426 STAT HW2 2.5. a. Neither. "1.7 times more ..." would mean a relative risk of 2.7. b. Let 1 denote the probability of getting invasive breast cancer for the women taking the drug and let 2 denote the probability of getting invasive breast cancer for the women taking placebo.
1 2
It is given that
= (1 - 0.45).
(i) the relative risk for those taking the drug compared to those taking 1 placebo: 2 = 0.55 (ii) the relative risk for those taking placebo compared to those taking the drug:
2 1
=
1 0.55
= 1.82
2.7. a. Quoted interpretation is that of relative risk. The correct interpretation is "The odds of survival for females was 11.4 times as high as the odds for males." b. Let 1 denote the probability of survival for females and let 2 denote
1 that for males. It is given that (1-1 ) = 2.9. It follows that 1 = 0.744. 1 (1-2 ) In addition we know (1-1 )2 = 11.4. So we have 2.9(1-2 ) = 11.4 and 2
2 = 0.203. (i) the proportion of survival for females: 1 = 0.744 (ii) the proportion of survival for females: 2 = 0.203 c. R = 2.16. a. The response variable is whether or not lung cancer is present. The explanatory variable is whether or not the patient smoked. 1
1 2
=
0.744 0.203
= 3.7
b. a case-control study c. The data cannot be used to compare smokers with nonsmokers in terms of the proportion suffered who lung cancer. This is because the column totals are artificially fixed. d. The odds ratio is given by ^ 688 59 = 2.97. = 650 21 The odds of getting lung cancer for smokers are 2.794 times the odds of getting lung cancer for smokers. The confidence interval for the log of the odds ratio is log(2.794) 1.96 1 1 1 1 + + + = (0.52, 1.54). 688 59 650 21
Since 0 is not included, we can state with 95% confidence that the odds ratio is different from 1, meaning that there is a positive association between smoking and lung cancer. 2.20 Table 1: Stage of Breast Cancer at Diagnosis and Living Arrangement advanced local total 59 85 144 109 100 209 53 36 89 221 221 442
living alone living with spouse living with others total
The null hypothesis is H0 : "stage of breas...