In the 2X2 contingency tables below, the data from a German study investigating the relationship between smoking status and invasive cervical cancer have been stratified by the number of sexual partners that a woman has had. Smoker
Cancer Yes No Total
Yes 12 25 37
No 21 118 139
Total 33 143 176
Two or More Partners
Smoker
Cancer Yes No Total
Yes 96 92 188
No 142 150 192
Total 238 242 480
a. Estimate the odds of cervical cancer for smokers relative to nonsmokers for women who have had at most one sexual partner.
b. Estimate the odds ratio for women who have had two or more sexual partners.
c. Within each stratum, are the odds of being diagnosed with cervical cancer higher for women who smoke or for those who do not smoke?
d. If possible, you would like to combine the information in these two strata to make a single overall statement about the relationship between smoking and cervical cancer. What might be the problem if you were to simply sum the entries in the two tables and calculate an odds ratio?
e. Conduct a test of homogeneity. Based on the results of the test, do you think it is appropriate to use the Mantel-Hansel method to combine the information in these two tables?
f. Compute the Mantel-Hansel estimate of the summary odds ratio.
g. Construct a 99% confidence interval for the summary odds ratio. Does this confidence interval contain the value 1? What does this mean?
h. At the 0.01 level of significance, test the null hypothesis that there is no association between smoking status and the presence of invasive cervical cancer. What do you conclude?