### Epid 2by 2 tables

```The Use of 2 by 2 Tables
IN
CAUSAL ASSOCIATIONS
Causality
ASSOCIATION BETWEEN
FACTOR AND HEALTH EVENT
F+
???
D+
Causality
APPARENT
ASSOCIATION
STATISTICAL
CAUSAL
Epidemiologic Methods
PROSPECTIVE OR COHORT
F+
F-
TIME
D+
D-
Epidemiologic Methods
F+
F-
TIME
D+
D-
RETROSPECTIVE OR CASE-CONTROL
Epidemiologic Methods
RISK ANALYSIS
THE USE OF THE 2X2 TABLE
D+
D-
F+
a
b
Total
a+b
F-
c
d
c+d
c/(c+d)
a+c
b+d
n
(a+c)/n
Tot
AR= (a/(a+b)-(c/(c+d)))
IR
AR
RR
a/(a+b)
RR= (a/(a+b))/(c/(c+d)))
Epidemiologic Methods
RISK ANALYSIS
THE USE OF THE 2X2 TABLE
(PROSPECTIVE or COHORT)
D+
D-
F+
a
b
Total
a+b
F-
c
d
c+d
c/(c+d)
a+c
b+d
n
(a+c)/n
Tot
IR
a/(a+b)
RR(exact)= (a/(a+b))/(c/(c+d)))
EXERCISE: CASE Problem
Calf Mortality Exercise
Given
300 calves born in corrals
90 calves born in barn
100
9
Crude mortality rate
(corrals)
CMR
0.333333333
33.3%
Crude mortality rate
Barn
0.1
10.0%
#2
EXERCISE: CASE Problem #2
2 X 2 Table
Corral
Barn
Prospective design
D+
100
9
109
D200
81
281
Incidence rate
total
(IR)
300
33.3%
90
10.0%
390
Relative Risk (exact)
Rre
3.333333333
Attributable Risk
AR
0.233333333
23.30%
Epidemiologic Methods
F+
F-
TIME
D+
D-
RETROSPECTIVE OR CASE-CONTROL
Epidemiologic Methods
RISK ANALYSIS
THE USE OF THE 2X2 TABLE
(RETROSPECTIVE or CASE CONTROL)
D+
D-
F+
a
b
Total
a+b
F-
c
d
c+d
a+c
b+d
n
Tot
IR
UNKNOWN
RR(approx)= Odds Ratio=(a*d/c*b)
EXERCISE: CASE Problem #2
2 X 2 Table
Retrospective design
D+
Corral
Barn
Odds Ratio
D-
total
100
200
300
9
81
90
109
281
390
OR
4.5
Causality
STATISTICAL ASSOCIATION
USE OF THE CHI SQUARE
F+
SA
D+
Causality
THE 2 by 2 TABLE.
STATISTICAL ASSOCIATION
Disease Outcome
Exposure to Risk
D+
D-
F+
a
b
F-
c
a+c
NULL HYPOTHESIS
a+b
ALTERNATE HYPOTHESIS
d
c+d
Level of sig (a=0.05)
b+d
n
df for 2X2= 1
FOR DECISION
(a+c)(a+b)(b+d)(c+d)
Compare ChiSquare calculated
To ChiSquare tabulated (3.84)
The Use of 2 by 2 Tables
IN
OUTBREAK INVESTIGATIONS
Causality
ASSOCIATION BETWEEN
Food Eaten & Disease (outcome)
F+
???
D+
Epidemiologic Methods
Food-Borne Outbreak
Eaten Risky Food
Not Eat Risky Food
F+
D+
F-
D-
Outcome Disease
OUTCOME NO DISEASE
Causality
THE 2 by 2 TABLE.
STATISTICAL ASSOCIATION
Disease Outcome
Exposure to Risk
D+
D-
F+
a
b
F-
c
a+c
NULL HYPOTHESIS
a+b
ALTERNATE HYPOTHESIS
d
c+d
Level of sig (a=0.05)
b+d
n
df for 2X2= 1
FOR DECISION