Drug combinations are used to treat most types of cancer, and are often essential to treatments with curative intent. Here I will present predictively accurate simulations of clinical trials of combinations of cancer therapies. The use of these simulations will be demonstrated by retrospective analysis of 25 years of FDA approvals, retrospective analysis of curative regimens for pediatric acute lymphocytic leukemia (ALL), prospective prediction of most approved combination therapies with immune checkpoint inhibitors for solid tumors, and prospective prediction of the efficacy of curative regimens for Diffuse Large B-Cell Lymphoma (DLBCL) and Peripheral T-Cell Lymphoma (PTCL). Pharmacological concepts of drug additivity and synergy are conventionally defined for pre-clinical experiments. In this talk I will illustrate how to adapt these concepts to human clinical data, accounting for inter-patient heterogeneity and intra-tumor heterogeneity in drug sensitivity. Simulations under this framework can use clinically measured single-drug response distributions (Progression Free Survival; PFS) to simulate multi-drug response distributions. This work advances upon our prior studies on inter-patient variation, by adding considerations of intra-tumor heterogeneity which is critical to understand treatments with curative intent. By modeling ‘drug additivity’ in human populations, we find that 95% of combination therapies FDA approved from 1995 to 2020 exhibit PFS distributions that are equal to the sum of their parts, or less. In an analysis of both positive and negative phase 3 trials, every successful drug combination was predicted to succeed by additivity (100% sensitivity) and most failed combinations were predicted to fail (78% specificity). Although we find that synergy is rare in humans, this does not mean approved treatments are ineffective; it means most effective, life-saving drug combinations are predictably so. I will next present models of curative drug combinations for several blood cancers. Our simulations implement multi-drug dose-response functions in heterogeneous populations of tumor cells, within heterogeneous cohorts of patients, and is calibrated on clinical and experimental data that quantifies heterogeneity in relevant parameters. For the most common childhood cancer, ALL, progress in response rates and cure rates from 1948 to 1988 are quantitatively consistent with a mathematical model of how combination therapy reduces the probability that cancer cells can survive every drug in a combination. In the most common adult blood cancer, DLBCL, we will present a mechanistically detailed simulation which reproduces PFS distributions from past trials of standard combination regimens, and which accurately predicted (before the trial result was first published) the survival improvement of a new combination, RCHP-polatuzumab-vedotin. Finally, I will illustrate the utility of these models for trial design in PTCL. These clinically accurate models can help to understand the efficacy of combination therapies in humans. Most importantly, model performance has reached a point that should have practical utility to the design of new drug combinations and the clinical trials that test them.