Epid 2by 2 tables

1
The Use of 2 by 2 Tables
IN
CAUSAL ASSOCIATIONS
2
Causality
ASSOCIATION BETWEEN
FACTOR AND HEALTH EVENT
???
F
D
3
Causality
APPARENT
ASSOCIATION
STATISTICAL
CAUSAL
4
Epidemiologic Methods
PROSPECTIVE OR COHORT
TIME
F
D
F-
D-
5
Epidemiologic Methods
TIME
F
D
F-
D-
RETROSPECTIVE OR CASE-CONTROL
6
Epidemiologic Methods
RISK ANALYSIS
THE USE OF THE 2X2 TABLE
D
D-
Total
IR
AR
RR
ab
F
a
b
a/(ab)
F-
c
d
cd
c/(cd)
Tot
ac
bd
n
(ac)/n
AR (a/(ab)-(c/(cd)))
RR (a/(ab))/(c/(cd)))
7
Epidemiologic Methods
RISK ANALYSIS
(PROSPECTIVE or COHORT)
THE USE OF THE 2X2 TABLE
D
D-
Total
IR
ab
F
a
b
a/(ab)
F-
c
d
cd
c/(cd)
Tot
ac
bd
n
(ac)/n
RR(exact) (a/(ab))/(c/(cd)))
8
EXERCISE CASE Problem 2
Calf Mortality Exercise Calf Mortality Exercise Calf Mortality Exercise

Given

300 calves born in corrals 300 calves born in corrals 300 calves born in corrals No. dead 100
90 calves born in barn 90 calves born in barn 90 calves born in barn No. dead 9


Crude mortality rate Crude mortality rate CMR 0.333333333 33.3
(corrals)

Crude mortality rate Crude mortality rate Barn 0.1 10.0
9
EXERCISE CASE Problem 2
2 X 2 Table 2 X 2 Table Prospective design Prospective design
D D- total Incidence rate (IR)
Corral 100 200 300 33.3
Barn 9 81 90 10.0
109 281 390


Relative Risk (exact) Relative Risk (exact) Rre 3.333333333

Attributable Risk Attributable Risk AR 0.233333333 23.30

10
Epidemiologic Methods
TIME
F
D
F-
D-
RETROSPECTIVE OR CASE-CONTROL
11
Epidemiologic Methods
RISK ANALYSIS
THE USE OF THE 2X2 TABLE
(RETROSPECTIVE or CASE CONTROL)
D
D-
Total
IR
ab
F
a
b
UNKNOWN
F-
c
d
cd
Tot
ac
bd
n
RR(approx) Odds Ratio(ad/cb)
12
EXERCISE CASE Problem 2
2 X 2 Table 2 X 2 Table Retrospective design Retrospective design
D D- total
Corral 100 200 300
Barn 9 81 90
109 281 390


Odds Ratio Odds Ratio OR 4.5
13
Causality
STATISTICAL ASSOCIATION
USE OF THE CHI SQUARE
SA
F
D
14
Causality
THE 2 by 2 TABLE.
STATISTICAL ASSOCIATION
Disease Outcome
D
D-
NULL HYPOTHESIS
F
a
b
ab
ALTERNATE HYPOTHESIS
Exposure to Risk
F-
c
d
cd
Level of sig (a0.05)
ac
bd
n
df for 2X2 1
FOR DECISION
Compare ChiSquare calculated
ChiSq (ad-bc)2n
To ChiSquare tabulated (3.84)
(ac)(ab)(bd)(cd)
15
The Use of 2 by 2 Tables
IN
OUTBREAK INVESTIGATIONS
16
Causality
ASSOCIATION BETWEEN
Food Eaten Disease (outcome)
???
F
D
17
Epidemiologic Methods
Food-Borne Outbreak
F
D
Eaten Risky Food
Outcome Disease
F-
Not Eat Risky Food
D-
OUTCOME NO DISEASE
18
Causality
THE 2 by 2 TABLE.
STATISTICAL ASSOCIATION
Disease Outcome
D
D-
NULL HYPOTHESIS
F
a
b
ab
ALTERNATE HYPOTHESIS
Exposure to Risk
F-
c
d
cd
Level of sig (a0.05)
ac
bd
n
df for 2X2 1
FOR DECISION
Compare ChiSquare calculated
ChiSq (ad-bc)2n
To ChiSquare tabulated (3.84)
(ac)(ab)(bd)(cd)