Incidence Density A cohort study (hypothetical) was conducted to look at survival after experiencing a myocardial infarction (heart attack). Ten participants were followed for 3 years, resulting in...

Advanced Epidemiology Methods: Measures of Occurrence and Association
Incidence Density
A cohort study (hypothetical) was conducted to look at survival after experiencing a
myocardial infarction (heart attack). Ten participants were followed for 3 years, resulting in
the following table:
Follow-up Time (Months) Event
3 Death
5 Censored
8 Death
12 Death
17 Censored
19 Censored
27 Death
32 Censored
36 Followed until end of study period
36 Followed until end of study period
1) What is the cumulative survival probability at the end of the follow-up period?
Solution:
The calculations for the cumulative survival probability at the end of the follow-up period are
shown in the following table:
Interval
(Start-
End)
(In
months)
People at
risk in the
beginning
of Interval
People
Died
during
the
Interval
People at
risk in the
end of
Interval
People
censored
during the
Interval
Proportion
Surviving
this
interval
Cumulative
Survival
Frequency
at the End
of Interval
0-3 10 1 9 0 9/10 = 0.9 0.9
3-5 9 0 9 1 8/9 = 0.89 0.89 × 0.9 =
0.8
5-8 8 1 7 0 7/8 = 0.875 0.88 × 0.9 ×
0.875 = 0.7
8-12 7 1 6 0 6/7 = 0.85 0.88 × 0.9 ×
0.875 ×
0.85 = 0.6
12-17 6 0 6 1 5/6 = 0.83 0.9 × 0.89 ×
0.875 ×
0.85 × 0.83
= 0.5
17-19 5 0 5 1 4/5 = 0.8 0.9 × 0.89 ×
0.875 ×
0.85 × 0.83
× 0.8 = 0.4
19-27 4 1 3 0 3/4 = 0.75 0.9 × 0.89 ×
0.875 ×
0.85 × 0.83
× 0.8 × 0.75
= 0.3
27-32 3 0 3 1 2/3 =0.67 0.9 × 0.89 ×
0.875 ×
0.85 × 0.83
× 0.8 × 0.75
× 0.67 = 0.2
32-36 2 0 2 0 2/2 = 1 0.9 × 0.89 ×
0.875 ×
0.85 × 0.83
× 0.8 × 0.75
× 0.67 ×
1.0= 0.2
This can be validated by directly calculating the no. of survivals at the end of the follow up
period. Two out of ten people survived and followed up till the end of follow up period.
Therefore, the cumulative survival probability =



Cumulative survival probability =


= 0.2
2) Using the same data, calculate the overall death rate per 100 person-years
Solution:
The death rate (in person-time frame) can be calculated by the following formula:
Death Rate =



Here,
Numerator = 4 (4 people have died during the follow-up period)
Denominator = 10 (total number of person observed is 10)
Therefore,
Death rate = 4/10 = 0.4 deaths per person-years
For 100 person-years,
Death rate = 0.4 × 100 = 40
Hence, the death rate would be 40 deaths per 100 person-years.
3) Calculate the rates separately for the 3 years of follow-up.
Solution:
For 1st year:
Death Rate =



Here,...