□
Inverse of the large
‐
strata variance weights
□
Mantel
‐
Haenszel weights.
Inverse variance weights have the form:
If there are no cases observed among either the exposed or
unexposed in a stratum, calculation of the variance for that
stratum involves a division by 0.
When the number of cases observed among either the
exposed or unexposed group is small, the large
‐
strata variance
formula may be inaccurate.
N
b
b

N
+
N
a
a

N
1
=
)]
R
I
C
(
[
Var
1
=
'
w
0i
i
i
0i
1i
i
i
1i
i
^
i
ˆ
ln
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
15
Choices of Weights
Mantel
‐
Haenszel Weights
Thus, to make the best use of our data, we prefer the
Mantel
‐
Haenszel weights:
Using the Mantel
‐
Haenszel weights, the summary
cumulative incidence ratio is:
T
N
b
=
'
w
i
1i
i
i
T
N
b
T
N
a
=
T
N
b
N
b
N
a
T
N
b
w
R
I
C
'
w
=
R
I
C
i
1i
i
I
1
=
i
i
0i
i
I
1
=
i
i
1i
i
I
1
=
i
0i
i
1i
i
i
1i
i
I
1
=
i
i
I
1
=
i
i
i
I
1
=
i
MH
=
'
ˆ
ˆ
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
16
Evans County Study
CIR
MH
Estimation
The Mantel
‐
Haenszel summary cumulative incidence ratio is:
After adjusting for confounding by age and ECG status, the
estimated risk ratio changed from 2.45 to 1.70. Confounding
by either or both of these variables led to an overestimation
of the risk ratio.
Assuming there is no confounding by other variables, no
residual confounding by these variables, no selection bias and
no information bias, these data indicate that men with high
CAT levels have a 70% higher 7
‐
year cumulative incidence of
CHD than men with low CAT levels.
1.70
=
8.90
15.10
=
90
58
*
5
+
161
39
*
15
+
76
17
*
7
+
282
8
*
17
90
32
*
14
+
161
122
*
9
+
76
59
*
3
+
282
274
*
1
=
R
I
C
MH
ˆ
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
17
95% CI for
ln
(CIR
MH
)
To construct the 95% confidence interval for
ln
(CIR
MH
),
we use the usual formula:
Where
MH
MH
R
I
C
Var
1.96
R
I
C
ˆ
ln
ˆ
ln
I
i
i
i
i
I
i
i
i
i
I
i
i
i
i
i
i
i
i
T
N
b
T
N
a
T
T
b
a
N
N
M
ˆ
ln
1
1
1
0
1
2
0
1
1
MH
R
I
C
Var
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
18
Evans County Study
CIR
MH
Confidence Interval Estimation
In this example,
Thus, the 95% confidence interval for
ln
(CIR
MH
) is:
and the 95% confidence interval for CIR
MH
is:
e
(0.020, 1.036)
= (1.02, 2.82)
0.067
=
R)
I
C
ar
V
ˆ
(ln
ˆ
1.036)
(0.020,
0.067
1.96
0.528
=
0.067
1.96
(1.70)
ln
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2018
19
Evans County Study
CIR
MH
Confidence Interval Interpretation
Assuming no residual confounding by age or ECG status, no
confounding by other variables, no selection bias and no
information bias, we conclude that there is evidence of a
significant elevation in the 7
‐
year cumulative incidence of
CHD associated with high CAT level compared with lower
levels, ranging in magnitude from 2% to nearly a three
‐
fold
higher cumulative incidence with 95% confidence.
You've reached the end of your free preview.
Want to read all 14 pages?
 Summer '14
 FrancisCook