Question

Consider a case-control study of the possible association between menopausal estrogen therapy and breast cancerdescribed by Ross et al. (1980). Only women with intact ovaries, which comprise 80% of the cases, were included inthe study. All the subjects were divided by TMD level (total milligram accumulated dose, TMD), and the individualmatches were ignored. The data are shown below

TMD   Cases  Controls Total

>1500    28        23         51

0-1499  71       159      230

Total    99        182      281

Carry out appropriate test to evaluate possible association between estrogen therapy and breast cancer. Also determine if the association is significant and interpret your findings.

Answer 1

The Chi-square test of independence is performed to test whether menopausal estrogen therapy and breast cancer are associated.

Hypothesis:

Null hypothesis: The variables menopausal estrogen therapy and breast cancer are independent

Alternative hypothesis: The variables menopausal estrogen therapy and breast cancer are dependent

Critical value

The critical value for the chi-square statistic is obtained from the chi-square distribution table for the degree of freedom = (r-1)(c-1) = (2-1)(2-1)=1 for significance level = 0.05, the critical value is,

Test statistic

The observed values are,

TMD	Cases	Control	Total
>1500	28	23	51
0-1499	71	159	230
Total	99	182	281

The expected values are obtained using the formula,

TMD	Cases	Control	Total
>1500	51*99/281=17.9680	51*182/281=33.0320	51
0-1499	230*99/281=81.0320	230*182/281=148.9680	230
Total	99	182	281

The Chi-Square value is obtained using the formula

Observed, Oi	Expected, Ei
28	17.9680	5.6012
71	81.0320	1.2420
23	33.0320	3.0468
159	148.9680	0.6756
	Total	10.5655

Conclusion:

Since the chi-square value is greater than the critical value, the null hypothesis is rejected at a 5% significance level.

Hence there is sufficient evidence to conclude that the variables menopausal estrogen therapy and breast cancer are associated.