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Additivity predicts the efficacy of most approved combination therapies for advanced cancer

Nature Cancer volume 4, pages 1693–1704 (2023)Cite this article

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Abstract

Most advanced cancers are treated with drug combinations. Rational design aims to identify synergistic combinations, but existing synergy metrics apply to preclinical, not clinical data. Here we propose a model of drug additivity for progression-free survival (PFS) to assess whether clinical efficacies of approved drug combinations are additive or synergistic. This model includes patient-to-patient variability in best single-drug response plus the weaker drug per patient. Among US Food and Drug Administration approvals of drug combinations for advanced cancers (1995–2020), 95% exhibited additive or less than additive effects on PFS times. Among positive or negative phase 3 trials published between 2014–2018, every combination that improved PFS was expected to succeed by additivity (100% sensitivity) and most failures were expected to fail (78% specificity). This study shows synergy is neither a necessary nor common property of clinically effective drug combinations. The predictable efficacy of approved combinations suggests that additivity can be a design principle for combination therapies.

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Fig. 1: Concept of the HSA and additivity models.
Fig. 2: Clinical trial selection process.
Fig. 3: Most drug combinations approved for advanced cancers are as effective as expected by either the highest single agent or additivity model.
Fig. 4: Progression-free survival of combination therapies compared to predictions of HSA and additivity.
Fig. 5: Additivity is a more accurate model than HSA.
Fig. 6: Additivity can predict the success and failure of phase 3 trials.
Fig. 7: HSA and additivity models make similar predictions when monotherapy efficacies are highly variable.
Fig. 8: Some combinations with shared characteristics are associated with lesser efficacy than expected by additivity.

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Data availability

All clinical trials included in the study are listed in Supplementary Tables 1 and 3. References to the clinical trials can be found in Supplementary References. PDX drug response data were obtained from the supplementary tables of Gao et al.44. Reprocessed CTRPv2 cell line drug responses were downloaded from osf.io/sym6h/ (ref. 33). Source Data for Figs. 3 and 4, including digitally traced Kaplan–Meier survival curves, imputed patient event times and predicted PFS distributions under the HSA and additivity models can be retrieved from Figshare at https://doi.org/10.6084/m9.figshare.22229677. Source data are provided with this paper.

Code availability

Source code can be retrieved from github.com/palmerlabunc/clinical-additivity.

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Acknowledgements

We thank the investigators and patients who participated in the clinical trials analyzed in this work. We thank E.V. Schmidt, C. Chen, D.M. Weinstock, S. Hughes, N.E. Sharpless and P.K. Sorger for discussions. We thank I. Zhou for assistance in data collection. H.H. is supported by the Korean Government Scholarship for Study Overseas, S.C.P. is supported by NIGMS grant T32-GM135095 and D.P. is supported by NIGMS grant T32-GM007753 and F30-CA260780. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. The authors received no specific funding for this work.

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Authors and Affiliations

  1. Department of Pharmacology, Computational Medicine Program, UNC Lineberger Comprehensive Cancer Center, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    Haeun Hwangbo, Sarah C. Patterson & Adam C. Palmer

  2. Curriculum in Bioinformatics and Computational Biology, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    Haeun Hwangbo

  3. North Carolina School of Science and Mathematics, Durham, NC, USA

    Andy Dai

  4. Harvard-MIT Division of Health Sciences and Technology, Harvard Medical School and MIT, Cambridge, MA, USA

    Deborah Plana

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Contributions

H.H., D.P. and A.C.P. conceived the study. H.H. implemented the method and performed data analysis. H.H., S.C.P. and A.D. collected clinical trial data. H.H. and A.C.P. wrote the manuscript. All authors reviewed the manuscript and approved the final version.

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Correspondence to Adam C. Palmer.

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A.C.P. has received consulting fees from AstraZeneca, Kymera and Merck, and research funding from Prelude Therapeutics. A.C.P. declares that these interests had no role in study design, analysis or decision to publish. The remaining authors declare no competing interests.

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Extended data

Extended Data Fig. 1 Addition of PFS times is consistent with the Bliss Independence model.

Our model of clinical drug additivity is formally defined as the addition of PFS times. This null hypothesis does not depend on assumptions about underlying tumor growth kinetics and cytotoxic mechanisms. However, mathematically, the addition of PFS times conveniently corresponds to the Bliss independence model under simplifying assumptions. Bliss independence is a common null hypothesis used to classify drug synergy or antagonism in cell-based experiments, which states that P(a + b) = P(a)P(b), where P(x) is the fraction of cells surviving toxin x. This corresponds to the addition of cytotoxic effects on a logarithmic scale. (A) When drug A kills 90% of cancer cells and drug B kills 99% of cancer cells, it will take PFSA and PFSB respectively to observe disease progression, assuming exponential growth of the surviving cancer cell population. If it takes PFSunt for an untreated tumor to progress, drug A and drug B extend PFS by tA = PFSA-PFSunt and tB = PFSB-PFSunt respectively. (B) When drug A and B are additive, A + B will produce 99.9% kill by Bliss Independence. PFS will be extended by tA + tB beyond that of an untreated patient. A mathematical derivation of the concordance between Bliss Independence and addition of PFS times, under simplifying assumptions can be found in Supplementary Notes 1.

Extended Data Fig. 2 Frei’s model of independent drug action is a model of highest single agent.

Bliss’ model and Frei’s model are applications of the addition rule of probability at different biological scales, resulting in different biological interpretations. Bliss’ model was developed to analyze fraction of organisms killed by multiple toxins. Bliss’ model has been applied in cancer research to analyze fraction of tumor cells killed by multiple therapies. In the context of a population of cancer cells, Bliss’ model implies that more cancer cells will be killed by drug A + B than either drug A or B alone. This results in a patient’s response being better than Highest Single Agent. Frei applied the same fundamental principle of probability to remission rates in a population of patients treated with multiple therapies. In the context of a population of patients, Frei’s model implies that more patients will respond to drug A + B then either drug A or B alone. However, this does not require or imply that an individual patient’s response to drug A + B is better than drug A or B alone. The improved response rate described by Frei’s model occurs even if each individual patient’s response is equal to that of the Highest Single Agent.

Extended Data Fig. 3 When patients receive no active therapy for advanced cancer, disease progression is commonly observed at the first scheduled scan.

Progression-Free Survival distributions are shown for patients receiving ‘Best Supportive Care’ (BSC) for (A) advanced colorectal cancer41; (B) BSC plus placebo for metastatic colorectal cancer42; (C) BSC for metastatic colorectal cancer43; (D) BSC plus placebo for advanced gastric or gastro-esophageal junction (GEJ) cancer44; (E) placebo for advanced GEJ cancer45; (F) BSC for advanced non-small-cell lung cancer (NSCLC)46; (G) Placebo for stage IIIB or IV NSCLC47, (H) BSC for advanced malignant pleural mesothelioma48; (I) BSC plus placebo for metastatic renal cell carcinoma49. Red vertical lines indicate the time of first tumor evaluation by radiological scans.

Source data

Extended Data Fig. 4 PFS of combination therapies and their constituent therapies observed in clinical trials compared with predictions of HSA and additivity.

Combinations from the main analysis, two additional combinations that did not strictly satisfy the inclusion criteria, and biomarker subgroups are included. All combination naming follows ‘experimental drug plus control drugs’ format. The clinical trial publications of the combination therapy are cited below the combination names. Panel numbers from Fig. 3 are annotated. BC, breast cancer; Dara., daratumumab; CRC, colorectal cancer; 5FU, 5-fluorouracil; CLL, chronic lymphocytic leukemia; MM, multiple myeloma; Dex., dexamethasone; Bev., bevacizumab; Pembro., pembrolizumab; Atezo., atezolizumab; Chemo., chemotherapy; ITT, intention to treat population; CPS, PD-L1 combined proportion score; LV, leucovorin; TPS, PD-L1 tumor proportion score.

Extended Data Fig. 5 Addition of PFS is a robust clinical definition of drug additivity.

(A) Combinations with reduced doses are mostly inadequate to assess drug interactions. The ideal set of measurements to assess effect addition is when two drugs are combined at full dose (left). The combination therapies analyzed here were administered at least 75% of the monotherapy doses. To test Loewe’s dose-additivity model, at least one measurement of combination activity should be along the equipotent line (right). In the combination therapies we have declined to analyze, the available data cannot determine the shape of the isobole, and therefore cannot test whether a combination is Loewe-synergistic. A typical case that we have declined to analyze is when one drug in the combination is administered at a lower dose than was used in its monotherapy studies. If a combination is administered with one agent at lower dose, and its efficacy is consistent with drug additivity assuming full dose, then two competing hypotheses could explain the observation: 1) The single-agent’s efficacy is not diminished with lowered dose, and the effect of the combination is additive. 2) The combination is synergistic (by Loewe’s model, that is, potency is enhanced). These two explanations are indistinguishable without data on the dose-response relationship in humans. Clinically administered doses are often set at the maximum tolerated dose identified in phase I trials, and for many cancer therapies, clinical studies have observed that lowering a drug’s dose as much as two-fold does not diminish its clinical efficacy56,57,58. For this reason, hypothesis 1 is a possibility unless one has data on single-agent efficacy at the relevant dose. (B) Multiplying Hazard Ratios results in unrealistic predictions with survival times that are far longer than arithmetic addition. Exponential survival functions were simulated with rate parameters of λ = 1, 0.2, and 0.25, for placebo, drug A, and drug B, respectively. The effects of an ‘additive’ combination were simulated by the addition of PFS times (the model proposed in this study, using correlation ρ = 0.3 and scan interval 1.5 months), or by multiplying the hazard ratios of single drugs relative to placebo, which results in a rate of λ = 0.05. Median PFS time from multiplying hazard ratios is four times as large as the most active single drug (14 months vs. 3.5 months), making it much more than the addition of single-drug PFS times. (C) Additivity is less affected by the correlation of monotherapy responses compared to HSA. Combination effects under the HSA model (top left) and the additivity model (top right) vary modestly by the level of correlation (rho) between the monotherapy drug responses. Here, examples of monotherapy PFS distributions were constructed from lognormal survival functions, with an experimental drug (μ = 1, σ = 1, natural log base) and control drug (μ = 1.2, σ = 1, natural log base). Either the HSA model (bottom left) or the additivity model (bottom right) was compared to the control drug by the Cox proportional hazard model. 500 samples were used for each simulated arms to calculate the hazard ratio. Under the HSA model, combination efficacy was modestly improved by lower correlation, but under the additivity model, correlation has negligible influence. Centers of the error bars indicate hazard ratio between the model and the control arm. Error bars indicate 95% confidence intervals. (D) The additivity model predicts near zero benefit when combining placebo or best supportive care (that is, wholly ineffective anti-cancer) drugs. Since wholly ineffective drugs will have the same effect (that is, no therapeutic benefit) on patients, the correlation in response should be ρ = 1. We have also included hypothetical cases where the correlation is lower to demonstrate that the level of correlation has a small impact on the predictions in this scenario.

Source data

Extended Data Fig. 6 Correlations between drug responses from preclinical models were used to compute expected PFS distributions.

(A) Distributions of pairwise Spearman correlations between anti-cancer agents from CTRPv2. (Mean of all drug pairs, 0.30; targeted therapies, 0.28; cytotoxic chemotherapy – targeted therapy pairs, 0.31; cytotoxic chemotherapies, 0.52) (B) Correlation between colorectal cancer PDXs’ best average response from 5-fluorouracil (5FU) and cetuximab. Spearman correlations were measured in pan-cancer cell lines for (C) docetaxel and 5FU (substitution for capecitabine), (D) lapatinib and 5FU (substitution for capecitabine), (E) topotecan (substitution for irinotecan) and 5FU, (F) oxaliplatin (substitution for cisplatin) and gemcitabine, and (G) oxaliplatin (substitution for cisplatin) and methotrexate (substitution for pemetrexed). (H) Correlation between trametinib and dabrafenib in melanoma cell lines. Sample sizes (n) are numbers of unique cancer cell cultures (not replicates of one culture) in panels C-H, and number of unique PDXs (not replicates of one PDX) in panel B.

Source data

Supplementary information

Supplementary Information

Supplementary Note 1 and Supplementary References

Reporting Summary

Supplementary Table

Supplementary Tables 1–3

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Source Data Extended Data Fig. 3

Digitized Kaplan–Meier curve. Original data sources are listed in reference. Data are also on Figshare.

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Source Data Extended Data Fig. 6

Statistical Source Data. Original data source is from CTRPv2 and Gao et al.51.

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Hwangbo, H., Patterson, S.C., Dai, A. et al. Additivity predicts the efficacy of most approved combination therapies for advanced cancer. Nat Cancer 4, 1693–1704 (2023). https://doi.org/10.1038/s43018-023-00667-z

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