The crude 7
‐
year cumulative incidence ratio 2.45 (1.58, 3.79)
was incorrectly centered and far too narrow due to
confounding by age and/or ECG status.
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
20
Cumulative Incidence Difference
Point and Interval Estimates
To calculate the estimated summary cumulative
incidence difference, we use a weighted average of
the stratum
‐
specific differences:
Where:
□
w
i
' = the weight for the estimated cumulative incidence
difference in the i
th
stratum
□
= the estimated cumulative incidence difference in
the i
th
stratum
D
I
C
i
ˆ
'
'
=
'
w
D
I
ˆ
C
w
D
I
ˆ
C
w
'
w
=
D
I
ˆ
C
*
w
=
D
I
ˆ
C
i
I
=1
i
i
i
I
=1
i
i
i
I
=1
i
i
I
=1
i
i
i
I
=1
i
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
21
Choice of Weights
Summary Cumulative Incidence Difference
Mantel
‐
Haenszel weights are not used for difference
measures of association.
Rather, we take weights as the inverse of the
variance of the stratum
‐
specific estimates of the CID.
Recall that
Thus, the weight for stratum i is:
N
)
b

N
(
b
+
N
)
a

N
(
a
=
)
D
I
(C
ar
V
3
0i
i
0i
i
3
1i
i
1i
i
i
ˆ
ˆ
)]
b

N
(
b
N
+
)
a

N
(
a
N
[
N
N
=
)
D
I
C
(
ar
V
1
=
'
w
i
0i
i
3
1i
i
i1
i
3
0i
3
0i
3
1i
i
i
ˆ
ˆ
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
22
Evans County Study
CID
inv var
Estimation
The summary cumulative incidence difference:
Assuming no confounding by additional variables, no residual
confounding by age and ECG status, no selection bias, and no
information bias, these data indicate that men with high CAT levels
have an 8.5% higher cumulative incidence of CHD than men with
low CAT levels.
Recall that the crude CID was estimated to be 13.1%. Adjustment
for age and ECG status led to a reduction in the estimated
cumulative incidence difference by (8.5
‐
13.1)/8.5 = 54%.
0.085
=
137.42
+
183.97
+
96.89
+
72.02
(0.085)
(137.42)
+
(0.108)
(183.97)
+
(0.058)
(96.89)
+
(0.063)
(72.02)
=
'
w
D
I
C
w
=
D
I
C
i
I
1
=
i
i
i
I
1
=
i
'
ˆ
ˆ
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
23
95% CI for CID
inv var
The 95% confidence interval for the summary incidence
rate difference is calculated in the usual way:
)
D
I
ar(C
V
1.96
D
I
C
VAR
INV
VAR
INV
ˆ
ˆ
ˆ
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
24
Variance of the CID
inv var
There is a simple expression for the estimated variance of a
summary cumulative incidence difference when the inverse of
the stratum
‐
specific variances are used as weights.
□
when X is an inverse variance weighted average of the stratum
‐
specific
quantities
As stated previously, given sufficient data so that the large
strata variance formula applies, using the inverse variances of
the stratum
‐
specific estimates as gives the most efficient, i.e.
minimum variance, summary incidence rate difference
available.
'
w
1
=
ar(X)
V
ˆ
i
I
=1
i
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
25
Evans County Study
CID
inv var
CI Estimation and Interpretation
In this example,
Thus, the 95% confidence interval for CID is:
The cumulative incidence difference for 7
‐
year cumulative
incidence of CHD, adjusted for age and ECG status, lies
between a slight deficit risk to an excess risk of 17%. The
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