 8 53,8 98988, 9 5243905, 6 52,96 78 0,040628 67888, 8 2758,2 66509, 7 638382, 9 9,40 29 0,000142 98961,9 14,0 98954, 9 5144916, 7 51,99 79 D, 046940 65130, 6 3057,2 63602, 0 571873, 2 8,78 30 0,000280 98947, 9 27,7 98934,1 5045961, 8 51,00 80 0,056879 62073, 4 3530,7 60308, 0 508271, 3 8,19 31 0,000422 98920, 2 41,7 98899,4 4947027, 7 50,01 81 0,069948 58542, 7 4094,9 56495, 2 447963, 2 7,65 32 0,000433 98878, 5 42,9 98857,1 4848128, 4 49,03 82 0,070994 54447,7 3865,5 52515, 0 391468, 1 7,19 33 0,000729 98835, 6 72,1 98799, 6 4749271, 3 48,05 83 D, 083205 50582, 3 4208,7 48477, 9 338953, 1 6,70 34 0,000999 98763, 6 98,6 98714, 2 4650471, 7 47,09 84 0,085465 46373, 5 3963,3 44391, 9 290475, 2 6,26 35 0,000210 98664, 9 20,7 98654, 5 4551757, 5 46,13 85 0,100148 42410, 2 4247,3 40286, 6 246083, 3 5,80 36 0,001045 98644, 2 103,0 98592, 6 4453103, 0 45,14 86 0,108792 38162, 9 4151,8 36087, 0 205796, 7 5,39 37 0,000834 98541,1 82,2 98500, 0 4354510, 3 44,19 87 D,121715 34011,1 4139, 7 31941, 3 169709, 7 4,99 38 0,000754 98458, 9 74,2 98421, 8 4256010, 3 43,23 88 0,149133 29871, 4 4454,8 27644, 0 137768, 4 4,61 39 0,000458 98384, 7 45,0 98362,1 4157588, 5 42,26 89 0,142495 25416, 6 3621,7 23605, 8 110124, 4 4,33 40 0,000853 98339, 6 83,8 98297, 7 4059226, 4 41,28 90 0,179487 21794, 9 3911,9 19838, 9 86518, 7 3,97 11 0,001325 98255, 8 130,2 98190, 7 3960928, 7 40,31 91 0,178519 17883, 0 3192,4 16286, 8 66679, 7 3,73 42 0,001614 98125, 6 158,3 98046,4 3862738, 0 39,37 92 0,214885 14690, 5 3156,8 13112, 2 50393, 0 3,43 43 0,001315 97967, 2 128,8 97902, 8 3764691, 6 38,43 93 0,210300 11533, 8 2425,6 10321, 0 37280, 8 3,23 44 0,001611 97838, 4 157,6 97759, 6 3666788, 8 37,48 94 0,226860 9108,2 2066,3 8075,1 26959, 8 2,96 15 0,001824 97680, 8 178,1 97591, 7 3569029, 2 36,54 95 0,268617 7041,9 1891,6 6096,1 18884, 8 2,68 46 0,001941 97502, 7 189,3 97408, 0 3471437, 4 35,60 96 0,271889 5150,3 1400,3 4450,2 12788, 6 2,48 47 0,003889 97313, 4 378,5 97124, 2 3374029, 4 34,67 97 0,305882 3750,0 1147,1 3176,5 8338,5 2,22 48 0,002561 96935, 0 248,2 96810, 9 3276905, 2 33,81 98 0,250000 2603,0 650,7 2277, 6 5162, 0 1,98 19 0,002339 96686, 7 226,2 96573, 7 3180094, 3 32,89 99 0,557692 1952,2 1088, 7 1407,8 2884,4 1,48 1004 1,000000 863,5 863,5 1476,5 1476,5 1,71 Radiol Oncol 2006; 40(2): 115-24. Slovenian abstracts 137 Radiol Oncol 2006; 40(2): 115-24. Popolne letne tablice umrljivosti za Slovenijo po spolu, 1982-2004, in možnosti uporabe v javnem zdravju Žagar T, Zadnik V, Pohar M, Primic Žakelj M Tablice umrljivosti se uporabljajo kot osnova za statistične izračune v mnogoterih znanstvenih strokah; tudi v javnemu zdravju in epidemiologiji. V zadnjih letih jih v Sloveniji uporabljamo predvsem v analizah relativnega preživetja, za kar potrebujemo popolne momentne tablice umrljivosti za posamezna koledarska leta in ločene po spolu. Ker takšne tablice umrljivosti za Slovenijo še niso na razpolago, smo jih pripravili sami za obdobje 1982-2004. V pričujočem prispevku je opisana metodologija po kateri smo tablice izračunali in primeri, v katerih so takšne tablice umrljivosti uporabne. Tablice so bralcu na razpolago, če pošlje prošnjo na naslov register@onko-i.si. Objavljene so tudi v mednarodni bazi tablic umrljivosti (angl. Human Life-Table Database), ki je dosegljiva na internetu (http://www.lifetable.de/). Tudi v prihodnje nameravamo računati tablice umrljivosti, takoj ko bomo dobili potrebne podatke. Radiol Oncol 2006; 40(2): 133-8.