1. Main Points to be Covered
Incidence versus Prevalence
The 3 elements of measures of incidence
Cumulative vs. person-time incidence
Calculating cumulative incidence by the Kaplan-Meier method
Calculating cumulative incidence by the life table method

2. Prevalence versus Incidence
Prevalence counts existing disease diagnoses, often at a single point in time
Incidence counts new disease diagnoses during a defined time period

3. Prevalence: 3 types
Point prevalence - number of existing cases at one point in time divided by population
Period prevalence - number of existing cases in a time interval (eg, one year) divided by population
Cumulative (lifetime) prevalence - proportion of people who have had the outcome at any time in the past

4. The Three Elements in Measures of Disease Incidence
E = an event = a disease diagnosis or death
N = number of persons in the population in which the events are observed
T = time period during which the events are observed

5. Disease Occurrence Measures: A Confusion of Terms
Terminology is not standardized and is used carelessly even by those who know better
Key to understanding measures is to pay attention to how the 3 elements of number of events, number of persons at risk, and time are used
Even the basic difference between prevalence and incidence is often ignored

6. HIV/AIDS infection rates drop in Uganda Kyodo News Service KAMPALA, Sept. 10 (Kyodo) - Infection rates of the HIV/AIDS epidemic among Ugandan men, women and children dropped to 6.1% at the end of 2000 from 6.8% a year earlier, an official report shows. The report, compiled by the Ministry of Health together with the World Health Organization and the Medical Research Council of Britain, says the results were obtained after testing the blood of women attending clinics in 15 hospitals around the country. The ministry deduced the figures for men and children from the blood tests on women, according to the report. The report says the average rate of infection for urban areas fell from 10.9% to 8.7%. In rural areas, the average was 4.2%, not much different from the 4.3% average a year earlier. The highest infection rate of 30% was last reported in western Uganda in 1992.

7. The word “rate” should be avoided
when existing cases at one point in
time are what was measured.
Although you may encounter “prevalence
rate,” rate should be reserved for
measuring incidence.
In general a rate is a change in one
measure with respect to change in a 2nd

8. Measures that are sometimes loosely called Incidence
Count of the number of events (E)
eg, there were 84 traffic fatalities during the holidays
Count of the number of events during some time period (E/T)
eg, traffic accidents have averaged 50 per week during the past year
Neither explicitly includes the number of persons (N) giving rise to the events

9. Two Measures Described as Incidence in the Text
The proportion of individuals who experience the event in a defined time period (E/N during some time T) = cumulative incidence
The number of events divided by the amount of person-time observed (E/NT) = incidence rate or density (not a proportion)

10. E/N E
E/T
E/NT

11. Cumulative Incidence
Perhaps most intuitive measure of incidence since it is just proportion of those observed who got the disease
Proportion=probability=risk
Basis for Survival Analysis
Two primary methods for calculating
Kaplan-Meier method
Life table method

12. Survival Analysis
Data analysis for which the outcome is time to an event
The time variable is usually called survival time
The outcome event is usually called a failure (normally an adverse event but it doesn’t have to be)
Cumulative incidence is the complement of cumulative survival (1 - cumulative survival)

13. Calculating Cumulative Incidence
With complete follow-up cumulative incidence is just number of events (E) divided by the number of persons (N) = E/N
Rarely have equal follow-up on everyone so need to account for different follow-up times
Can be due to losses to follow-up
Can be due beginning follow-up at different times

14. Cumulative Incidence in the Setting of a Cohort Study
If number of events (E) for all 1000 is known, cumulative
incidence is just E/ But 7 persons left the cohort.

15. Cumulative incidence with Kaplan-Meier estimate
Set in a cohort
subjects have different starting dates
subjects have different amounts of follow-up time
Requires date last observed or date outcome occurred on each individual (end of study can be the last date observed)
Analysis is performed by dividing the follow-up time into discrete pieces
calculate probability of survival at each event

17. 3 Ways Censoring Occurs 1) Death (if death is not the study outcome)
2) Loss to follow-up (refuse, move, can’t be found)
3) End of study observation (if still alive and haven’t experienced outcome)
Each subject either experiences the outcome or is censored in a survival analysis

18. c

19. Calculating Cumulative Incidence
Probability of two independent events occurring is the product of the two probabilities for each occurring alone
eg, if event 1 occurs with probability 1/6 and event 2 with probability 1/2, then the probability of both event 1 and 2 occurring = 1/6 x 1/2 = 1/12
Conditional probability of living to time 2 given that one has already lived to time 1 is independent of the probability of living to time 1

20. Cumulative calculated by multiplying probabilities for each
prior failure time: e.g., 0.9 x x = and
0.9 x x x x x = 0.180

21. Graphical representation of K-M survival
analysis (survival curve with discrete steps)

22. Kaplan-Meier Cumulative Incidence of the Outcome
Cannot calculate by multiplying each event probability (=probability of repeating event)
(in our example, x x x x x = )
Obtain by subtracting cumulative probability of surviving from 1; eg, ( ) = 0.82
Since it is a proportion, it has no time unit connected to it, so time period has to be added; e.g, 2-year cumulative incidence

23. Kaplan-Meier using STATA
Need a data set with one observation per person.
Each person either experiences event or is censored.
Need a variable for the time from study entry to date
of event or date of censoring (time variable=timevar).
Need a variable indicating whether follow-up ended with
the event or with censoring (failure variable=failvar)

28. Two assumptions in survival analysis
Censoring is unrelated to survival (unrelated to the probability of experiencing the outcome)
There are no temporal trends in the probability of the outcome

29. Life table method of estimating cumulative incidence
Key difference from Kaplan-Meier is that probabilities are calculated for fixed time intervals, not at the exact time of each event
Fixed time intervals can vary in length but are often uniform
Probability of surviving each fixed time interval is calculated
Cumulative survival is product of probabilities from each prior time period

30. Life table method of estimating cumulative incidence
Since exact event times not used, assumption that events and censoring occur uniformly during the fixed time intervals
Calculations are based on assigning censored individuals follow-up for half of the time period (follows from uniformity assumption)
Subtract one-half of subjects lost during interval from denominator at interval beginning

31. 6 deaths
in 2 years;
3 censored
before 2
years of
follow-up c

32. Example of Life Table Calculation from the Text Data
Taking the full 2-year period as one interval:
6 deaths in the numerator and 10 (initial number) minus
0.5 x 3 censored persons in the denominator = 6 / 8.5
= 0.71, the cumulative probability of death
( ) = 0.29, the cumulative probability of survival
(NB - text gives this incorrectly as 0.39)
Note this differs from the Kaplan-Meier cumulative
survival estimate of 0.18

33. Example of Life Table Calculation Using Two One-Year Intervals
Taking two 1-year time intervals:
First year: Starts with 10 at risk, 3 deaths, 2 censored, probability of survival is 7 / x 2 = 7/9 = 0.777
Second year: Starts with 5 at risk, 3 deaths, 1 censored,
probability of survival is 2 / x 1 = 2/4.5 = 0.444
Cumulative probability of survival = x = 0.345
This differs from both the Kaplan-Meier estimate and the life table using only one 2-year interval.

34. Life Table Method
Can see from inspecting the data used in the text that for these 10 observations the life table uniformity assumption doesn’t hold
Life table more commonly used on large secondary data sets where information on exact failure times are not available
With very large numbers the uniformity assumption is more likely to be valid

35. Life Table of Breast Ca Survival

36. Summary Points
Prevalence counts existing cases and incidence counts new cases
Word “rate” is very loosely used
Two main types of incidence rate
incidence based on proportion of persons
incidence based on person-time
Kaplan-Meier or life table method of estimating cumulative incidence assume losses unrelated to outcome probability and that there are no temporal trends in outcome probability