Survival Analysis

1. Short Talk : Life Table &Kaplan-Meier Method
PG Student : Dr.Pravin
PG Guide : Dr.Todkar sir
Activity Guide : Dr.Jatti sir

2. Purpose
1.There has been short notes on Life Tables
& Kaplan-Meier Method in PG exams
2. Short Talk is presented so that all the
PGs will be well acquainted with topic

3. Contents :
1.Introduction – Natural history of disease
2. Five approaches of expressing prognosis
3.Life Tables
4.Kaplan-Meier Method

4. Natural History of Disease
The disease results from complex interaction
between man, an agent ( or cause of disease )
and environment
Natural history of disease signifies the way in which
a disease evolves over time from the earliest stage of
its prepathogenesis phase to termination as recovery,
disability or death ,in the absence of treatment or
prevention
It is described as consisting of two phases :
Prepathogenesis (i.e. Process in environment ) &
Pathogenesis ( Process in man ) .

5. 1. Prepathogenesis Phase : In this phase the disease
agent has not entered the human ,but factors favouring
its interaction with human host are already existing in
the environment.
2. Pathogenesis phase begins with the entry of
disease agent in the susceptible human host .
 In case of infectious diseases, the agent multiplies &
induces tissue physiological changes ,the disease
progresses through period of incubation later through
early & late pathogenesis .
The final outcome of disease may be recovery
disability or death.

6. NATURAL HISTORY OF DISEASE

8. Natural history of disease in quantitative terms :
Importance :
1.To describe severity of disease to establish
priorities for clinical services & public health
programmes .
2.Quantification is important to establish baseline for
natural history , so that as new treatments become
available, the effects can be compared.
3. It is important to identify different treatments
or management strategies for different stages of
disease.
4. Patients are often concerned about prognosis.

10. • Five approaches of expressing prognosis
• I. Case-fatality
• II. 5-year survival
• III. Observed Survival
• IV. Median survival Time
• V. Relative survival

11. Case- Fatality:
• It is defined as the number of people who die of
disease by number of people who have the disease
• Case Fatality = No. of people who die of disease/
No. of people who have disease× 100

12. Person years
It is total sum of number of years that each member
in study population is under observation.
The individuals are observed for different periods of
time ,the unit used for counting the observation time
is person –year.

18. Person years :
• Limitations: person –years : Each person year is
assumed to be equivalent to every other person year
(i.e. the risk is same in any person- year observed )
• Despite this issue , Person –years are useful as
denominators of rates of events in many situations,
as randomized trials , cohort studies

19. Five-Year Survival
The 5 –year survival is the percentage of patients
who are alive 5 years after treatment begins or 5
years after diagnosis.

23. Median Survival Time:
 It is defined as the length of time that half (50%) of
the study population survives.
Mean survival time is average of survival times
Advantages:
Median survival time is less affected by extremes ,
where as mean survival times can be significantly
affected by even single outlier
In case of median survival , we would only have to
observe the deaths of half of the group under
observation & in case mean survival have to
observe all deaths in study population.

24. Relative survival:
 It is defined as the ratio of observed survival in
people with the disease to expected survival if the
disease were absent.

25. Life Tables (Observed survival )
• The actual observed survival of patients
followed over time, based on knowledge
the interval within which event has
occurred.
• Life Tables are used for this purpose
• It is peculiar type of cohort analysis.

26. Hypothetical study of Treatment results (2000-2004)
Followed to 2005 ( None lost to Follow –Up)
Yr of
Treat
ment
No. of
Patients
treated
NO. ALIVE ON ANNIVERSARY OF TREATMENT
2001 2002 2003 2004 2005
2000 84 44 21 13 10 8
2001 62 31 14 10 6
2002 93 50 20 13
2003 60 29 16
2004 76 43

27. • Survival analysis in Patients Treated (2000-2004)
Yr of
Treat
ment
No. of
Patients
treated
NO. ALIVE AT END OF YEAR
1st Yr 2nd Yr 3rd Yr 4th Yr 5th Yr
2000 84 44 21 13 10 8
2001 62 31 14 10 6
2002 93 50 20 13
2003 60 29 16
2004 76 43
Total 375 197 71 36 16 8

28. Probability Of Survival For Each Year Of The Study
Total no. of patients who were alive 1 year after initiation of
treatment / Total number of patients who started treatment
1. Probability of Surviving 1st year (P1)
= 197/375 =0.525
2. Probability of Surviving 2nd year (P2)
= 71/197-43 = 0.461
3. Probability of Surviving 3rd year (P3)
= 36/71-16 = 0.655
4. Probability of Surviving 4th year (P4)
= 16/36-13 = 0.696
5. Probability of Surviving 5th year (P5)
= 8/16-6 = 0.800

29. Cumulative Probabilities of Surviving Different
Lengths of Time :
1. Probability of Surviving 1 year
= P1 = 0.525 = 52.5 %
2. Probability of Surviving 2 years
= P1×P2 =0.525×0.461 = =0.242
3.Probablity of Surviving 3 years
= P1×P2×P3 = 0.525×0.461×0.655 =0.159
4.Probablity of Surviving 4 years
= P1×P2×P3×P4 = 0.525×0.461×0.655×0.696 =0.800
5. Probability of Surviving 5 years
= P1×P2×P3×P4×P5 = 0.525× 0.461× 0.655 ×0.696
×0.800 = 0.088

30. • Survival curve for hypothetical example of patients
treated from 2000-2004 & followed until 2005

32. Calculating Life Table
Interval
since
beginning
treatment
Alive at
begining
of
interval
Died
during
interval
Withdrew
during
interval
No.at
risk of
dying
during
interval
Col 2-
1/2 col4
Proportion
who died
during
interval
Col3/col5
Proportion
who
didn’t die
during
interval
1- Col.6
Cumu
lative
surviv
al
x IX dx Wx I’x qx px Px
1st yr 375 178 0 375 0.475 0.525 0.525
2nd yr 197 83 43 175.5 0.473 0.527 0.277
3rd yr 71 19 16 63 0.302 0.698 0.193
4th yr 36 7 13 29.5 0.237 0.763 0.147
5th yr 16 2 6 13 0.154 0.846 0.124

33. • Life Table uses :
1.Finding out expectancy of life at birth or any age
2.Estimating no. of males who can marry and hence
become target group for family planning methods
Similarly number of children requiring high school
education facilities , number of old people requiring
social support can be estimated
3.Life insurance companies to fix their premiums
and polices.
4.Estimating survival rates after radiotherapy or
neurosurgery or anti malignancy treatment in the
patients

34. Kaplan –Meier Method
Kaplan –Meier method also known as product limit
method is statistical method used in analysis of time
to event data
Kaplan –Meier method is simplest way of
computing the survival over time in spite of all
difficulties associated with subjects or situations
It is one of the best options to be used for measuring
the fraction of subjects living after treatment

35. In the Kaplan-Meier method predetermined intervals
,as done in Life tables, are not used.
The exact point in time when each death or the
event of interest, occurred is identified so that each
death or event terminates the previous interval &
new interval is started & For this new row is used
in the Kaplan- Meier table.
 Survival probability for each time interval is
calculated as the number of subjects surviving
divided by number of patients at risk .

36. • Hypothetical example of study of six patients
analyzed by Kaplan-Meier method

37. • Calculating Survival Using Kaplan-Meier Method
Times to
Deaths
from
starting
Rx
(Months
)
No. Alive
at Each
Time of
death(Inclu
ding those
who died at
that time)
No .
Who
Died at
Each
Time
Proportion
who died
at That
Time
(Col.3/Col.2 )
Proportion
who
survived at
That Time
(1-Col.4)
Cumulativ
e
survival
4 6 1 0.167 0.833 0.833
10 4 1 0.250 0.750 0.625
14 3 1 0.333 0.667 0.417
24 1 1 1.000 0.000 0.000

39. Kaplan- Meier Method uses :
• It is used to estimate survival function based on time
to the occurrence of the event
• Life tables are less commonly used nowadays and
have been replaced with the Kaplan-Meier method.

40. Assumptions made is using Life tables &
Kaplan-Meier Method
There has been no change in the effectiveness of
treatment or in survivorship over calendar time.
Participants are lost to follow up. If large proportion
of the study population is lost to follow up, the
findings of study will be less valid
Third assumption is related with use of
predetermined intervals as in case of traditional life
tables

41. • References :
• 1.Gordis Epidemiology
• 2.Park’s Textbook of Preventive & Social Medicine

42. Thank You