(1) GENERIC Data Sets
(2) BD2.REC. There are 10 single-year age-strata (ages 0 through 9). The question is whether odds ratios are heterogeneous (H0: OR1 = OR2 = . . . = OR10 vs. H1: at least on age-specific odds ratio differs). The c2int statistic has 9 df and derives p = .25. We therefore proceed under the assumption of no interaction. The aOR = cOR = 1.65. Therefore, the crude odds ratio seems to provide the "best" estimate given available information: cOR = 1.65 (95% confidence interval: 1.48, 1.85). This suggests is between a 48% and a 85% increase in leukemia and lymphoma risk with in utero X-rays exposure.
(3) BI-HELM1.REC. Incidence of bicycle helmet use.
(B) Stratified by School Area
S. C. / C. C.
|Santa Clara Use Rate||Contra Costa Use Rate||Incidence Ratio||p value (uncorrected chi-square)|
|1||3: Miner / Fair Oaks||21%||22%||0.97||.91 (NS)|
|2||4: Sedg / Strandwood||55%||36%||1.54||.0014|
|3||5: Sakamoto / WalAcres||33%||58%||0.58||.00000065|
|4||6: Toyon / Disco Bay||32%||22%||1.46||.048|
|5||7: Lietz / Belshaw||38%||42%||0.91||.46 (NS)|
(C) Test for Interaction
H0: RR1 = RR2 = RR3 = RR4 = RR5 vs. H1: At least one stratum-specific relative risk parameter differs ("interaction")
Let alpha = .05
Chi-square / interaction (4, N = 1651) = 32.69, p = .0000014
Conclusion: Reject H0. Significant interaction is confirmed.
The crude (unstratified) comparison was confounded. Interaction was also present. There was no significant difference in two of the five strata (strata 3 and strata 7). In two of the strata, Santa Clara schools showed better helmet-use rates. In one stratum, the Contra Costa district fared better.
(A) cOR ~= 1.5
(B) OR1 = 2.7; OR2 = 1.1
(C) Data suggest an interaction between smoking and number of sexual partners. In women with no or one partner, smoking is positively associated with cervical cancer. In women with multiple sexual partners, this association seems small or non-existent. We might also view the crude odds ratio as confounded, since it fails to reflect these complex relationships. Recommendation: report strata-specific odds ratios. (Comment: This interpretation differs from that in the text by Pagano & Gauvreau.)
(A) Smoking & lung cancer: OR = 4.8 (Cornfield 95% confidence limits for OR: 2.5, 9.5). There is a significant association between
smoking and lung cancer, with smokers having approximately 5-times the risk as non-smokers.
(B) Asbestos & lung cancer: OR = 21.3 (Cornfield 95% confidence limits for OR: 10.5, 43.9). There is an exceedingly strong association between asbestos and lung cancer, with exposed individuals having approximatley 21-times the risk as non-exposed individuals.
(C) Asbestos & lung cancer controlling for smoking (stratified analysis):
Strata-specific odds ratios:
ORsmokers = 60.0 (95% confidence limits, mid-P exact method: 21.9, 181.1)
ORnon-smokers = 2.0 (95% confidence limits, mid-P exact method: 0.6, 6.6)
Test for interaction:
H0: OR1 = OR2 vs. H1: OR1 not = OR2
Let alpha = .05
Chi-square, interaction(1, N = 285) = 17.93, p = .000023
Reject the null hypothesis
Conclude: significant interaction
Recommendation: report strata-specific odds ratios.
cOR = 21.3, aOR = 16.2; also see strata-specific results, above. Confounding is present, since the crude odds ratio fails to accurately reflect the relationship between asbestos exposure and lung cancer risk.
Discussion of results:
- Strata-specific results should be reported and interpreted.
- It should be made clear that there is a very high, significant risk between asbestos exposure and lung cancer in smokers (60-times the risk in asbestos-exposed smokers).
- It should be made clear that there is an insignificant, weak, positive association between asbestos exposure and lung cancer in non-smokers.