Incidence
Conditional
Survival
Proportion
Cumulative
Survival
Proportion
K
t
k
A
k
N
k
CI
k
S
k
・
Cumulative survival proportion over the whole time interval is the
product of the conditional survival proportions for every
subinterval t
k1
to t
k
.
・
Censored observations have the same probability of the event
after censoring as those remaining under observation.
[Measure of Association]
Incidence Rate (IR)
Incidence Rate Ratio (IRR)
IR
E
−
¿
IR
E
+
¿
¿
IRR
=
¿
Range: 0 to ∞
No association: 1
・
(IRR1)*100% greater rate of outcome among subjects exposed to
exposure.
・
A rate of outcome among exposed subjects is IRR times higher than
that of rate among unexposed subjects.
Incidence Rate Difference (IRD)
E
−
¿
E
+
¿
−
IE
¿
IRD
=
IR
¿
synonym: attributable rate
Range: −∞ to ∞
This difference reflects the rate of outcome among exposed subjects
that can be attributed to the exposure.
Cumulative Incidence (CI)
Cumulative Incidence Ratio (CIR)
CI
E
−
¿
=
Pr
[
Y
=
1
∨
A
=
1
]
Pr
[
Y
=
1
∨
A
=
0
]
CI
E
+
¿
¿
CIR
=
¿
Range: 0 to ∞
No association: 1
Study participants who were Exposed have AA times the CI of
Outcome compared to participants who were unexposed over the
study periods.
Cumulative Incidence Difference
(CID)
E
−
¿
E
+
¿
−
CI
¿
CID
=
CI
¿
Synonym: attributable risk
Range: 1 to +1
No association: 0
NNT = 1/CID
Odds Ratio
Pr
[
A
=
1

A
=
1
]
/
Pr
[
Y
=
0
∨
A
=
1
]
Pr
[
Y
=
1

A
=
0
]
/
Pr
[
Y
=
0
∨
A
=
0
]
Range: 0 to ∞
No association: 1
The odds of A = 1 is OR times that of those that do not have A.
[Attributable Fraction]
Attributable risk percent (AR%)
CI
E
+
¿
×
100
E
+
¿
−
CI
E
−
¿
¿
CI
¿
AR
=
¿
Proportion of disease burden
among the exposed caused by
exposure
Population attributable risk
percent
CI
Total
−
CI
E
−
¿
CI
Total
=
AR × Pr
[
A
=
1
∨
Y
=
1
]
¿
Proportion of disease burden
among total population by
exposure
DAG
[The association & Causation]
The association flows regardless of the direction of the allows
The causation flows the direction of the allow (left to right)
[Confounder]
Definition of a confounder is:
・
Associated with the exposure (A) in the study base that produce
the case
・
Associated with the outcome (Y) in the nonexposed
・
Is not a downstream consequence of exposure or outcome
[Collider]
・
A common effect
・
Depicted as two arrows intersecting at a variable
・
Blocks the flow of association
[Systematic bias]
・
A structural association between exposure and outcome
that does not arise from the causal effect
・
Assume the average causal null hypothesis
・
Incorrect estimate of the effect, if a causal effect
・
Biased estimates are not valid
[Mediator]
・
No confounding, no backdoor path
[Conditioning]
・
A common cause: blocks the flow of association
・
A common effect: opens the flow of association
・
A consequence of a common effect: opens the flow of association
・
A Mediator: Blocks the flow of association
[Control for Confounding]
・
Randomization: known & unknown confounders
・
Restriction, matching: known confounders only
・
IP weighting/ standardization: known confounders only
・
Stratification: known confounders only
[Selection bias]
・
Can occur in any types of study (observational & randomized
study)
・
By conditioning on the common effect of the exposure and the
outcome
[Confounding]
・
Definition:
− Presence of common causes or lack of exchangeability
・
There is confounding when
−
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 Fall '18