1. Lecture 3: Measuring the Occurrence of Disease
Reading:
Gordis – Chapter 3
Lilienfeld and Stolley –
Chapter 4
Chapter 6, pp ,

2. Counting cases
One’s knowledge of science begins when he can measure what he is speaking about and express it in numbers Lord Kelvin ( )
To examine the transmission of disease in human populations, we need to be able to measure the frequency of disease occurrence and of deaths from the disease.

3. Measures
How do we express the extent of morbidity and mortality resulting from disease?
Counts
Ratio
a fraction with no specified relationship
Proportions
what fraction of the population is affected
Rates
how fast things are occurring

4. Measures Measures of morbidity Prevalence: a proportion
Cumulative incidence: a rate
Incidence density: a rate
Measures of mortality
Mortality rate: a rate
Standardized mortality (SMR)

5. Defining case Natural course of disease
Exposure  onset  symptoms  dx  outcome
Recovery
Death
Chronic disease
Incubation
period
Clinical
Stage
Subclinical
Stage

6. Counts Prerequisite for epidemiologic investigation
Simplest measure of disease frequency
Frequency of affected individuals
Useful for planning adequacy of health care allocation at a particular level
For example:
Number of West Nile virus cases

7. Ratio
A fraction with no specified relationship between numerator and denominator
Range: 0 to 
A/B
Examples
sex ratio (M:F)

8. Ratio Number of men with syphilis, 1991 2,412
Number of women with syphilis. 1991
2,314
Ratio of male to females
2,412/2,314 = 1.04
(The numerator is not included in the denominator)

9. Proportion Type of ratio Numerator included in denominator
May be expressed as percentage
Percentage = proportion x 100 %
Range: 0 to 1
A/(A+B)
Example
Prevalence

10. Prevalence All individuals with a disease at a given point in time
Dimensionless - should not be described as a rate - may be described as a percent
number of cases (A) today
P =
total population (A+B) today

11. Prevalence
Proportion of individuals in a population who have the disease or condition of interest at a specific time period
Utility
Describe health burden of a population
Status of disease in a population
Estimate the frequency of exposure
Project health care needs of affected individuals

12. Types of prevalence
Point prevalence – proportion of all cases at a specific point in time
Period prevalence – proportion of all cases during a period of time

13. Point and period prevalence
Point prevalence
Do you currently have asthma?
Period prevalence
Have you had asthma during the last five years?
Every person in the numerator had the disease at some time during the period specified.
Period prevalence consists of the point prevalence at the beginning of a specified period of time plus all new cases that occur during that period.

14. Rate A special type of proportion Unit of time in denominator
A/(A+B) per time interval
Always two components:
New cases and time

15. Incidence Incidence is an important rate…
It is the proportion of people (at risk) who develop diseased during a specific time period.
Three key elements:
Only new cases included in numerator
Total population at risk in the denominator
Time element – period over which new cases developed
Two main types of Incidence:
Cumulative Incidence
Incidence Rate (a.k.a. incidence density)

16. Cumulative Incidence
One of the most widely used measures of disease risk.
Estimate of probability (risk) that an individual will develop disease during a specified period of time
Cumulative Incidence =
No. of new cases in a given period of time
No. of people at risk during that time

17. Incidence rate (incidence density)
Cumulative Incidence gives each individual equal weight, but different people stay in the study for different length- having different contribution.
Measure of the true rate of disease development
Incidence rate =
No. of new cases in a given period of time
total person-time of observation

18. Person-time 5-year (1/95-1/00) Incidence rate
1/96
1/97
1/98
1/99
1/00
Total A 3 B C 5 D 1 E 4
Total years at risk
• = enter the study, X = having disease,
 loss to follow-up 16 x  x x x
5-year (1/95-1/00) Incidence rate
= 2/16 = 12.5/100 person-years of observation

19. Prevalence vs. incidence
1/95
1/96
1/97
1/98
1/99
1/00 A B C D E
• = enter the study, X = having disease,
 loss to follow-up, disease developing x  x x x
1/97-1/00 cumulative incidence cases: A, E
1/97-1/00 period prevalence cases: A, D, E
1/98 point prevalence: A, D

20. Relationship between prevalence and incidence
Incidence is a proxy for “risk”, whereas prevalence is best for assessing disease burden or case load in a geographic area.
There is a well known relationship between them, namely –
Prevalence = Incidence x Duration of disease
P = I x D

21. + Incident cases Whole population at time t
Prevalent cases
Prevalent cases
Prevalent cases
Minus
cures or deaths due to disease
Prevalent cases

22. Examples of P = I x D
If the incidence of diabetes mellitus is 1% per year and its approximate duration is 5 years, then what is its expected point prevalence?
Assuming equal incidence of disease, which is more prevalent: pancreatic cancer or brain cancer?
Average duration of pancreatic cancer = 3 months
Average duration of brain cancer = 1.5 years

23. Measures of mortality Annual mortality rate from all causes =
Total no. of death from all causes in 1 year
No.of people in the population at midyear
Case-fatality rate =
No. of individuals dying during a specified period of time after disease onset
No. of individuals with the specified disease

24. Three common forms of rates
Crude rates
e.g. crude birth rate, crude death rate
Specific rates
e.g. sex-specific, age-specific, race-specific
Adjusted rates
e.g. age-adjusted

25. Crude rate: example
Suppose County B recorded 4000 births and 1500 deaths in Using U.S. Census data, we find that the population size is 200,000.
Crude birth rate =
No. of live births in time interval T
Total population
= 4,000/200,000 = 20 births per 1,000
Crude death rate =
No. of deaths in time interval T
= 1,500/200,000 = 7.5 deaths per 1,000

26. Specific Rates for Mortality in Older Adults
Rates for selected leading causes of death among older adults, by sex, and race -- United States, 1996*
Sex Race
Cause of death† Total Male Female White Black
Heart disease , , , , ,937
(612,199)
Malignant neoplasms , , , ,338
(382,988)
Cerebrovascular diseases
(140,448)
* MMWR Dec 17, 1999 / 48(SS08);7-25

27. How do we compare rates across populations?
Crude rates are not helpful because …
Populations differ in their age distributions
Populations differ in their racial distributions
Populations differ in their SES distributions

28. How do we compare rates across populations?
We compare rates across populations by putting them on an even playing field -
that is, we either standardize one population on another or
we use an outside standard and adjust our populations to that standard.

29. For our purposes, the most important is age-adjustment
Two types of age-adjustment
Direct Method
Indirect Method (SMR = standard mortality ratio)

30. Direct method: example
Population A Population B
AGE N Risk Cases N Risk Cases
<
>
CRUDE RISK = 250/800 = 31% 130/800 = 16%
Crude risk indicates different risks of disease between populations.
But age-specific rates indicate similar risks.

31. Direct method: example
Using the total of the two populations as the standard population
Population A Population B
AGE Std. Risk Cases Std. Risk Cases
pop. pop.
<
>
AGE-ADJUSTED RISK = 24% 250/800 = 24%

32. Direct method: example
Apply risks in population B to population A (using population A as the standard population.
Population A Population B
AGE Std. Risk Cases Std. Risk Cases
pop. pop.
<
>
AGE-ADJUSTED RISK = 31% 250/800 = 31%

33. Direct method
What information is needed to calculate age-adjusted death rate, using the direct method?
Standard population distributed by age
Age-specific death rates in study populations
The actual value of an age-adjusted rate is meaningless because it depends on the choice of the standard population.
It is only meaningful in comparison to other rates which have been adjusted by the same method and the same standard population.

34. Indirect method Apply rates from a standard population
to each age stratum in the study population
to obtain expected number.
This adjusted rate interpreted as:
the rate that would have been experienced by the study population if their rates had been similar to the standard population.

35. Standardized mortality ratio (SMR)
Observed number of cases per time
Expected number of cases per time
SMR = 0
indicates observed is not unusual
SMR > 1.0
indicates morbidity (or mortality) exceeds expected
SMR = 2.0 indicates two-fold increase
SMR < 1.0
indicates morbidity (or mortality) is less than expected

36. SMR: example- death in white miners
Est. pop. of white miners
Death rate in general pop.
Expected death
Observed death
Age
(1)
(2)
(3)=(1)X(2)
(4)
20-24
74598
12.26
9.14 10
25-29
85077
16.12
13.71 20
30-34
80845
21.54
17.41 22
35-44
148870
33.96
50.55 98
45-54
102649
56.82
58.32
174
55-59
42494
75.23
31.96
112
Total
534533
181.09
436
SMR = 436/ = 2.41

37. SMR disadvantage
SMR produces a ratio instead of a rate. It gives relative information but does not describe the mortality in the population.
SMR depends on the choice of the standard population.