The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

140 CHAPTER 8 Contingency Tables

situation, the relative risk is the same as the hazard ratio. This will be

explained in Chapter 10.

A closely related concept is the odds ratio. Suppose we want to do

a case - control study to look at the risk that smoking cases with respect

to lung cancer rather than a cohort study. For such a study, we would

have a 2 × 2 table of the form given as Table 8.12.

Now Table 8.13 shows the calculation for a particular small case -

control study.

Table 8.12

2 × 2 Assessment of an Odds Ratio

Factor Cases Controls

Yes a B

No c D

Total a + c b + d

OR (odds ratio) = ( a / c )/( b / d ) = ad /( bc )

Table 8.13

2 × 2 Assessment of an Odds Ratio

Smoker Lung cancer cases Controls

Yes 18 15

No 9 12

Total 29 27

OR (odds ratio) = 18(12)/[(15)9] = 1.6

Table 8.11

Assessment of Relative Risk in a 2 × 2 Table from Lung Cancer

Cohort Study

Lung cancer

Smokers Present Absent Total

Yes 98 202 300
No 35 665 700
RR (relative risk) = a ( c + d )/[ c ( a + b )] = 98(700)/[35(300)] = 6.53