Summary statistics for binary data lecture

Summary statistics for

Binary Data

By Dr Zahid Khan

Senior Lecturer King Faisal University

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.

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.

4Case Control Studies

• 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.

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• 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.

Case Control Studies

7Smoking

status CA Lung Positive

CA Lung Negative

Total

Yes a b a + b

No c d c +d

Total a + c b + d a +b +c + d

Biopsy Results

8Smoking

status CA Lung Positive

CA Lung Negative

Total

Yes 60 40 a + b

No 40 160 c +d

Total 100 200 a +b +c + d

Biopsy Results

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

10Cohort Studies

• 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.

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12Relative Ratio/Risk (RR)

• 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

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Smoking status CA Lung Positive

CA Lung Negative

Total

Yes a b a + b

No c d c +d

Total a + c b + d a +b +c + d

Biopsy Results

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Smoking status CA Lung Positive

CA Lung Negative

Total

Yes 50 495 500

No 25 975 1000

Total 75 1425 1500

Biopsy Results

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

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

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.

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

Cross over trials or matched case control studies.

Subject Getting B

Positive Negative Total

SubjectGetting A

Positive e f e+f

Negative g h g+h

Total e+g f+h n

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

Questions !!!!!!

• Thank You.