Hypothesis Test: Null and Alternative Hypotheses
H
0
:
There is no association between CAT level and 7
year cumulative incidence of CHD
□
C
1
= C
0
↔
C
1
 C
0
= 0
↔
C
1
/C
0
= 1
↔
ln
(C
1
/C
0
)= 0
H
a
:
There is an association between CAT level and 7
year cumulative incidence of CHD
□
C
1
≠ C
0
↔
C
1
 C
0
≠ 0
↔
C
1
/C
0
≠ 1 ↔
ln
(C
1
/C
0
) ≠ 0
Methods for Count Data
Hypothesis Test: Choice of X
2
1
0
2
0
2
~


H
X
Var
H
X
E
X
Z
Note: The “Roadmap” shows the formulas for this statistical
test based on setting X =
a,
the number of exposed cases. As
an exercise, compute the teststatistic based on the formulas
from the “Roadmap”.
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2016
20
Methods for Count Data
Hypothesis Test: Variance of X
00106
0
487
1
122
1
609
71
1
609
71
N
1
N
1
C
1
C
T
M
C
where
N
C
1
C
N
C
1
C
H
CID
Var
H
X
Var
0
1
1
0
1
0
0
.
)
(
,
)
(
)
(
)

(
)

(
Methods for Count Data
Construct and Interpret the Hypothesis Test
These data are not very compatible with the state of nature
described by the null. If the null were true, we would expect
to observe results as extreme or more extreme 6 times per
100,000 iterations of this study.
If we were interested in a testing framework, with a pre
specified 2sided alpha of 0.05, we would reject the null
hypothesis and conclude that there is a statistically significant
association between catecholamine level at baseline and the
7year cumulative incidence of CHD (assuming no
confounding, no selection bias, no information bias).
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2016
21
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2016
22
95% Confidence interval for CID:
These data are consistent with 7year cumulative
incidence differences ranging from 5 to 21% with
95% confidence (assuming no confounding, no
selection bias, no information bias)
)
0.209
0.053,
(
=
0.001582
1.96
0.131
Methods for Count Data
Point estimate for the Cumulative Incidence Ratio
There is a 2.5fold higher 7year cumulative incidence of CHD
among those with high CAT levels compared to those with low
levels (assuming no confounding, no selection bias, no
information bias).
45
.
2
09
.
0
22
.
0
487
44
122
27
ˆ
0
1
N
b
N
a
R
I
C
Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2016
23
Methods for Count Data
Variance for
ln
(
Cumulative Incidence Ratio) (
ln
(CIR))
95% Confidence interval:
Let X =
ln
(CÎR) =
ln
(2.45) = 0.8959
ar(X)
V
ˆ
1.96
X
0.0495
=
487
*
44
443
+
122
*
27
95
=
N
b
b

N
+
N
a
a

N
=
C
N
C

1
+
C
N
C

1
=
R)
I
C
(
ar
V
=
(X)
ar
V
0
0
1
1
0
0
0
1
1
1
ˆ
ˆ
ˆ
ˆ
ˆ
ln
ˆ
ˆ
Methods for Count Data
Confidence Interval for
Cumulative Incidence Ratio (CIR)
95% Confidence interval for
ln
(CIR):
95% Confidence interval for (CIR):
These data are consistent with cumulative incidence ratios
ranging from 1.6 to 3.8 with 95% confidence (assuming no
confounding, no selection bias, no information bias)
1.332)
(0.4598,
=
0.0495
1.96
0.8959
3.79)
(1.58,
=
e
=
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 Fall '16
 MURRAY
 Epidemiology, Statistical hypothesis testing, TH Chan School of Public Health, Harvard TH Chan, TH Chan School