Web-based Supporting Materials for “Using multiple risk models with preventive interventions”
by Mitchell H. Gail
This online appendix contains supplementary Figures A.1, A.2, A.3, A.4, A.5, A.6 and A.7.
Figure A.1. Plot of the relative reduction in expected loss, RRL, compared to a perfectly
discriminating model for breast cancer, against the AUC of the breast cancer (health outcome 1)
risk model. Solid loci correspond to risk models for breast cancer and for stroke (health outcome
2). Dashed loci correspond to a risk model for breast cancer, but an assumption that all women
have the same (average) stroke risk. When used, the stroke risk model has good discriminatory
accuracy (AUC2 = 0.973). Open circles (o) represent the baseline relative risks from tamoxifen,
rr1 =0.5 and rr2 =1.6. Solid circles (•) represent a 20% improvement in breast cancer prevention
efficacy compared to tamoxifen, rr1 =0.4 and rr2 =1.6. Plus signs (+) represent a 20% reduction
in stroke risk from compared to tamoxifen, rr1 =0.5 and rr2 =1.28. Risks of breast cancer and
stroke are assumed to be independent.
Figure A.2. Plot of the relative reduction in expected loss, RRL, compared to a perfectly
discriminating model for breast cancer, against the AUC of the breast cancer (health outcome 1)
risk model. Solid loci correspond to risk models for breast cancer and for stroke (health outcome
2). Dashed loci correspond to a risk model for breast cancer, but an assumption that all women
have the same (average) stroke risk. When used, the stroke risk model has poor discriminatory
accuracy (AUC2 = 0.587). Open circles (o) represent the baseline relative risks from tamoxifen,
rr1 =0.5 and rr2 =1.6. Solid circles (•) represent a 20% improvement in breast cancer prevention
efficacy compared to tamoxifen, rr1 =0.4 and rr2 =1.6. Plus signs (+) represent a 20% reduction
in stroke risk from compared to tamoxifen, rr1 =0.5 and rr2 =1.28. Risks of breast cancer and
stroke are assumed to be independent.
Figure A.3. Plot of 100,000 times expected loss against the AUC of the breast cancer (health
outcome 1) risk model. Solid loci correspond to risk models for breast cancer and for stroke
(health outcome 2). Dashed loci correspond to a risk model for breast cancer, but an assumption
that all women have the same (average) stroke risk. When used, the stroke risk model has
intermediate discriminatory accuracy (AUC2 = 0.745). Open circles (o) represent the baseline
relative risks from tamoxifen, rr1 =0.5 and rr2 =1.6. Solid circles (•) represent a 20%
improvement in breast cancer prevention efficacy compared to tamoxifen, rr1 =0.4 and rr2 =1.6.
Plus signs (+) represent a 20% reduction in stroke risk from compared to tamoxifen, rr1 =0.5 and
rr2 =1.28. Risks of breast cancer and stroke are assumed to be independent.
Figure A.4. Plot of 100,000 times expected loss against the AUC of the breast cancer (health
outcome 1) risk model. Solid loci correspond to risk models for breast cancer and for stroke
(health outcome 2). Dashed loci correspond to a risk model for breast cancer, but an assumption
that all women have the same (average) stroke risk. When used, the stroke risk model has good
discriminatory accuracy (AUC2 = 0.973). Open circles (o) represent the baseline relative risks
from tamoxifen, rr1 =0.5 and rr2 =1.6. Solid circles (•) represent a 20% improvement in breast
cancer prevention efficacy compared to tamoxifen, rr1 =0.4 and rr2 =1.6. Plus signs (+) represent
a 20% reduction in stroke risk from compared to tamoxifen, rr1 =0.5 and rr2 =1.28. Risks of
breast cancer and stroke have mean correlation 0.107 induced by correlation 0.25 in the
underlying normal model of Section 2.1.
Figure A.5. Plot of 100,000 times expected loss against the AUC of the breast cancer (health
outcome 1) risk model. Solid loci correspond to risk models for breast cancer and for stroke
(health outcome 2). Dashed loci correspond to a risk model for breast cancer, but an assumption
that all women have the same (average) stroke risk. When used, the stroke risk model has poor
discriminatory accuracy (AUC2 = 0.587). Open circles (o) represent the baseline relative risks
from tamoxifen, rr1 =0.5 and rr2 =1.6. Solid circles (•) represent a 20% improvement in breast
cancer prevention efficacy compared to tamoxifen, rr1 =0.4 and rr2 =1.6. Plus signs (+) represent
a 20% reduction in stroke risk from compared to tamoxifen, rr1 =0.5 and rr2 =1.28. Risks of
breast cancer and stroke have mean correlation 0.198, induced by correlation 0.25 in the
underlying normal model of Section 2.1.
Figure A.6. Plot of 100,000 times expected loss against the AUC of the breast cancer (health
outcome 1) risk model. Solid loci correspond to risk models for breast cancer and for stroke
(health outcome 2). Dashed loci correspond to a risk model for breast cancer, but an assumption
that all women have the same (average) stroke risk. When used, the stroke risk model has good
discriminatory accuracy (AUC2 = 0.973). Open circles (o) represent the baseline relative risks
from tamoxifen, rr1 =0.5 and rr2 =1.6. Solid circles (•) represent a 20% improvement in breast
cancer prevention efficacy compared to tamoxifen, rr1 =0.4 and rr2 =1.6. Plus signs (+) represent
a 20% reduction in stroke risk from compared to tamoxifen, rr1 =0.5 and rr2 =1.28. Risks of
breast cancer and stroke have mean correlation -0.080, induced by correlation -0.25 in the
underlying normal model of Section 2.1.
Figure A.7. Plot of 100,000 times expected loss against the AUC of the breast cancer (health
outcome 1) risk model. Solid loci correspond to risk models for breast cancer and for stroke
(health outcome 2). Dashed loci correspond to a risk model for breast cancer, but an assumption
that all women have the same (average) stroke risk. When used, the stroke risk model has poor
discriminatory accuracy (AUC2 = 0.587). Open circles (o) represent the baseline relative risks
from tamoxifen, rr1 =0.5 and rr2 =1.6. Solid circles (•) represent a 20% improvement in breast
cancer prevention efficacy compared to tamoxifen, rr1 =0.4 and rr2 =1.6. Plus signs (+) represent
a 20% reduction in stroke risk from compared to tamoxifen, rr1 =0.5 and rr2 =1.28. Risks of
breast cancer and stroke have mean correlation -0.192, induced by correlation -0.25 in the
underlying normal model of Section 2.1.