Question

It has been noted that metal workers have an increased risk for cancer of the internal nose and paranasal sinuses, perhaps as a result of exposure to cutting oils. A study was conducted to see whether this particular exposure also increases the risk for squamous cell carcinoma of the scrot.um (Rousch et al., 1982). Cases included all 45 squamous cell carcinomas of the scrot.um diagnosed in Connecticut residents from 1955 to 1973, as obtained from the Connecticut Tumor Registry. Matched controls were selected for each case based on the age at death (within eight years), year of death (within three years), and number of jobs as obtained from combined death certificate and directory sources. An occupational indicator of metal worker (yes/no) was evaluated as the possible risk factor in this study;

results are shown in the following Table:  

	controls
cases	yes	no
yes	2	26
no	5	12

a) Find a 95% confidence interval for the odds ratio measuring the strength of the relationship between the disease and the exposure.

b) Test for the independence between the disease and the exposure.

Answer 1

Here the table is 2 x 2 contigency table is given below

	controls
cases	yes	no	Total
yes	2	26	28
no	5	12	17
Total	7	38	45

Here odds ratio = ad/bc = (2 * 12)/(5 * 26) = 0.1846

Here 95% critical test statstici = +- 1.96

standard error = SE = sqrt [1/a + 1/b + 1/c + 1/d] = sqrt [1/2 +1/26 + 1/5 + 1/12] = 0.90653

L = ln (Odd Ratio) = ln (0.1846) = -1.6895

Lower Limit = EXP( L - 1.96 SE) = EXP (-1.6895 - 1.96 * 0.90653) = 0.03123

Upper Limit = EXP[L + 1.96E] = EXP (-1.6895 + 1.96 * 0.90653) = 1.09122

(b) Here for test for independence we will see that if the 95% confidence interval for the odds ratio consit the value of 1 so here we can say that disease is independent from the exposure. Here the 95% confidence interval limits are given above.