Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
1
EPI202 – Epidemiologic Methods II
Murray A. Mittleman, MD, DrPH
Department of Epidemiology, Harvard TH Chan School of Public Health
Module
Stratified Data Analysis for Count Data
(Closed Cohort and Cross
‐
sectional Studies)
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
2
Key Concepts
Notation
Hypothesis tests
Point and interval estimates for the cumulative
incidence ratio
Point and interval estimates for the cumulative
incidence difference
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
3
Notation for Count Data
(closed cohort and cross
‐
sectional studies)
Recall our notation for an unstratified table of count
data in closed cohort or cross
‐
sectional studies:
Notation
E
Ē
Cases
a
b
M
1
Non
‐
cases
c
d
M
0
N
1
N
0
T
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
4
Notation for Count Data
(closed cohort and cross
‐
sectional studies)
Now we stratify the data by one or more confounding
variables, so that each stratum consists of subjects who have,
on average, the same risk for disease, with the possible
exception of the exposure effect.
We have i=1,...,I of these strata, which are formed by each
unique combination of levelsof the confounding variables for
which there are data.
Notation
E
Ē
Cases
a
i
b
i
M
1i
Non
‐
cases
c
i
d
i
M
0i
N
1i
N
0i
T
i
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
5
Evans County Study Revisited
609 white men free of disease at baseline, are followed to investigate the
association between the 7
‐
year cumulative incidence of coronary heart
disease (CHD) and endogenous catecholamines (CAT).
We stratify by two potential confounders
□
age group (<55 / 55+)
□
electrocardiogram status (N=normal / A=abnormal).
Age<55
ECG=N
Age<55
ECG=A
Age 55+
ECG=N
Age 55+
ECG=A
Cat Level
Hi
Low
Hi
Low
Hi
Low
Hi
Low
Cases
1
17
3
7
9
15
14
5
Non
‐
cases
7
257
14
52
30
107
44
27
Total
8
274
17
59
39
122
58
32
CI
12.5
6.2
17.6
11.9
23.1
12.3
24.1
15.6
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
6
Hypothesis Test for Unstratified Data
Recall the hypothesis test statistic:
In closed cohorts (count data) with no confounding,
□
X = number of exposed cases = a
□
E(XH
₀
) = number of exposed cases expected under H
₀
= total number of cases * Pr(E) = M
₁
(N
₁
/T)
□
)
H

Var(X
]
)
H

E(X

[X
=
Z
0
2
0
2
T
N
N
M
M
=
)
H

Var(X
3
0
1
0
1
0
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
7
Hypothesis Test for Stratified Data (1)
In closed cohorts or cross
‐
sectional studies (count
data) with confounding, we stratify the data on all
confounding variables to form I strata
We then calculate the test statistic:
2
1
H

X
Var
H

X
E
X
2
χ
~
Z
0
i
I
1
i
i
2
I
1
i
0
i
I
1
i
i
i
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
8
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