Life table and survival analysis 04122013

community medicine/vital stat

1. LIFE TABLE AND SURVIVAL ANALYSIS 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 Population living at all individuals ages in a selected year 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 l t = number alive at the beginning of time t d t = 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 P t = 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) = p t ∗ P t

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 368220 5883178 63.18 5-10 10.42 91000 1042 10-15 149225 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. 5 th column ‘ nlx ’ – total no of person-years lived by the cohort at each age. 6 th column ‘ tx ’ – total no. of person-years lived after exact age x, the last value of nlx is written in last row of tx . 7 th 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