Introductory Biostatistics

and for heavy smokers,

a¼ 14

r 1 c 1

n

¼

ð 17 Þð 110 Þ

163

¼ 11 : 47

r 1 r 2 c 1 c 2

n^2 ðn 1 Þ

¼

ð 17 Þð 146 Þð 110 Þð 53 Þ

ð 163 Þ^2 ð 162 Þ

¼ 3 : 36

ad

n

¼

ð 14 Þð 50 Þ

163

¼ 4 : 29

bc

n

¼

ð 3 Þð 96 Þ

163

¼ 1 : 77

These results are combined to obtain thezscore:

z¼

ð 11  9 : 38 Þþð 70  58 : 55 Þþð 14  11 : 47 Þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

6 : 34 þ 22 : 28 þ 3 : 36

p

¼ 2 : 76

and azscore of 2.76 yields a one-tailedpvalue of 0.0029, which is beyond the
1% level. This result is stronger than those for tests at each level because it is
based on more information, where all data at all three smoking levels are used.
The combined odds ratio estimate is

ORMH¼

7 : 47 þ 28 : 05 þ 4 : 29

5 : 85 þ 16 : 60 þ 1 : 77

¼ 1 : 64

representing an approximate increase of 64% in lung cancer risk for those
employed in the shipbuilding industry.
Note: An SAS program would include these instructions:

DATA;
INPUT SMOKE SHIP CANCER COUNT;
CARDS;
11111
11235

MANTEL–HAENSZEL METHOD 221