M2 Medical Epidemiology
How to Fairly Compare
Disease Frequencies Between
Groups
How to Fairly Compare Disease
Frequencies Between Groups



Simple epidemiologic indices: review/summary
Interpreting epidemiologic comparisons:
overview
– chance
– bias
– confounding
Adjustment of epidemiologic indices for
confounding
– direct
– indirect
Simple epidemiologic indices: review/summary
Questions:

What fraction of a group has the condition
now?

What fraction of the community carries the
condition at any one time?

What is the endemic level of the condition,
relative to the size of a community?

What fraction of UI students has hay fever
now?
Simple epidemiologic indices: review/summary
Answer:



Point prevalence, or prevalence for short.
A dimensionless proportion.
Sometimes erroneously called “prevalence
rate”
Simple epidemiologic indices: review/summary
Questions:

What is the cumulative risk (probability) of
developing a condition at least once during a
fixed time period?

What fraction of a group can we predict will
have developed a condition over a given time
period, or during an epidemic?

Why must I take this medicine, doctor? What
are my chances of a heart attack in the next
ten years, if I don't?
Simple epidemiologic indices: review/summary
Answers:
Cumulative incidence

A dimensionless proportion

Called the attack rate when describing
infectious disease outbreaks,
– e.g., The attack rate in the county during the West
Branch hepatitis outbreak was estimated as 6.5%=65
cases/1000 population.

One women in 11 (9%) is expected to develop
breast cancer during her lifetime.
Simple epidemiologic indices: review/summary
Questions:




How strong is the process causing new cases?
How many new cases occur per person per unit
time, or other unit of experience (e.g., per
passenger-trip, per passenger-mile traveled)?
How many new cases of esophageal cancer
occur in Illinois/1000 population per year?
How many ruptured spleens occur from
automotive accidents in Illinois, per million
person-miles traveled?
How many new HIV infections occur per 1000
acts of vaginal intercourse? Of anal intercourse?
Simple epidemiologic indices: review/summary

Answer:
Incidence density (rate, dimension = new
cases per unit of experience, such as personyear, passenger-mile, sexual acts)
– e.g. 5 new cases per 1000 persons per year =
– 5 new cases per 1000 person-years =
– .005 new cases per person per year

Units = e.g.
– New cases / [persons x years]
– New cases / million passenger-miles
– New cases / 100 sexual acts
Simple epidemiologic indices: review/summary
Examples:
Mortality rate: The death density, i.e. the
incidence density of death.
For political units in which records are kept
routinely and where the population size may
be constantly changing, often calculated
using the mid-year population as
denominator.
The mid-year population approximates the total
person-years exposure in the population for
the full year.
10
Simple epidemiologic indices: review/summary
Examples:
Case-Fatality rate: The cumulative incidence
of death due to a disease, during the course
of the disease.

i.e. the fraction of cases which result in death
from the illness.

Equivalently, the chance of dying from a case
of the disease.
Case Fatality Rate





The cumulative incidence of death due to a
disease, during the course of the disease.
i.e. the fraction of cases which result in death
from the illness.
Equivalently, the chance of dying from a case
of the disease.
Number of deaths from a specific
disease/number of cases of the disease.
Usually overestimates. Why?
Simple epidemiologic indices: review/summary
Type of
incidence
Numerator
Cumulative
Density
Number of new cases
Denominator Population at risk at Person-years at risk, sometimes
beginning of interval approximated by population at
risk at midperiod
Assumptions Constant population Constant risk over observation
observed over entire span, so that 1 person observed
period
for two years gives same
information as 2 persons observed
for 1 year
Uses
To estimate risk for
specified period and
prognosis after
disease event
For inference about causal
processes; to adjust for different
lengths of observation for each
individual, loss to follow-up,
Simple epidemiologic indices: review/summary
Incidence density (ID) vs. Cumulative incidence (CI)
Question:
In a population of 100 persons, deaths occur at
the rate (incidence density) of 52 per 100
person-years or, equivalently, 1 per 100
person-weeks.
After one year of this, what proportion of the
100 people will have died?
Simple epidemiologic indices: review/summary
Answer:
41%,
not 52%
Simple epidemiologic indices: review/summary
For all factors stable,
P = ID x MD
where
P = Prevalence
MD = Mean Duration
Example




If incidence is 12 new cases per 1000
person-years.
And duration of illness is 6 months.
What is the average prevalence?
6 per thousand
Simple epidemiologic indices: review/summary
Relative Risk = RR
either
CUMULATIVE INCIDENCE RATIO
CIR = CI1/CI0
or
INCIDENCE DENSITY RATIO
IDR = ID1/ID0
Association: a statistical feature of
comparisons(s), with six possible explanations:





Causation, with exposure promoting disease
Chance
Bias : 2 categories
Selection Bias
Measurement bias
Confounding variable(s)
Causation, with disease promoting
appearance of the exposure
Always ask: are there plausible alternative
explanations for the data?
Chance


due to random variation from sampling or
measurement
addressed using
– statistical tests of hypotheses (p-values)
– confidence intervals
– power analyses
Bias. 2 types


Selection, the way you selected
subjects for the study biased your
results.
Measurement, the way you measured
variables in your subjects biased the
results.
Selection bias


Bias from the use of a non-representative group
as the basis of generalization to a broader
population of subjects or patients.
For instance, a common bias of this type
appears when
– the prognosis of patients newly diagnosed with a
given disease is inferred from the study of
hospitalized patients with this disease at a major
referral center,
and
– the disease in question has a broad spectrum
behavior.
Selection bias






More commonly
We have 2 groups
Exposed and unexposed
We compare them with regards to an
outcome.
But the way we selected the 2 groups
causes differences in the outcome that have
nothing to do with the exposure.
Example if we used hospitalized smokers as
the exposed and healthy volunteer nonsmokers as the unexposed.
Selection Bias (Admission Rate -- Berkson)
DISEASES OF BONES AND ORGANS OF MOVEMENT VS.
RESPIRATORY DISEASE: TWO CROSS-SECTIONAL COMPARISONS
DISEASES OF BONES AND ORGANS OF
MOVEMENT
GENERAL
POPULATION
RESPIRATORY
DISEASE
THOSE
HOSPITALIZED
IN PRIOR 6
MONTHS
YES
NO
TOT.
YES
NO
TOT.
YES
17
207
234
5
15
20
NO
184
2376
2560
18
219
237
TOTAL
201
2583
2784
23
234
257
ODDS-RATIO = 1.06
ODDS-RATIO =
4.06
1
ADAPTED FROM ROBERTS RS, SPITZER WO, DELMORE T, AND SACKETT DL. J
CHRON DIS 31:119-28.
Selection Bias (Berkson)
Necropsies
TB
CANCER
CASES
CONTROLS
PRESENT
54
133
ABSENT
762
683
TOTAL
816
816
6.6
16.3
% WITH TB
EOR = 0.36, P<.001 (CHI-SQUARE)
More Selection Biases



Whenever we compare a group of
patients who use a drug to those who
don’t in a non experimental
observational study (cohort, not
randomized).
The 2 groups differ in many respects.
One of the most important respects is
that the patients on the drug have a
reason to be on it (indication). The
others don’t. Called “Bias by indication”.
Bias by indication


For example calcium channel blockers
have 2 indications hypertension and
coronary disease.
If you compare hypertensive patients
who are on Ca blockers to those who
are on other agents (not randomized,
totally at the discretion of their doctors),
we would find:
Bias by indication



Patient on Ca blockers have higher
prevalence of CAD
Also higher prevalence of risk factors for
CAD
So if you do an observational study of
hypertensive patients, comparing the
outcome in those on Ca blockers to
those on other agents, you may find
Bias by indication



That patients on Ca blockers have
much worse outcomes.
This is bias by indication.
You can adjust and correct for
preexisting heart disease and for risk
factors, but may not be enough.
Bias by indication





If you compare hypertensive patients who are
on minoxidil or hydralazine to those on other
agents you find
That patients on those agents have higher BP
Is it because they don’t work as well ?
No, the opposite. They are reserved for those
with severe resistant hypertension.
That is the indication for those agents.
Survivor Treatment Bias




Patients who received statin during
admission for MI had much lower inhospital mortality.
Statin?
The ones who died are different.
Some died very soon after admission
(no statin).
Competing Medical Issues Bias


Some were so sick that they were
treated with multiple drugs, modalities,
ICU etc.
No statin
Bias by contraindication



If you compare hypertensive patients who are
on beta blockers to those on other agents
you find that they have better outcomes.
That does not mean they are better for you.
No, this comparison is biased by
contraindication.
Beta blockers are contraindicated in severe
COPD, CHF, PVD etc.
Measurement bias
Systematic or non-uniform failure of a
measurement process to accurately represent
the measurement target, e.g.
– different approaches to questioning, when
determining past exposures in a casecontrol study.
– more complete medical history and physical
examination of subjects who have been
exposed to an agent suspected of causing a
disease than of those who haven't been
exposed to the agent.
Measurement Bias -- Recall Bias
INFLUENCE OF INTENSITY OF SEARCHING FOR
EXPOSURE UPON REPORTED PROPORTIONS EXPOSED
PRIOR EXPOSURE TO IRRADIATION
ROUTINE
QUESTIONING &
RECORD SEARCH
INTENSIVE
QUESTIONING
AND RECORD
SEARCH
36 CASES OF
NISHIYAMA ET
AL.1
28
47
22 CASES OF
RAVENTOS ET
AL.2
0
50
STUDY
1
Nishayama, Schmidt, And Batsakis, J Amer Med Assoc 181:1034-38.
1
Raventos, Horn, And Ravdin, J Clin Endocr Metab 22:886-91.
Measurement Bias
Family information bias
The flow of family information about exposures
and illnesses
is stimulated by and directed to a new case
in its midst.
Measurement Bias
REPORTED
PARENTAL
HISTORY
1
WITH
RHEUMATOID
ARTHRITIS (%)
WITHOUT
RHEUMATOID
ARTHRITIS (%)
NEITHER PARENT
27
50
ONE PARENT
58
42
BOTH PARENTS
15
8
TOTAL
100
100
ADOPTED FROM SCHULL AND COBB, J CHRON DIS 22:217-22.
Measurement Bias -- Family Information
EFFECT OF THE SOURCE OF FAMILY INFORMATION UPON
THE RESULTS OF THE FAMILY HISTORY
REPORTED
PARENTAL
HISTORY
1
SIBLING PROVIDING FAMILY HISTORY
WITH
WITHOUT
RHEUMATOID
RHEUMATOID
ARTHRITIS (%)
ARTHRITIS (%)
NEITHER PARENT
27
50
ONE PARENT
58
42
BOTH PARENTS
15
8
TOTAL
100
100
ADOPTED FROM SCHULL AND COBB, J CHRON DIS 22:217-22.
Avoid confounding
Confounding refers to distortion of the
true biologic relation between an
exposure and a disease outcome of
interest, due to a research design and
analysis that fail to properly account for
additional variables associated with
both. Such variables are referred to as
confounders or, less formally, as
lurking variables.
Confounding
ONE-MONTH INFANT SURVIVAL STATUS
SURVIVAL
AMOUNT OF
CARE
DEAD
ALIVE
TOTAL
MORTALITY
(%)
LESS
20
373
393
5.1
MORE
6
316
322
1.9
TOTAL
26
689
715
3.6
Confounding
ON ONE-MONTH INFANT SURVIVAL STATUS: CLINIC A
SURVIVAL
AMOUNT OF
CARE
DEAD
ALIVE
TOTAL
MORTALITY
(%)
LESS
3
176
179
1.7
MORE
4
293
297
1.4
TOTAL
7
469
476
1.5
ONE-MONTH INFANT SURVIVAL STATUS: CLINIC B
SURVIVAL
AMOUNT OF
CARE
DEAD
ALIVE
TOTAL
MORTALITY
(%)
LESS
17
197
214
7.9
MORE
2
23
25
8.0
TOTAL
19
220
239
8.0
Confounding
COMMUNITY A (E.G. STATE OF ILLINOIS)
AGE GROUP
NUMBER IN DEATHS MORTALITY
COMMUNITY IN YEAR
(% PER
YEAR)
YOUNGER
70,000
700
1%
OLDER
30,000
3000
10%
TOTAL
100,000
3700
3.7%
COMMUNITY B (E.G. DANVILLE)
AGE GROUP
NUMBER IN
DEATHS MORTALITY
COMMUNITY IN YEAR
(% PER
YEAR)
YOUNGER
30,000
300
1%
OLDER
70,000
7000
10%
TOTAL
100,000
7300
7.3%
Direct Rate Adjustment
CITY A
TOTAL
CITY A
POPULATION
OBSERVED
DEATHS
CITY A MORTALITY
RATE (PER 100,000 P-Y)
300,000
54
54/3 =18
CITY B
TOTAL
CITY B
POPULATION
OBSERVED DEATHS
CITY B
MORTALITY RATE
(PER 100,000 P-Y)
100,000
22
22
Age specific mortality rate
CITY A
AGE
GROUP
CITY B
Number Number Mortality Number
of Deaths
in
Rate
in
POPULA
(PER
POPULA
TION
100,000
TION
P-Y)
Number Mortality
of Deaths
Rate
(PER
100,000
P-Y)
0-19
60,000
12
20
20,000
3
15
20-50
180,000
18
10
20,000
1
5
>50
60,000
24
40
60,000
18
30
TOTAL
300,000
54
18
100,000
22
22
Direct Rate Adjustment
CITY A
AGE
GROUP
Standard
Population
Agespecific
CITY B
Expected
Deaths
Mortality
Rate
(/100K)
Agespecific
Expected
Deaths
Mortality
Rate
(/100K)
0-19
20,000
20
4
15
3
20-50
40,000
10
4
5
2
>50
40,000
40
16
30
12
TOTAL
100%
24
17
Direct Rate Adjustment
ANY CITY
AGE
GROUP
Standard
Population
Agespecific
Mortality
Rate
Expected
Deaths
(PER
100,000
P-Y)
0-19
20%
…
…X0.2
=…
20-50
40%
…
…X0.4
=…
>50
40%
…
…X0.4
=…
TOTAL
100%
Age
adjusted
mortality
rate
Direct Rate Adjustment
CITY A
STANDARD
POPULATION
CITY A
AGE-SPECIFIC
MORTALITY RATE
OBSERVED
DEATHS (PER
100,000 P-Y)
0-19
50%
20/100,000 P-Y
10
20-50
30%
10/ "
3
>50
20%
40/ "
8
TOTAL
100%
AGE
GROUP
Direct Rate Adjustment
CITY A
STANDARD
POPULATION
CITY A
AGE-SPECIFIC
MORTALITY RATE
OBSERVED
DEATHS (PER
100,000 P-Y)
0-19
50%
20/100,000 P-Y
10
20-50
30%
10/ "
3
>50
20%
40/ "
8
AGE
GROUP
TOTAL
100%
DIRECTLY ADJUSTED RATE=DAR=21/100,000 P-Y
21
Direct Rate Adjustment
CITY B
STANDARD
POPULATION
CITY B
AGE-SPECIFIC
MORTALITY RATE
OBSERVED
DEATHS (PER
100,000 P-Y)
0-19
50%
15/100,000 P-Y
7.5
20-50
30%
5/ "
1.5
>50
20%
30/ "
6
AGE
GROUP
TOTAL
100%
DIRECTLY ADJUSTED RATE=DAR=15/100,000 P-Y
15
Direct Rate Adjustment
CITY A
STANDARD
POPULATION
CITY A
AGE-SPECIFIC
MORTALITY RATE
OBSERVED
DEATHS (PER
100,000 P-Y)
0-19
33.3%
20/100,000 P-Y
6.67
20-50
33.3%
10/ "
3.33
>50
33.3%
40/ "
13.33
AGE
GROUP
TOTAL
100%
OR, DAR=(1/3)(20+10+40)PER 100,000P-Y=23.3/100,000 PY
23.33
Direct Rate Adjustment
CITY B
AGE
GROUP
0-19
20-50
>50
TOTAL
STANDARD
POPULATION
CITY B
AGE-SPECIFIC
MORTALITY RATE
OBSERVED
DEATHS (PER
100,000 P-Y)
33.3%
15/100,000 P-Y
5
33.3%
5/ "
1.66
33.3%
30/ "
10
100%
OR, DAR=(1/3)(15+5+30) PER 100,000 P-Y=16.7/100,000 P-Y
16.67
Indirect Rate Adjustment
Calculate “Expected Deaths”

Divide Observed Deaths by Expected
Deaths (O/E)

SMR (Standardized Mortality Ratio)
Indirect Rate Adjustment



Calculate SMR standardized mortality
ratio.
SMR = Observed mortality / Expected
mortality
To Calculate that you need to calculate
expected mortality.
Indirect Rate Adjustment
STANDARD POPULATION MORTALITY = 28/100,000 P-Y
0-19 year old: 24/100k ; 20-50: 16/100k;
>50: 50/100k
CITY A
AGE
GROUP
STANDARD
CITY A
POPULATION
POPULATI AGE-SPECIFIC
ON
MORTALITY
RATE
0-19
60K
20-50
180K
>50
60K
TOTAL
300K
EXPECTED
DEATHS
(PER 100,000
P-Y)
Indirect Rate Adjustment
STANDARD POPULATION MORTALITY = 28/100,000
P-Y
0-19: 24; 20-50: 16;
>50: 50
CITY A
AGE
GROUP
STANDARD
CITY A
POPULATION
POPULATI AGE-SPECIFIC
ON
MORTALITY
RATE
EXPECTED
DEATHS
(PER 100,000
P-Y)
0-19
60K
24/100,000 P-Y
14.4
20-50
180K
16/ "
28.8
>50
60K
50/ "
30.0
TOTAL
100%
73.2
Indirect Rate Adjustment
Calculate “Expected Deaths”

Divide Observed Deaths by Expected
Deaths (O/E)

SMR (Standardized Mortality Ratio)
Indirect Rate Adjustment
STANDARDIZED MORTALITY RATIO
(SMR) =
OBSERVED DEATHS/EXPECTED
DEATH
54/73.2 = 74%
Indirect Rate Adjustment
STANDARD
POPULATION
28/100,000 P-Y
MORTALITY
0-19: 24; 20-50: 16;
=
>50: 50
CITY B
AGE
GROUP
STANDARD
CITY B
POPULATION
POPULATI AGE-SPECIFIC
ON
MORTALITY
RATE
EXPECTED
DEATHS
(PER 100,000
P-Y)
0-19
20K
24/100,000 P-Y
4.8
20-50
20K
16/ "
3.2
>50
60K
50/ "
30
TOTAL
100%
38.0
Indirect Rate Adjustment
STANDARDIZED MORTALITY RATIO
(SMR) =
OBSERVED DEATHS/EXPECTED
DEATHS
22/38 = 58%
Proportional Mortality
 The
4 leading causes of death in
Chamapign County are….
 CAD is the leading cause being
responsible for 32% of all deaths in the
County in 2002.
Proportional Mortality

Number of deaths from a specific
cause/ Total number of deaths in same
time
Proportional Mortality Ratio
PMR
Proportional Mortality Ratio
Proportion of deaths from specified cause
/Proportion of deaths from specified
cause in comparison population
Proportional Mortality Ratio
PMR
 CAD
is responsible for 32% of all
deaths in the County in 2002.
(Compared to 40% in the State of
Illinois)
 PMR = 32%/40% = 32/40 = 0.8
 Is that good or bad ?
PMR
Relative frequency of other causes of death can
affect the PMR for the cause of interest
An epidemic of a fatal disease in your
population will decrease PMR for all other
causes
Low mortality from a very common cause (CAD
for example) in your population will increase
PMR for all other causes
PMR
 Fast,
easy, cheap
 Can be calculated when all you have is
death certificates
 Don’t need information on demography
of population.
 “Leading Causes of Death”
How does one decide whether to present a set of
data using crude, adjusted, or category-specific
indices?
If possible, use crude indices only to produce a
quick picture of the magnitude of a problem in a
population, for the purpose of establishing a prima
facie need for public health and/or medical
services, and as a first-cut at estimating the
resources needed.
How does one decide whether to present a set of
data using crude, adjusted, or category-specific
indices?
Use category-specific indices when you wish to
focus attention on the problem in one or a few
population subgroups, when space is available to
give a detailed presentation in order to communicate
the fullest understanding of the data, and especially
if specific indices vary between two populations
being compared in a different manner in different
population subgroups (e.g. effects are modified by
age, sex or race).
How does one decide whether to present a
set of data using crude, adjusted, or
category-specific indices?

Use adjusted rates when
– you wish to avoid possible confounding,
– but do not have the space to present the full
schedules of specific indices, or your
audience does not have the patience for
that,

Avoid adjusted rates when
– there variable being adjusted out is an
“effect modifier,” that is, the relationship
between groups being compared changes
from stratum to stratum -- more later on this.
How does one decide whether to present a set of
data using crude, adjusted, or category-specific
indices?
Note that



crude indices require one only to know the numerator
cases and the denominator (population size or
exposure-time) of each total population to be compared;
indirect adjustment requires knowledge of only the
numerator cases from the total populations and the
(joint) distributions of confounder(s) in the populations to
be compared;
direct adjustment and specific rates require knowledge
of both the numerator cases and the corresponding
denominators within levels of the confounding
variable(s), for all populations under comparison.
Note that


A directly adjusted rate of a single
community means nothing by itself. It is
only used to compare different
communities and only if all of them are
adjusted to the same standard
population.
SMR of a single community IS useful. It
does by itself compare 2 populations.