KEY: Case-Control Studies

(1) DOLL1950

(A) 2-by-2 Table
Cases Controls 
Smoke+ 647 622 1269
Smoke - 2 27 29
649 649 1298
(B) Exposure proportion, cases = 647 / 649 = .997; Exposure proportion, controls = 622 / 649 = .958
(C) Exposure odds ratio (sample estimate) = 14.0 (95% confidence interval for OR : 3.5, 122.2; exact method as computed by STATCALC. reference: Mehta et al., 1985).
(D) H0: EOR = 1 vs. H1: EOR not = 1
Let alpha = .05.
Chi-square, Yates (1, N = 1298) = 20.32, p = .000007
Reject H0.
There is a strong, significant positive association between smoking and lung cancer; the odds ratio estimate suggests that smokers have ~14x the risk of lung cancer, compared with non-smokers.

(2) ESOPH_CA.REC: Tobacco Analysis

(A) p^1 = 64 / 200 cases = 32.0%; p^2 = 150 / 775 = 19.4%
(B) EOR^ = 1.96 (95% confidence interval: 1.36, 2.82)
(C) H0: EOR = 1 vs. H1: EOR not = 1
Let alpha = .05
Chi-square, Yates (1, N = 975) = 14.11, p = .00017
Reject the null hypothesis
(D) These results are highly significant. Heavy tobacco consumption seems to double the risk of esophageal cancer, compared with moderate to low consumption.

(3) ESOPH_CA.REC: Age Analysis

(A) p^1 = 144 / 200 cases = 72.0%; p^2 = 303 / 775 = 39.1%
(B) EOR^ = 4.01 (95% confidence interval: 2.80, 5.74)
(C) H0: EOR = 1 vs. H1: EOR not = 1
Let alpha = .05
Chi-square, Yates (1, N = 975) = 68.00, p < .000001
Reject the null hypothesis
(D) These results are highly significant. The older age-group has 4 times the risk of this outcome.
 

(4) BD2.REC (In utero X-ray Exposure and Childhood Leukemia/Lymphoma)

The odds ratio associated with in utero exposure to irradiation is 1.7 (95% confidence interval: 1.5, 1.9; p value < .00000005 by the uncorrected chi-square method). This represents a weak but statistically significant association between in utero irradiation and childhood leukemia and lymphatic cancers.
 

(5) IUD

Cases Controls
IUD + 89 640
IUD - 194 3193
Totals
 283 3833
(A) p^1 = 89 / 283 = .314; p^2 = 640 / 3833 = .167; OR^ = 2.29 (95% conf. int. for OR: 1.76, 2.98)
(B) H0: OR = 1 vs. H1: OR is not equal to 1

Let alpha = .05
Chi-square, Yates' (1, N = 4116) = 38.34, p < .000001
Reject H0
(C) IUDs (about) doubled the risk of infertility.

 

(6) PROSTATE.REC

(A) p^1 = 61 / 175 = .349; p^2 = 93 / 258 = .360

(B) OR^ = 0.95 (95% confidence interval: 0.62, 1.45)
(C) H0: OR = 1 vs. H1: OR is not equal to 1
Let alpha = .05
Chi-square, Yates' (1, N = 433) = 0.02, p = .88
Do not reject H0
(D) This study found no significant association between vasectomy and prostate cancer.
(E) Assumptions: EOR = 1.5, m2 / m1 = 1.47; p2 = 36%; alpha = .05. Based on the assumptions as stated, power = 53.0%
(F) Same assumptions as above, sample sizes to achieve power = .8:
  To detect an OR of 1.3: m1 = 835, m2 = 1228, N = 2063
  To detect an OR of 1.5: m1 = 352, m2 = 518, N = 870
  To detect an OR of 2.0: m1 = 123, m2 = 181, N = 304
  To detect an OR of 3.0: m1 = 51, m2 = 75, N = 126
 

(7) ASBESTOS

(A) Lung cancer and smoking: OR^ = 4.80 (Cornfield 95% confidence limits for OR: 2.5, 9.5). Smoking increased the risk of lung cancer by a factor of 5.

(B) Lung cancer and asbestos exposure: OR^ = 21.33 (Cornfield 95% confidence limits for OR: 10.5, 43.8). Asbestos exposed workers were at 21 times the risk of lung cancer, as compared to non-exposed workers.

Comment: It might now be interesting to sort out the relationship between asbestos and lung cancer by looking at the risk of lung cancer in smokers and non-smokers, separately.