Hundreds of clinical trials are currently underway testing combinations of Immune Checkpoint Inhibitors (ICIs) with other cancer therapies in the hope that drug combinations will be more effective than monotherapy. Enhanced efficacy is proposed to result from drug additivity or synergy involving mechanisms such as immune priming. In this paper we re-analyze progression free survival data from thirteen recent Phase III trials of ICI combinations and find that observed benefits are fully and accurately accounted for by an increased chance that each patient will respond to a single-agent, consistent with the predictions of drug independence, with no requirement for additive or synergistic efficacy. Thus, the likely anti-tumor efficacy of new ICI combinations can be reliably predicted from monotherapy data (Pearson r=0.98, P < 5×10-9, n = 4173 patients and 8 types of cancer), although predicting adverse effects is not yet possible. Realizing the clinical potential of drug additivity or synergy is likely to require biomarkers that identify patients in whom multiple constituents of a drug combination are active.