Var h x e x z note the roadmap shows the formulas for

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 test-statistic 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 2-sided 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
7-year 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 7-year 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 2.5-fold higher 7-year 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
=
e
) 1.332 0.4598, ( ) ar(X) V 1.96 X (
ˆ


Harvard TH Chan School of Public Health
EPI202 – Epidemiologic Methods II
Fall 2016
24
Key Concepts
 Formulas
 Person-time (poisson) based methods for use
in open and closed cohort studies
 Methods for case-control studies
 Count-based (binomial) methods for closed
cohort and cross-sectional studies