This document summarizes key concepts related to analyzing binary and categorical data. It discusses binary variables, prevalence, rates, case-control studies, cohort studies, relative risk, number needed to treat, and crossover trials. For case-control studies, it provides an example comparing smoking status between lung cancer patients and normal individuals, calculating an odds ratio of 6. For cohort studies, it gives data comparing lung cancer incidence between smokers and non-smokers, calculating a relative risk of 4. It also discusses how to calculate absolute risk difference and number needed to treat from cohort study data.

1. Summary statistics for Binary
Data
By Dr Zahid Khan
Senior Lecturer King Faisal
University

2. Binary Variable
• A variable with two values like Alive or dead, Male or
Female.
• Values assigned are 0 and 1 mostly.
• Prevalence:
• The number of people in a population with a
particular condition divided by the number of people
in the population.
• e.g 3 persons have Diabetes in 1000 population so
prevalence is 3 per 1000.

3. Rate
• The proportion of events that occur within
given time period. E.g Birth rate, Mortality
rate.
• Incidence Rate:
• The number of new cases occurring over a
specified period of time.

4. Case Control Studies
4
• In a CASE-CONTROL STUDY, the investigator
compares one group among whom a problem is
(e.g., malnutrition) with another group, called a
control or comparison group, where the problem is
absent to find out what factors have contributed to
the problem.

5. 5

6. Case Control Studies
6
• A study was conducted to find out the association
of smoking to lung cancer. 100 cases of lung cancer
were interviewed about their smoking status and
60 of them were smokers. 200 Normal people
were also interviewed and 40 of them were
smokers. Find the odd ratio in the given scenario
and interpret your result as well.

7. Biopsy Results
Smoking
status
CA Lung
Positive
CA Lung
Negative
Yes
a
b
No
c
d
Total
a+c
b+d
7
Total
a+b
c +d
a +b +c + d

8. Biopsy Results
Smoking
status
CA Lung
Positive
CA Lung
Negative
Yes
60
40
No
40
160
Total
100
200
8
Total
a+b
c +d
a +b +c + d

9. 9
• Odd ratio = a/c
b/d
= a/c x d/b
= 60 x 160
40 x 40
=6
• Interpretation:
• Lung cancer patients are six times more
likely to be smokers than normal persons

10. Cohort Studies
10
• In a COHORT STUDY, a group of individuals that is
exposed to a risk factor (study group) is compared
with a group of individuals not exposed to the risk
factor (control group).
• The researcher follows both groups over time and
compares the occurrence of the problem that he or
she expects to be related to the risk factor in the
two groups to determine whether a greater
proportion of those with the risk factor are indeed
affected.

11. 11

12. Relative Ratio/Risk (RR)
12
• Ratio of incidence of the disease (or death)among
exposed and the incidence among non-exposed.
• It is a direct measure (or index) of the “strength” of
the association between suspected cause and
effect

13. Biopsy Results
Smoking status
CA Lung
Positive
CA Lung
Negative
Yes
a
b
No
c
d
Total
a+c
b+d
13
Total
a+b
c +d
a +b +c + d

14. Biopsy Results
Smoking status
CA Lung
Positive
CA Lung
Negative
Yes
50
495
No
25
975
Total
75
1425
14
Total
500
1000
1500

15. • Relative risk = Incidence of disease Among Exposed
Incidence of disease among non exp
• RR = a/a+b c/c+d
= 50/500 25/1000
= 50/500 x 1000/25
=4
• Interpretation:
• Smokers are 4 times more likely to develop
lung cancer than non smokers
15

16. NNT & Absolute Risk Difference
•
•
•
•
•
•
•
•
ARD is also known as Absolute Risk Reduction.
Number Needed to Treat (NNT)= 1/ ARD or
NNT = 1/P2-P1
ARD = P2 – P1
P1 = a/(a+b) & P2 = c/(c+d)
P1= 50/500 & P2 = 250/1000
P1= 0.1 & P2= 0.25 => P2-P1 = 0.15
NNT = 1/0.15 = 6.66 or 7

17. Cross over trials or matched case
control studies.
• Cross over trials or Matched case-control
studies are those trials in which the results of
a test or treatment can be recorded as one of
the two alternatives.
• Two treatments or tests carried out on pair
obtained by matching individuals or pair might
consists of successive treatment of same
individual and result can be recorded as
responded or did not respond, improved or did
not improve, test positive or negative.

18. Cross over trials or matched
case control studies.
No of pair
receiving
treatment A
No of pair
receiving
treatment B
Pairs of patients
Responded
Responded
e
Responded
Did not Respond
f
Did not Respond
Responded
g
Did not Respond
Did not Respond
h
Total
n

19. Cross over trials or matched
case control studies.
Subject Getting B
Positive
Subject
Getting A
Total
Negative
Total
Positive
e
f
e+f
Negative
g
h
g+h
e+g
f+h
n

20. Cross over trials or matched
case control studies.
• Proportion responding to treatment A pA =
(e+f)/n
• Proportion responding to treatment B pB =
(e+g)/n
• Difference = pA-pB = ( f-g)/n
• OR paired = f/g

21. Questions !!!!!!
•
Thank You.