community medicine/vital stat

1. By- Dr. Saurav Kumar

2.  How Long will I live????
 How long do we live????

3. Brief Overview
 Edmond Halley was the first person to show us how to properly calculate
and construct life table.
 Life table tell us how long people live on an average
 It converts a cross sectional information into a longitudinal cohort
information

4.  Average life spam: How long do we live
 Suppose we have a population of 10 people and we follow them till they all
die
 1,2,10,20,35,45,50,60,70,80
 So the average life span is
1+2+10+20+35+45+50+60+70+80 =37.3
10

5. Definition
 A life table comprises of a set of values showing how a
group of infants born on the same day and living under
similar conditions would gradually die out. In other
word a life table summarise the mortality or longevity of
any cohort.

6. LIFE TABLE
 It is a special kind of table to calculate life expectancy at birth & subsequent
ages respectively.
 It is the tabular display of life expectancy & probability of dying at each age
(or age group) for a given population , according to the age-specific death
rates.
 Life table (also called a mortality table or actuarial table) is a table which
shows, for age, what the probability is that a person of that age will die before
his or her next birthday ("probability of death").

7. • From this starting point, a number of inferences can be
derived-
– The probability of surviving any particular year of age
– Remaining life expectancy for people at different ages

8.  It can answer the question of the chance of survival after being diagnosed
with the disease or after beginning the treatment
 The event can be any other health event—not just death− It can be relapse,
receiving organ transplant, pregnancy (in a study of infertility), failure of
treatment, recovery, etc.
 We can use life tables for other vital events like natality, reproduction,
chances of survival.

9. Types of life tables
 Period or static life tables show the current probability of death (for people
of different ages, in the current year)
 Cohort life tables show the probability of death of people from a given
cohort (especially birth year) over the course of their lifetime.
 Complete vs Avridge
 Multiple decremental tables
 Incremental – Decremental life table

10. Cohort Vs Period
Cohort Period
The cohort life table presents the
mortality experience of a particular
birth cohort
The period life table presents what
would happen to a hypothetical
cohort if it experienced throughout
its entire life
All persons born in a year

11. Complete vs Abridge
Complete Abridge
A complete life table contains data
for every year of age
Typically contains data by 5-10
year age interval
In India 5 year interval is selected

12. Single decremental vs Multiple
decremental
Alive Alive
Death Death Death
Death

13. Icremental- Decremental
married
Divorced
Single Widowed
Death

14. Construction of life table
To construct a life table, two things are
required
1. Population living at all individuals
ages in a selected year
2. Number of deaths that occurred in
these ages during the selected year

15. Example
 A group of 200 subjects were followed for three years
 Deaths (events) occurred throughout the three years
 What is the chance of surviving at the end of the three years?

16. Following a Population

17. Clinical Life Table Notation
 lt = number alive at the beginning of
time t
 dt = number of deaths during the time
interval

18. Apply Notation
 Apply notation to the table in the example

19. Fill in the “Number at Beginning”
Column- Fill in the missing cells
200-20=180
180-30=150
180
150
q t = d t/l t
p t =1-q t

20. Clinical Life Table Notation
 l t= number alive at the beginning of
time t
 d t= number of deaths during the time
interval
 q t = d t/l t = probability of dying during
the time interval
 p t =1-q t = probability of surviving in
the time interval

21. Calculate Probabilities of Dying
(q) and Surviving (p)

22. Clinical Life Table Notation
Pt = cumulative probability of surviving at the
beginning of the time interval
= cumulative probability of surviving at the end
of the previous interval
- At the beginning of the study (zero time),
- P(1) = 1.0
- P(t+1) = pt ∗ Pt

23. Calculate the Cumulative
Probabilities of Surviving (P)

24. Uses
 To determine expectation of life – imp. Health status indicator.
 Useful to analyse the number of survivors at different age groups
- At age 5 to find no. of children likely to enter primary school.
- At age 18 to find no. of person who become eligible for voting etc.

25.  To find mortality of given population – for international comparison.
 By modified life table technique , we can find the survival rate after treatment
in chronic diseases.
 To compute insurance premium & annuities.

26. Construction of life table & its properties
 Life table are constructed after each census.
 We usually follow a cohort of 1,00,000 newborn babies & follow them
through various ages(0, 1,5,15…)till all die.
Requirements
 Age- specific death rates of a given population during the selected year.
 Population living at all ages for the selected year.

27. Age
interval
Age-
sp.
Death
rates
No.
living
‘lx’
No.
dying
‘ndx’
‘nlx’ ‘Tx’ Avg
remaining
life ‘ex’
0- 1 68.9 100000 6890 94832 5978010 59.87
1-5 21.1 93110 2110 36822
0
5883178 63.18
5-10 10.42 91000 1042
10-15
14922
5
246724
75+ 249.9 97499 97499

28.  First column – age interval( 0-1, 1-5)
 Second column – age specific death rates/ 1000 population.
 Third column ‘lx’ – No. of individuals alive at their nth birthday.
 Fourth column ‘ndx’– No. of individuals dying during the age interval for
1,00,000 population who were born alive.
Age
interval
Age-
sp.
Death
rates
No.
living
‘lx’
No.
dying
‘ndx’
‘nlx’ ‘Tx’ Avg
remaining
life ‘ex’

29.  5th column ‘nlx’ – total no of person-years lived by the cohort at each age.
 6th column ‘tx’ – total no. of person-years lived after exact age x, the last
value of nlx is written in last row of tx.
 7th column ‘ex’- expectation of life at age x
ex = tx / lx,
at birth = 5978010/100000 = 59.78.
Age
interval
Age-
sp.
Death
rates
No.
living
‘lx’
No.
dying
‘ndx’
‘nlx’ ‘Tx’ Avg
remaining
life ‘ex’

30. Interpretation
1.Avg. remaining life( exp. of life at birth) is used to describe health status of
the population.
- for international comparison.
2. In our life table , it is shown that expectation of life at one year(63) is more
than that at birth(59).

31. 3. Using life table we are able to predict the chance that an
individual will live to a particular age.
- l5/ l0 = 91000/100000 = 0.91= 91%
probability of surviving for a person in this cohort upto
5yrs is 91%.
4. LIC people commonly use life table for computing life
insurance premium.
5. Years of potential life lost ( YPLL), DALYs, QALYs

32. Application to health problems
 Comparison of communities.
 Analysis by cause of death.
 Population problems
 Morbidity analysis
 Hospital studies
 Clinical medicine.

33. Survival Analysis

34. OUTLINE
 What is Survival Analysis?
 Censored Data
 Kaplan-Meier Estimator
 Log-Rank Test
 Cox Regression Model

35. WHAT IS SURVIVAL ANALYSIS?
 Branch of statistics that focuses on time-to-event data and their
analysis.
 Survival data deals with time until occurrence of any well-defined
event.
 The outcome variable examined is the survival time
 Special because it can incorporate information about censored data
into analysis.

36. OBJECTIVES OF SURVIVAL
ANALYSIS?
 Estimate probability that an individual surpasses
some time-to-event for a group of individuals.
◦ Ex) probability of surviving longer than two
months until second heart attack for a group of MI
patients.
 Compare time-to-event between two or more groups.
◦ Ex) Treatment vs placebo patients for a
randomized controlled trial.
 Assess the relationship of covariates to time-to-event.
◦ Ex) Does weight, BP, sugar, height influence the
survival time for a group of patients?

37. SITUATIONS WHEN WE CAN USE SURVIVAL
ANALYSIS
 We can use survival analysis when you wish
to analyze survival times or “time-to-event”
times
 “Time-to-Event” include:
◦ Time to death
◦ Time until response to a treatment
◦ Time until relapse of a disease
◦ Time until cancellation of service
◦ Time until resumption of smoking by
someone who had quit
◦ Time until certain percentage of weight loss

38. MORE EXAMPLES
 Suppose you wish to analyze the time it takes for a student
to complete a series of classes.
◦ Response /Status Variable: Time it takes to complete,
status
◦ Predictor Variables: Age, Gender, Race, GPA
 Suppose you are interested in comparing the time until you
lose 10% body weight on one of two exercise programs.
◦ Response/Status Variables: Time it Takes, Status
◦ Predictor Variables: Age, Gender, Starting Weight,
BP, BMI, Exercise Program

39. DATA
 Survival data can be one of two types:
◦ Complete Data
◦ Censored Data
 Complete data – the value of each sample unit is observed
or known.
 Censored data – the time to the event of interest may not be
observed or the exact time is not known.

40. CENSORED DATA
 Censored data can occur when:
◦ The event of interest is death, but the patient is still alive at the time of
analysis.
◦ The individual was lost to follow-up without having the event of
interest.
◦ The event of interest is death by cancer but the patient died of an
unrelated cause, such as a car accident.
◦ The patient is dropped from the study without having experienced the
event of interest due to a protocol violation.

41. Thank you