Life Expectancy. BPS-Statistics Indonesia. Islamabad, Pakistan September, 2017

Transcription

1 Life Expectancy BPS-Statistics Indonesia Islamabad, Pakistan September, 2017

2 INTRODUCTION Life table is an analytical tool for estimating demographic indicators. Strength : ready to use with the absence of standardized population Life table is a table consist of a life history of a population by age in a single statistical model

3 Life table is a way to analyze Age Specific Death Rate (ASDR) and survival analysis Life table explains the history of a group of population (hypothetical group) or a cohort with gradually death history.

4 Benefits of Life Table To compare mortality rates among population (different region, different cohort etc) To measure the improvement of health development, especially for the children (from the e0 number) As a Base for life insurance calculation : Premium insurance

5 The World Health Organization (WHO) began producing annual life tables for all Member States in These life tables are a basic input to all WHO estimates of global, regional and country-level patterns and trends in all-cause and causespecific mortality.

6 Types of Life Table 1. Complete life table 2. Abridged life table

7 Complete Life Table Create in a complete table, Disaggregate by a single age, Note for qx : interval x to x+1 Example : q30 for interval 30 to 31

8 Example of Complete Life Table Single year Sumber: Depertment Statistics of Singapore

9 Abridged Life Table Abridged Life Table is a more compact and simple life table, the accuracy is almost the same as Complete Life Table, Disagregated by 5 year age group, For country with unequal distribution of population, Abridged Life Table is more precise Notation : n= age interval and x= exact age x, such as : n q x, nd x, n p x, and n L x, while for l x, T x, and e x just the same and related with population at age x Example : 5q30 for interval 30 to 35

10 Example of Abridged Life Table: Life Table Indonesia, 2000, Male 5 year interval (breakdo wn) 5 year interval Sumber: Ministry of Health Republic of Indonesia, 2002

11 Example Abridged Life Table: Life Table Indonesia, 2000, Female Sumber: Ministry of Health Republic of Indonesia, 2002

12 Example of Abridged Life Table: Life Table Indonesia, 2000, Male + Female Sumber: Ministry of Health Republic of Indonesia, 2002

13 Abridged Life Table: Life Table Indonesia, 2010 Sumber: Kajian Lif e Table Indonesia Berdasarkan Hasil SP2010, BPS, 2005

14 Model of Standard Life Table UN Models: Far Eastern Latin American South Asian Chilean General Princeton Model (Coale Demeny): West (reference for Indonesia) South East North

15 Kolom-kolom x n nqx npx Life lx Table ndx (Abridged) nlx Tx ex (1) (2) (3) (4) (5) (6) (7) (8) (9) x = Exact age (in year) n = Aged Interval nqx = probability of dying between exact age x and x+n npx = probability of surviving between age x and x+n l x = Number of survivors at exact age x ndx = Number of people dying between age x and x+n L x = years lived between age x and x+n T x = total years lived after exact age x e x = expectation of life, average number of life after exact age x Note : for complete life table, n=1

16 Calculation of Complete Life Table

17 Mortality table for woman, Indonesia year x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) : 105 : 109

18 Mortality table for woman, Indonesia year x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 2, : 105 : 109

19 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 2, : 105 : 109

20 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 2, : 105 : 109

21 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e 0 x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 2, : : : : 109 1

22 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e 0 x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 100,000 2, Radix : : : : 109 1

23 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 100,000 2, , : : : : 109 1

24 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 100,000 2, , , , , : : : : : :

25 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 0, ,000 2, , , , , : : : : : :

26 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 0, ,000 2, , , , , , : : : : : :

27 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 0, ,000 2, , , , , , , , , : : : : 105 0, : : : :

28 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 0, ,000 2,256 98, , , , , , , , , : : : : 105 0, : : : :

29 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 0, ,000 2,256 98, , , , , , , , , , : : : : 105 0, : : : :

30 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 0, ,000 2,256 98, , , , , , , , , , , : : : : 105 0, : : : :

31 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e 0 x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 0, ,000 2,256 98, , , , , , , , , , , , ,400 : : : : : 105 0, : : : : :

32 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e 0 x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 0, ,000 2,256 98, , , , , , , , , , , , ,400 : : : : : 105 0, : : : : : ,324,402

33 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 0, ,000 2,256 98,109 7,324, , , , , , , , , , , , ,400 : : : : : 105 0, : : : : : ,324,402

34 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 0, ,000 2,256 98,109 7,324, , , ,666 7,226, , , , , , , , , ,400 : : : : : 105 0, : : : : : ,324,402

35 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 0, ,000 2,256 98,109 7,324, , , ,666 7,226, , , ,544 7,128, , , ,463 7,031, , , ,400 6,933,620 : : : : : : 105 0, : : : : : : ,324,402

36 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 0, ,000 2,256 98,109 7,324,402 73,24 1 0, , ,666 7,226, , , ,544 7,128, , , ,463 7,031, , , ,400 6,933,620 : : : : : : 105 0, : : : : : : ,324,402

37 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 0, ,000 2,256 98,109 7,324,402 73,24 1 0, , ,666 7,226,293 73,93 2 0, , ,544 7,128, , , ,463 7,031, , , ,400 6,933,620 : : : : : : 105 0, : : : : : : ,324,402

38 x q x [ (4)/(3) ] l x d x L x T x [ (5) ] e x [ (6)/(3) ] (1) (2) (3) (4) (5) (6) (7) 0 0, ,000 2,256 98,109 7,324,402 73,24 1 0, , ,666 7,226,293 73,93 2 0, , ,544 7,128,627 73,05 3 0, , ,463 7,031,083 72,12 4 0, , ,400 6,933,620 72,17 : : : : : : : 105 0, ,53 : : : : : : : ,29 7,324,402

39 Probability of a person age 0 dying before the first birthday, col (2) : Probability of dying (q 0 ) = d 0 /l 0 = 2,256/100,000 = 0,02256 Probability of a person age 0 survived and reached his 1st year : Probability of survived (p 0 ) = l 1 = 97,744/100,000 = 0,97744 atau (1- q 0 ) General formula: q x d l x x and l p x 1 x lx

40 Col (5): L x L 0 = 0,3 l 0 + 0,7 l 1 L 1 = 0,4 l 1 + 0,6 l 2 L 2 = ½ ( l x + l x+1 ) = ½ ( l 2 + l 3 ) col (6): T x T 0 = L 0 + L 1 + L 2 + L L n T 1 = L 1 + L 2 + L 3 + L L n formula: i w i x T L x i

41 Kolom (7): e x formula: Life Expectancy at birth: e x e 0 T l T l x x 0 0

42 The life table is called longitudinal life table. Weakness : difficult to have mortality data by single age cross section Life Table is more practical and simple. This table describe mortality for synthetic cohort dying follow the mortality trend by age that exist for a group of population in the particular time period.

43 Calculation of Abridged Life Table

44 Formula for Abridged Life Table : l 0 = 100,000 l x+n = l x - n d x nd x = nq x x l x or (l x - l x+n ) (number of dying between x and x+n) nq x np x = nd x / l x (probability of dying between x and x+n) = 1 n q x L 0 = 0,3 l 0 + 0,7 l 1 4L 1 = 1,9 l 1 + 2,1 l 5 5L x = 5/2 (l x + l x+5 ) or n L x = n/2 (l x + l x+n )

45 T x nl x e x = i=x L i = T x - T x+n = T x / l x e 0 = T 0 / l 0 (life expectancy at birth)

46 Abridged Life Table for Australian Males Age (x) n l x n d x n q x n p x n L x T x e x , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,9 71,1 70,9 67,1 62,2 57,3 52,7 48,1 43,4 38,6 33,9 29,4 25,0 20,9 17,1 13,7 10,7 8,2 6,1 4,2

47 Notes: Calculation of the last row for age 85 for Abridged Life Table using specific treatment as it is an open interval q 85 is always equal to 1,0 and d 85 = l 85, When ASDR of age 85 is known, value for L85 is expected as L85 = l85 / M85, when it is unknown then, L85 = l85 x log10 l85,

48 Exercise 1 1. Fill in and complete this following Abridged Life Table : x n q x l x n d x n L x T x e x 0 0, , , , , , , , , , , , , , , , , , , , , ,00000 ASDR 100+ = 0,4329

49 Exercise 2. Question based on exercise no 1: a) For someone who has reached age 50 year old, how many years in average he/she could survive? b) What is the probability of someone aged 60 year old will reach aged 65 year old? c) What is the life expectancy for a 15 year old individual? d) From a radix person, is there any probability that someone will reach age of 100 year old? If yes, how many are they?

50 ASDR 100+ = 0,4329 Exercise 3 Fill in Complete Life Table :

51 Exercise 4. Question based on Ex 3: a) What is probability of someone aged 60 year old will reach aged 61? b) What is the life expectancy for a 1 year old individual? c) From radix person, how many person will survive and reach aged 75 year old? d) For some one who has reached age 60 year old, how many years in average he/she will get survive?

52 Thank you Terima Kasih