measures of central tendency: mean, median; mode

This document describe the central tendency of the data mainly about mean, median and mode. Also, this chapter has calculated the central tendency for ungrouped and grouped data. In addition, it has given interpretation for each central tendency.

1. Chapter Three Mortality 1

2. Ch-3 Mortality In this chapter we will discuss:- Concepts and Measurement of Death Statistics Definition of Death and Related Events Basic Mortality Measures Standardization Methods Life Tables and Types of life table Constructing Life Tables

3. Ch-3 Mortality Mortality studies are important to know the socio-economic and demographic implications of death. Death is one of the principal vital events that occur in human beings once in their lifetime . Death is the permanent disappearance of all evidence of life at any time after birth has taken place (UN – WHO).

4. Ch-3 Mortality Live birth is the complete extraction from its mother of a product of conception irrespective of the duration of pregnancy, after such separation, shows any evidence of life. Death rate: the relative frequency of deaths in a specific population. Mortalit y : t h e s t ate o r c ond iti o n o f b ei n g subject to death. Morbidity is being unhealth . Mortality rate: a measure of the number of deaths in a population, scaled to the size of that population, per unit of time .

5. Ch-3 Mortality A fetal death is the disappearance of life prior to complete expulsion from its mother of a product of conception irrespective of the duration of pregnancy. Data Requirements for Mortality Statistics 2 types of data to measure levels & patterns of mortality: the number of deaths, the size of the population exposed to the risk of death.

6. Ch-3 Mortality Due to lack of registration system in the developing world, the data on death events are usually obtained from censuses and sample surveys.

7. Basic Mortality Measures Crude Death Rate (CDR) Specific Death Rates Age-sex Specific Death Rates (ASSDR) we see one by one. 1. Crude Death Rate (CDR):- I t is defined as the number of deaths in a year per 1,000 of the mid-year population. D: the number of deaths in a year. P: mid-year population. C D R =  

8. Basic Mortality Measures CDR is a rough measure. sine it doesn’t take into account the effects of variations in age structure as well as variations among different population groups. Example: in country A among 5000 mid year population 250 were died by different reason. CDR= 250/5000=0.05*1000=50 deaths per 1000 per year.

9. Basic Mortality Measures 2. Specific Death Rates(SDR) It used to specific categories of deaths of population. Example: In country B among age group 25-34 of 5000,000 mid year population 200,000 were died by different reasons. ASDR= 200,000/5,000,000=0.04*1000=40 ==40 deaths per 1000 population per year for age group 25-34.

10. Basic Mortality Measures These categories may be subdivisions of the population or death according to age , sex, occupation , educational leve l, causes of death, etc. Therefore, specific death rates are calculated in relation to particular group of population. For instance, commonly used are age and sex .

11. Basic Mortality Measures 3. Age-Sex Specific Death Rates (ASSDR) is defined as the number of deaths of males or females , in a particular age group per 1,000 male or female populations in the age group . --- It is calculated as

12. Basic Mortality Measures 4. Cause Specific Death Rate is the number of deaths from a given cause or group of causes during a year per 100,000 of the mid year population(P). = *100,000  

13. Basic Mortality Measures Gr a ph i c a l P r e s ent a t io n o f A SS D R It allows observing the pattern of mortality , and enables comparisons among different mortality schedules. Graphical presentation of ASDR in Ethiopia for the male population in 1984.

14. Standardization Methods Standardization is a general statistical method used in many areas other than mortality analysis. It is the procedure of adjusting crude rates to eliminate from them the effect of differences in population composition with respect to age and other variables like sex,… .

15. Standardization Methods Why it need?? This is necessary because: Crude rates are affected by demographic composition of the population for which they are calculated. The purpose of standardization is, therefore, to allow a more precise composition of crude rates by eliminating the effect of differences in age composition and other variables(sex, residence..) . age composition is a key factor affecting crude rates

16. Standardization Methods Types of standardization Standardization can be direct or indirect. Direct standardization Pr o vi d e s t h e b e s t b a s i s f o r d e t er m in in g t h e difference between two crude rates. T h e r a t e s fr o m 2 o r m o re s tu d y po p u l a t i on s are a p p li ed t o a c o m m o n po pu l a t io n di st r i b ut i o n(standard population).

17. Direct standardization Direct standardization It involves taking a standard population and applying it to the specific rates for the population being compared. It serves to provide the best basis for determining the relative difference between mortality in two areas or at two dates.

18. Direct standardization Steps in the direct standardization procedure: Select a standard population . We need to have ASDR of study population . Expected deaths = ASDR x number of people in the corresponding age group of the standard population . Find the total number of the expected deaths/ sum the product= total expected death rate . Standard death rate= The age standardized death rates for the standard population is the same as its own death rate

19. Direct standardization We can standardize the death rate for both age and sex jointly . In doing this, each age-sex specific death rate is multiplied by the proportion of the total standard population in that age-sex group.

20. Direct standardization Example

21. Direct standardization Example From the above calculations, we can conclude that age-standardized death rate for country A is higher than country B, which implies that mortality is higher in country A than B. However, it cannot be concluded that mortality is twice as high in country A as in the standard population.

22. Indirect standardization The direct method requires age-specific death rates for the area under study population . When we lack the age-specific death rates of the area under study population. But if we have a count or an estimate of the total number of deaths , an estimate of crude death rates and if the age distribution of the population is available, it is possible to adjust the death rates by indirect method.

23. Indirect standardization The formula for indirect standardization is given as: Where, for the “ standard” population, ma= is age-specific death rates and M represents the CDR; and For the population under study, d represents the total number of deaths and Pa represents the population at each age.

24. Indirect standardization The steps in calculating the age adjusted death rate (AADR) by indirect method are: Obtain the ASDRs for the standard population. Set down the population by age for the area under the study population. Compute the cumulative product of the death rates in step 1 and the population in step 2. Divide the result in step 3 into the total number of deaths registered in the study area. Multiply the result in step 4 by the CDR of the standard population to derive the adjusted death rates.

25. Age ASDR f or the sta n da r d population (M a ) Population in thousands (P a ) M a P a <1 27 228 6156 1- 4 1.1 876 963.6 5 - 9 0.5 981 490.5 10 -14 0.4 836 334.4 15-19 0.9 725 652.5 20-24 1.2 598 717.6 25-29 1.3 527 685.1 30-34 1.6 507 811.2 35-39 2.3 415 954.5 40-44 3.7 364 1346.8 45-49 5.9 324 1911.6 50-54 9.4 279 2622.6 55-59 13.8 212 2925.6 60-64 21.5 183 3934.5 65-69 31.4 128 4019.2 70-74 47.2 84 3964.8 75-79 72 52 3744 80-84 117.2 31 3633.2 85+ M 198.6 22 4369.2 All ages 9.5 7374 E x p ec ted d ea ths =  M a P a ---- ---- 44237 Registered deaths (D) 1711982 95,486 ---- Ratio= Registered deaths =95486/44237 E x p ec t e d d ea t h s ---- 2.1585 ---- Age-adjusted death rate = 9.5xRatio ---- 20.5 ----

26. Different Mortality Terms infant mortality rate ( less than one year ) Neonatal >> >> 3 types ( less one month ) Early, late and post F o e t a l d e a t h ( s til l bi r th ) before birth Late foetal death rate Perinatal Mortality rate Child mortality(under five) Maternal death rate due to pregnancy & birth

27. Infant Mortality Rate (IMR) There are several possibilities for estimating infant mortality rates depending on the availability and quality of information on births and deaths. Conventionally, infant mortality rate is defined as the number of death of infants less than one year of age to the number of live births occurring that year, times 1,000. That is, IMR= *1000  

28. Infant Mortality Rate (IMR) Example: In a given year of 325,000 births 1750 infants were died before 1 st birth day. IMR=1750/325,000=0.0054*1000=5.4 Means 5.4 infant deaths per 1000 live births per year.

29. Neonatal Mortality Rates (NMRs) NMR is the number of deaths of infants under 1 month of age during a year per 1000 live births during the year. The three commonly used measures of neonatal mortality are :- i. Early Neonatal MR = *1000 ii. Late Neonatal MR= *1000 iii. Post-Neonatal MR= *1000  

30. Neonatal Mortality Rates (NMRs) Example in country Y the number of birth deaths before 28 days of life were 2750 among 325,000 live births. Find Neonatal MR. NMR=2750/325,000 =0.0085*1000 =8.5=9 means 9 neonatal deaths per 1000 live births.

31. F o e t a l D e a t h ( s til l bi r th ) F o e t a l d e a t h ( s til l bi r th ) o c c u r s b e f o re t h e c o m pl e t e extraction of a fetus from the mother’s womb. According to the WHO, a late foetal death occurs after the twenty-eight week of gestation. Used Late foetal death rate= *1000 In o r d er t o m ini m i z e m ea su re m ent er r o r s th at o cc u r during registration of births or infant death , a Perinatal Mortality Rate (PMR) was developed.  

32. F o e t a l D e a t h ( s til l bi r th ) It is calculated using the formula: perinatal MR= *1000 Child mortality refers under 5 year deaths.  

33. Maternal Death Rate (MDR) T h e d e a t h o f a w o m an w h i l e p r e gn a n t , o r w i th i n 42 days of termination of pregnancy is MDR. Maternal(mother) death is related to or aggravated by pregnancy or its management, but not from accidental or incidental causes. MDR= *1000  

34. 34 Life Table A life table is a tool to analyze and present the mortality experience of a population. The first life table was published in 1693 by Halley with the assumption that a population is stationary. Milne (1815) prepared the first scientifically correct life table based on population & death data classified by age .

35. Types of Life Table Life tables differ in several ways with respect to: the reference year of the table, the age detail, single/group and the number of factors comprehended by the table. Two types based on the reference year of the table: the current or period life table, and the generation or cohort life table. The current life table is constructed based on current mortality rates with refers to a short period of time, usually a year.

36. Types of Life Table The generation life table is constructed based on the m o r t a l it y ra t e s e xp er i e n c e d b y a p ar ti c u l ar b i r t h cohort , e.g., all persons born at some particular time. Life tables are also classified into two: complete and abridged according to the length of the age interval. Co m pl e t e ( u n a b r i dg e d ) - w h e n t h e l i f e t a b l e is prepared for each single year of age. Abridged - when the life table is prepared using age intervals of 5 or 10 .

37. Various Life Table Functions The basic life table functions are: n q x : P robability of dying in the interval [x, x+n ], given survival to age x. n p x : P robability of surviving in the interval [x, x+n ]. l x : Number living at beginning of age interval. n d x : Number dying during age interval. n L x : Stationary population in the age interval. T x : S t a t i on ary p o p u l a ti o n i n t hi s a n d a l l subsequent age intervals. e x : A v era g e n u m b er o f y ears o f li f e re m a i ni n g at beginning of age interval

38. Assumptions in Life Tables A number of assumptions are considered such as: the cohort is closed against in or out migration, people die at each age according to a schedule that is fixed in advance and does not change, c o ho r t o r i gi n a t e s f r o m s o m e s t a n d a r d n u m b er of births like 1,000, or 10,000, or 100,000 - 'radix' , at each age (except the first and last few years of life), deaths are evenly distributed, the cohort contains members of only one sex .

39. qx Probability of Dying ( q x ) It gives the probability of dying between exact ages x and x+1. q x cannot be calculated directly since death rates ( M x ) used in its calculation are based on mid-year population rather than population at the beginning . qx =  

40. qx = is the population aged x at the beginning of the year. = (if d e a th s are e v e nly d is t r ib u t e d throughout the year ). Dx is the number of deaths in the year of persons aged x and Px is the population age x, obtained considering the mid-year population . (June 30 or Yekatit 30)  

41. qx The specific death rate( = , qx= = = = = Since the assumption of evenly distribution of deaths does not hold for the very young age groups specifically in areas with high mortality levels. qx = , a x is the probability of living in a year.  

42. qx The value a a 1 , ... vary from country to country. Developing countries ax Group 0.3 <1 year 0.4 1-4 years 0.5 >4years

43. 1.nqx n q x is calculated instead of q x – n: length of the interval n q x - probability of dying between ages x and x + n. n a x is the proportion of the interval lived by those who die. Died/lived a = . 1 i n l o w - m o r t a li ty areas a n d 0. 3 i n h ig h - mortality areas, while 0.4 is used for all 4 a 1 s. n q x =1.0 for the last open-ended age group. nqx = ,n=the length of the interval, Mx =ASDR  

44. 2.nPx n p x is the probability of surviving between exact age x and x+n . It is the complement of nqx . Example: the probability of surviving between age 5 and 10 is given as  

45. 3.   The number of persons alive at exact age X. It is different from the function discussed, so that it refers exact age rather to an age interval. is an arbitrary number called Radix. It is usually 1000, 10,000, 100,000 ….etc. To calculate it is necessary first to choose a suitable radix. Then using n value = = = The number of persons alive at age 10 is given as =  

46. 4.   Is the number of persons dying between exact age X and X+n . It is just the difference between two Ix s. Or, = * n Example: To calculate the number of persons dying between age 10 and 15 . 5 = N.B for the last open ended age group, the number of persons dying is the same as the number alive at it start. = …. =  

47. 5.   Is the number of person-years lived between exact age X and X+n . Each person surviving through the interval contribute “n” pearson-years, While those who die during the interval will contribute only n* years. =n( + ) If , n=5  

48. 5.   If we used five age interval, the , n=5 , n=4 , n=1 N.B, for the last open ended age grouped data is obtained using ASDR. That is = / = / , = , It is best to estimate using model life table or a life table for a country with a similar level of mortality.  

49. 6.   It is the total number of person-years lived after exact age X. It is column cumulated from the bottom. = + The last age group , = The main purpose of this function is in the calculation of the next function that is the expectation of life.  

50. 7.   It is the expectation of life at age x or The average no. of life r emaining . It is the average number of years a person aged X has left to live. = =  

51. Example of abridged life table Calculate abridge life table for males in rural Ethiopia 1984 census. Assume closed migration, even death, and arbitrary radix 100,000.

52. Example of abridged life table Given males in rural area with in 4 digits Age group MYP Px Death Dx ASDR Mx Year lived ax No. of year interval “n” Probability of dying “ nqx ” 545203 41485 0.07609 0.3 1 0.0722 1-4 2330529 39888 0.01712 0.4 4 0.0658 5-9 2851420 14638 0.00513 0.5 5 0.0253 10-14 1810093 6259 0.00346 0.5 5 0.0171 ….. …… …….. …. …… … ….. …… …… …… ….. …. …… 75-79 110250 2132 0.01934 0.5 5 0.0922 80+ 213609 7133 0.0333 0.5 5 1.0000

53. Example of abridged life table Given with in 4 digits Age Interval Probability of dying “ nqx ” Probability of surviving “ nPx ” Survivors to exact age Ix No.of persons dying ndx Person –years lived nLx No.lived above Tx Expectation of life ex 0.0722 0.9278 100,000 7,220 94946 6216890 62.17 1 0.0658 0.9342 92,780 6,104 358917 6120500 65.97 5 0.0253 0.9747 86,675 2,192 427892 5761582 66.47 10 0.0171 0.9829 84,482 1444 …… ….. 63.13 ….. ….. ……. ….. …. …. …… …… 75 0.0922 0.9078 55,223 5091 263390 607332 11.00 80+ 1.0000 0.0000 50,131 50,131 343942 343942 6.86

54. Interpretation of a Simple Life Table T w o d i f fer e n t in t e r p r e t a t i on s d e p e n din g o n t h e interpretation given to the life table as a whole. 1. The life table is viewed as depicting the lifetime mortality experience of a single cohort of newborn babies… more common 2. The life table is viewed as a stationary population. In the 1 st interpretation, the cohort of newborn babies (radix) of the table, is usually assumed 100,000

55. Interpretation of a Simple Life Table x to x + n : period of life between 2 exact ages, e.g., “15–20” = 5-year interval between the 15 th & 20 th birthdays. n q x : p roportion of the persons in the cohort alive at the beginning age interval ( x ) who will die before reaching the end of that age interval ( x + n ). – Example : n q x in 15–20 is 0.0187 : i.e., out of every 100,000 persons alive and exactly 15 years old, 1870 will die before reaching their 20 th birthday.

56. Interpretation of a Simple Life Table I x : number of persons living at the beginning of the age interval ( x ) out of the total number of births assumed as the radix of the table. Example : Out of 100,000 newborn babies, 83,034 persons would survive to exact age 15. n d x : number of persons who would die within the age interval ( x to x + n ) out of the total number of births. Example : There would be 1,555 deaths between exact ages 15 and 20 to the initial cohort of 100,000 newborn babies.

57. Interpretation of a Simple Life Table n L x : nu m b er o f p e r s o n - y ears t h a t wo u l d b e li v e d within the age interval ( x to x + n ). Example: The 100,000 newborn babies would live 411,283 person-years between exact ages 15 and 20. Of the 83,034 persons who reach 15, the 81,479 who survive to age 20 would live 5 years each (81,479 x 5= 407, 395 person-years) The 1,555 who die would each live varying periods of time less than 5 years, averaging about 2.5 years: 1,555 x 2.5 = 3887.5 person-years == 3, 888 person years.

58. Interpretation of a Simple Life Table T x : total number of person-years that would be lived after the beginning of the indicated age interval. – Example: The 100,000 newborn babies would live 4,914,890 person-years after their 15 th birthday. e x : a v e r a g e re m a in i n g l i f e t i m e f o r a p er s o n who survives to the beginning of the age interval. E x a m pl e : A p er so n w h o r e a c h e s his/ h er 15 th birthday should expect to live 59.19 years more, on the average.

59. Other Examples Example one Construct abridge life table by sex in urban area of Ethiopia, 1984………. For male Assignment and female Example two Construct abridge life table by sex in rural area of Ethiopia, 1984 census. Only female ………….. Example three Construct abridge life table for single year in Ethiopia, 1984

60. Analysis of Socioeconomic Structure Types of Multiple Decrement Tables Multiple decrement tables incorporating conventional life table components and Using life table techniques have been employed in the analysis of various socioeconomic characteristics of the population. In particular, in the analysis of labor force , martial composition , and educational status.

61. Analysis of Socioeconomic Structure These tables may be constructed as multiple decrement tables. T here are two or more forms of exit from initial cohort. One of which is mortality and The other some change in social or economic status. Exit from non-working population, or entry into the labor force; exit from the single population.

62. Analysis of Socioeconomic Structure Another form of constructing the tables involves the use of prevalence rates . In which the life table stationary population is distributed into different statuses according to the prevalence of those statuses in the actual observed population. Commonly working life table and schooling-life table.

63. Working- life tables It has been prepared by combining mortality rates with labor force participation rates. It is useful in understanding the mechanisms and implications of changes in the labor force. It also indicate the average number of working years to be expected after a given age by all persons in the labor force attaining the age . Usefull for studying growth and change in the activity rates.

64. Working life tabel There are several ways to construct a complete working-life table. Assumptions Should be stationary population according to the work status of the actual population at the same age. Mortality rates of the general population and the labor force should be the same.

65. Cont…… The special columns Iwx * , Lwx * , Twx * , and ewx * represent the same functions as in a standard life table except that these columns refer to working life. This is indicated by the notation w. The functions Iwx *, ewx * and ex refer to exact age at each birth day. The rest of functions refer to age intervals between two exact age ages.

66. School-Life Tables Another type of multiple decrement life table is school life table. It combines mortality rates and school enrollment rates. It estimates the average number of years of school life for the total population and the enrolled population. This is indicated by the notation s.

67. Cont…… Tables Function Standard Life table Working life table Schooling life tabel Rate Mx Wx Sx 100,000 Lx Lx Lx Lwx / Lsx Mx *Lx Wx *Lx Sx *Lx nLx Lwx * Lsx * Ix Iwx * Isx * nTx Twx * Tsx * ex ewx * inactive years of life esx * Ax and Qx

68. Thank you