Supplemental Appendix 1: List of Trials by NCT numbers

NCT00192165 / NCT00726583 / NCT01015222 / NCT01219699
NCT00215605 / NCT00731263 / NCT01021072 / NCT01253707
NCT00329004 / NCT00732836 / NCT01039155 / NCT01263145
NCT00428545 / NCT00752011 / NCT01054313 / NCT01337765
NCT00429234 / NCT00756847 / NCT01057264 / NCT01339871
NCT00454090 / NCT00761644 / NCT01087983 / NCT01363232
NCT00458731 / NCT00770731 / NCT01088763 / NCT01378377
NCT00491855 / NCT00811993 / NCT01110083 / NCT01411410
NCT00495872 / NCT00813384 / NCT01110486 / NCT01430572
NCT00507585 / NCT00818831 / NCT01115790 / NCT01454804
NCT00522652 / NCT00841191 / NCT01117623 / NCT01455532
NCT00529022 / NCT00861419 / NCT01136733 / NCT01514123
NCT00530907 / NCT00880321 / NCT01152203 / NCT01532011
NCT00543504 / NCT00895128 / NCT01155453 / NCT01548144
NCT00554268 / NCT00895362 / NCT01171924 / NCT01552434
NCT00600496 / NCT00895687 / NCT01178112 / NCT01624766
NCT00610493 / NCT00920257 / NCT01183663 / NCT01665183
NCT00630552 / NCT00940381 / NCT01187199 / NCT01857193
NCT00658970 / NCT00941499 / NCT01192165 / NCT01901172
NCT00678133 / NCT00955812 / NCT01197170 / NCT01928459
NCT00678769 / NCT00972686 / NCT01201694 / NCT05182191
NCT00687622 / NCT00980239 / NCT01209143
NCT00725933 / NCT01014936 / NCT01213238

Supplementary Appendix 2: Synergy and antagonism interaction examples

Note: univariateodds ratios calculated here will not match those presented in the main text, as those presented in the main text are multivariate.

Table 1. Synergy example:Frequency of clinical benefit stratifying by anti-metabolite and VEGF/R inhibitor use
Anti-Metabolite / VEGF/R inhibitor / # Total / # Clinical Benefit / OR for clinical benefit
No / No / 708 / 177 (25%) / 1.0 (REF)
No / Yes / 675 / 248 (37%) / 1.7
Yes / No / 49 / 9 (18%) / 0.7
Yes / Yes / 66 / 35 (53%) / 3.4
Odds ratio for clinical benefit is calculated in reference to patients who did not receive anti-metabolite chemotherapy and did not receive VEGF/R inhibitors.
Abbreviations: OR, odds ratios; REF, reference, VEGF/R, vascular endothelial growth factor or receptor

To illustrate a synergistic interaction, supplementary table 1 presents univariateodd ratios (ORs) for clinical benefit stratifying by antimetabolite chemotherapy and vascular endothelial growth factor or receptor (VEGF/R) inhibitor use.

We first calculate the OR for clinical benefit forVEGF/R inhibitor use in patients not treated with anti-metabolite chemotherapy (Table 1; Row 2). The equation is:

Among patients not treated with anti-metabolite chemotherapy, the probability of clinical benefit in patients treated with VEGF/R inhibitors is 0.37 and thus odds of clinical benefit is 0.37/(1-0.37)=0.58. Similarly, the probability of clinical benefit in patients not treated with VEGF/R inhibitors is 0.25 and the odds of clinical benefit is 0.25/(1-0.25)=0.33.

Therefore the OR for clinical benefit for VEGF/R inhibitor use in patients not treated with anti-metabolite chemotherapy is 0.58/0.33=1.7. This calculation is then repeated for the remaining two scenarios (Table 1; Rows3-4).

In the event of no interaction (not synergistic or antagonistic), thepredictedunivariate OR for clinical benefit would be: 1.7 x 0.7 = 1.2. However, the observed OR for clinical benefit was 3.4. As the observed OR is substantially greater than the predicted OR, this represents a synergistic interaction.

Table 2. Antagonism example: frequency of clinical benefit stratifying by melanoma diagnosis and VEGF/R inhibitor use
Melanoma diagnosis / VEGF/R inhibitor / # Total / # Clinical Benefit / OR for clinical benefit
No / No / 663 / 147 (22%) / 1.0 (REF)
No / Yes / 686 / 271 (40%) / 2.3
Yes / No / 94 / 39 (41%) / 2.5
Yes / Yes / 55 / 12 (22%) / 1.0
Odds ratio for clinical benefit is calculated in reference to patients who were not diagnosed with melanoma and did not receive VEGF/R inhibitors.
Abbreviations: OR, odds ratios; REF, reference, VEGF/R, vascular endothelial growth factor or receptor

Conversely, to illustrate an antagonistic interaction, supplementary table 2 presents univariate odd ratios (ORs) for clinical benefit stratifying by melanoma diagnosis and VEGF/R inhibitor use. In the event of no interaction, the predicted univariate OR for clinical benefit would be: 2.3 x 2.5 = 5.8. However, the observed OR for clinical benefit was 1.0. As the observed OR is substantially smaller than the predicted OR, this represents an antagonistic interaction.