EPI 202 Summary
[pvalue]
・
the probability that a result as extreme or more extreme than the one we observed would occur due to
random variation, if the null hypothesis were true
・
A
small
pvalue:
It is unlikely that the observed data would have been obtained if the null hypothesis were true
We may conclude that the data are not very compatible with the state of nature specified by the null
Decide to reject the null hypothesis in a testing framework
[Null hypothesis and Alternate Hypothesis]
H
0
: p
1
is not different from p
0
versus H
A
: p
1
is different from p
0
[Limitation of hypothesis test]
No information on direction or magnitude
No information about the range of effects that are consistent with the observed data
No information on the power of the study (Reject the null hypothesis if the null hypothesis is false)
No information on the consistency of the data with alternative, nonnull states of nature
[Confidence Intervals]
Narrow confidence intervals = Powerful study Wide confidence intervals = Weak study
100(1α)% of CI does ot include the null value of X, we can usually reject the null hypothesis
The null value for difference measure of association: 0
The null value for ratio measures of association: 1
[Random Variability in Observational Studies]
・
Exposure is not randomly assigned => Additional assumptions are needed
−
Cohort Study:
the source population = the unexposed group
A full census of exposed individuals from the source population or a random sample of these individuals
−
Casecontrol study:
Sample the study base to obtain the controls
The cases are either a full census of all cases produced by this study base or a sample of these cases
・
After all known confounders are adjusted, the data can be regarded as a random sample of the
conditional relation
[PersonTime Data]
H
0
: There is no association between exposure and outcome. (I
1
=I
0
I
1
I
0
= 0 I
1
/I
0
= 1 ln(I
1
/I
0
) = 0)
Ha: There is an association between exposure and outcome. (I
1
≠I
0
I
1
I
0
≠0 I
1
/I
0
≠1 ln(I
1
/I
0
)≠0)
The hypothesis test statistic
IRD
IRR
E
´
E
Cases
a
b
M1
Person
Time
N
1
N
0
T
X
=
^
IRD
=
a
N
1
−
b
N
0
E
(
X

H
0
)
=
E
(
^
IRD

H
0
)
=
0,
^
Var
(
IRD
)
=
a
N
1
2
+
b
N
0
2
^
IRR
=
a
N
1
/
b
N
0
Let X
=
ln
(
^
IRR
)
^
Var
(
X
)
=
^
Var
(
ln
(
^
IRR
)
)
=
1
a
+
1
b
Z
2
=
[
X
−
E
(
X

H
0
)
]
2
Var
(
X

H
0
)
x
1
2
X
=
a
E
(
X

H
0
)
=
M
1
×N
1
/
T
^
Var
(
X

H
0
)
=
M
1
N
1
N
0
T
2
Pr
[
x
2
>
●
]
<
0.05
95% Confidence Interval:
X ±
1.96
√
^
Var
(
X
)
95% CI for ln(IRR)
X ±
1.96
√
^
Var
(
X
)
95% CI for IRR:
e
X ±
1.96
√
^
Var
(
X
)
We
reject
the
null
hypothesis
at
the
0.05
level
of
significance.
We conclude that there is statistically significant evidence for an association between exposure and
outcome in this data at the level 0.05 of significance, assuming no confounding, no information bias, and
These data are consistent with IRD/IRR ranging from A to B with 95% confidence.
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 Summer '14
 FrancisCook