A New Bliss Independence Model to Analyze Drug Combination Data
Open accessAbstract
The Bliss independence model is widely used to analyze drug combination data when screening for candidate drug combinations. The method compares the observed combination response (Y(O)) with the predicted combination response (Y(P)), which was obtained based on the assumption that there is no effect from drug-drug interactions. Typically, the combination effect is declared synergistic if Y(O) is greater than Y(P). However, this method lacks statistical rigor because it does not take into account the variability of the response measures and can frequently cause false-positive claims. In this article, we introduce a two-stage response surface model to describe the drug interaction across all dose combinations tested. This new method enables robust statistical testing for synergism at any dose combination, thus reducing the risk of false positives. The use of the method is illustrated through an application describing statistically significant "synergy regions" for candidate drug combinations targeting epidermal growth factor receptor and the insulin-like growth factor 1 receptor.
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Even when replicates are available, multiple testing problems arise from repeatedly performing a statistical test across all combination doses.
“Even when replicates are available, multiple testing problems arise from repeatedly performing a statistical test across all combination doses (Zhao et al 2014).”
From Evaluation of Drug Combination Effect Using a Bliss Independence Dose–Response Surface Model (2018) · cites this paper as Zhao et al 2014
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“In the experiments in which neonicotinoids were used in combination, we used ‘effect-based strategy’ method, in particular, the Bliss independence model (see Zhao et al., 2014; Foucquier and Guedj, 2015).”
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“S2) 57 .”
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“Preclinical studies For combination assays, the interaction between romidepsin and doxorubicin was evaluated using the Bliss Independence model (25).”
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“Based on calculations using the Bliss additivity model, we determined that the combination effect was synergistic when using 125 kBq/kg bw HER2-TTC + 50 mg/kg bw olaparib and 300 kBq/kg bw HER2-TTC + 50 mg/kg bw olaparib [26] (Table S3).”
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“Considering the differences in chemical nature and cellular targets of fenbendazole and amphotericin B, we also calculated the Bliss synergism scores (51) against C.”
BackgroundPatient-Derived Cells to Guide Targeted Therapy for Advanced Lung Adenocarcinoma
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Anti‐Tumorigenic Potential of a Novel Orlistat‐AICAR Combination in Prostate Cancer Cells
Wright, C. A., Iyer, A. K. V., Kaushik, V., & Azad, N. (2017) · Journal of Cellular Biochemistry · doi:10.1002/jcb.26033 · Cited by 35 · see citing works
“The Bliss model was used to compute the expected combined effects of two drugs as the product of their individual effects based on the assumption that there is no effect from drug-drug interactions, as previously described [Bliss, 1939; Zhao et al., 2014].”
MethodDrug Combination Modeling: Methods and Applications in Drug Development
Pearson, R. A., Wicha, S. G., & Okour, M. (2022) · The Journal of Clinical Pharmacology · doi:10.1002/jcph.2128 · Cited by 35 · see citing works
Huber, A. D., Wright, W. C., Lin, W., Majumder, K., Low, J. A., Wu, J., Buchman, C. D., Pintel, D. J., & Chen, T. (2020) · Cellular and Molecular Life Sciences · doi:10.1007/s00018-020-03505-y · Cited by 34 · see citing works
“1 3 combination of EE2 and TNC calculated using the Bliss independence model [51].”
MethodHe, M., Wang, D., Zou, D., Wang, C., Lopes-Bastos, B., Jiang, W. G., Chester, J. D., Zhou, Q., & Cai, J. (2016) · Oncotarget · doi:10.18632/oncotarget.13413 · Cited by 34 · see citing works
“In order to assess the combined effects of cisplatin and curcumin on the ovarian cancer spheroids, the responses were measured by Bliss independence reference models of synergy [43], using Graphpad Prism® (Version 6.”
MethodCurrier, M. A., Sprague, L., Rizvi, T. A., Nartker, B. A., Chen, C., Wang, P.-Y., Hutzen, B. J., Franczek, M., Patel, A. V., Chaney, K. E., et al. (2017) · Oncotarget · doi:10.18632/oncotarget.14885 · Cited by 32 · see citing works
“We thank Dr. Winfried Just (Ohio University, Athens, OH) for helpful consultation regarding Bliss Independence Modeling of in vivo synergy.”
MethodSomers, K., Evans, K., Cheung, L., Karsa, M., Pritchard, T., Kosciolek, A., Bongers, A., El‐Ayoubi, A., Forgham, H., Middlemiss, S., et al. (2019) · Leukemia · doi:10.1038/s41375-019-0683-6 · Cited by 32 · see citing works
Shigeta, S., Lui, G. Y. L., Shaw, R. C., Moser, R. D., Gurley, K. E., Durenberger, G., Rosati, R., Diaz, R. L., Ince, T. A., Swisher, E. M., et al. (2021) · Molecular Cancer Therapeutics · doi:10.1158/1535-7163.mct-20-0809 · Cited by 29 · see citing works
“Drug synergy was calculated using the Bliss method and graphed using Combenefit software (23, 24).”
MethodCombinatorial drug approaches to tackleCandida albicansbiofilms
Cremer, K. D., Staes, I., Delattin, N., Cammue, B. P. A., Thevissen, K., & Brucker, K. D. (2015) · Expert Review of Anti-infective Therapy · doi:10.1586/14787210.2015.1056162 · Cited by 31 · see citing works
Wilkinson, M., Smith, H. G., McEntee, G., Kyula, J., Pencavel, T. D., Mansfield, D., Khan, A., Roulstone, V., Hayes, A. J., & Harrington, K. J. (2016) · Oncotarget · doi:10.18632/oncotarget.12820 · Cited by 30 · see citing works
“A recently published modification of Bliss independence analysis could not be used because of the number of variables within our dataset [58].”
MethodGrundy, M. A., Balakrishnan, S., Fox, M., Seedhouse, C., & Russell, N. H. (2018) · Oncotarget · doi:10.18632/oncotarget.26540 · Cited by 30 · see citing works
The recent progress of deep-learning-based in silico prediction of drug combination
Liu, H., Fan, Z., Lin, J., Yang, Y., Ran, T., & Chen, H. (2023) · Drug Discovery Today · doi:10.1016/j.drudis.2023.103625 · Cited by 29 · see citing works
Meyer, L. K., Delgado-Martín, C., Maude, S. L., Shannon, K., Teachey, D. T., & Hermiston, M. L. (2019) · PLoS ONE · doi:10.1371/journal.pone.0220026 · Cited by 29 · see citing works
“Drug-drug interactions were assessed using the Bliss independence model of synergy [14]”
MethodSalimi, A., Schroeder, K. M., Schemionek, M., Vieri, M., Maletzke, S., Gezer, D., Masouleh, B. K., & Appelmann, I. (2022) · BMC Cancer · doi:10.1186/s12885-022-09775-y · Cited by 29 · see citing works
“The Bliss formula was used to analyze the efficacy of drug combination in comparison with monotherapy, using equation: Yab,P = (Ya + Yb)- (Ya × Yb), which defines the concepts of synergy, antagonism and additive effects between two inhibitory drugs [25].”
MethodAhn, S., Saha, A., Clark, R., Kolonin, M. G., & DiGiovanni, J. (2022) · Oncogene · doi:10.1038/s41388-022-02466-9 · Cited by 29 · see citing works
“To investigate the synergistic, anticancer effect of the combination of AMD3100 and D-CAN, we used the Bliss Independence Model as previously described [71].”
MethodActivity of the antiestrogenic cajanin stilbene acid towards breast cancer
Fu, Y., Kadioglu, O., Wiench, B., Wei, Z., Wang, W., Luo, M., Yang, X., Gu, C., Zu, Y., & Efferth, T. (2015) · The Journal of Nutritional Biochemistry · doi:10.1016/j.jnutbio.2015.06.004 · Cited by 29 · see citing works
“3-μM and 1-μM tamoxifen resulted in a synergistic effect towards inhibition ofMCF-7 cell growth as evaluated by Bliss model equation [34].”
MethodInformatics Approaches for Predicting, Understanding, and Testing Cancer Drug Combinations
Tang, J. P. (2017) · Methods in molecular biology · doi:10.1007/978-1-4939-7154-1_30 · Cited by 28 · see citing works
“Bliss The effect as if two drugs are acting independently Synergy landscape [78]”
BackgroundSingle-Stranded DNA Gap Accumulation Is a Functional Biomarker for USP1 Inhibitor Sensitivity
da Costa, A. A. B. A., Somuncu, O., Ravindranathan, R., Mukkavalli, S., Martignetti, D. B., Nguyen, H. Q., Jiao, Y., Lamarre, B. P., Sadatrezaei, G., Moreau, L. A., et al. (2024) · Cancer Research · doi:10.1158/0008-5472.can-23-4007 · Cited by 28 · see citing works
“Assessment of synergy was calculated based on the Bliss model of synergy using Combenefit software (40, 42).”
A novel resveratrol–salinomycin combination sensitizes ER-positive breast cancer cells to apoptosis
Venkatadri, R., Iyer, A. K. V., Kaushik, V., & Azad, N. (2017) · Pharmacological Reports · doi:10.1016/j.pharep.2017.03.024 · Cited by 27 · see citing works
Somers, K., Wen, V. W., Middlemiss, S., Osborne, B., Forgham, H., Jung, M., Karsa, M., Clifton, M., Bongers, A., Gao, J., et al. (2019) · Oncogene · doi:10.1038/s41388-018-0666-5 · Cited by 27 · see citing works
Bollmann, L. M., Skerhut, A. J., Asfaha, Y., Horstick‐Muche, N., Hanenberg, H., Hamacher, A., Kurz, T., & Kassack, M. U. (2022) · International Journal of Molecular Sciences · doi:10.3390/ijms232113398 · Cited by 25 · see citing works
Ono, A., Sano, O., Kazetani, K., Muraki, T., Imamura, K., Sumi, H., Matsui, J., & Iwata, H. (2017) · PLoS ONE · doi:10.1371/journal.pone.0181243 · Cited by 25 · see citing works
Weidenauer, K., Schmidt, C., Rohde, C., Pauli, C., Blank, M. F., Heid, D., Waclawiczek, A., Corbacioglu, A., Göllner, S., Lotze, M., et al. (2023) · Leukemia · doi:10.1038/s41375-023-01951-8 · Cited by 25 · see citing works
“To identify synergistic effects of drug combinations, a synergy score was computed using the Bliss Independence Model [22].”
BackgroundMethodRuiz, N. Q., Campo, Y. C., Stashenko, E. E., & Fuentes, J. L. (2017) · Photochemistry and Photobiology · doi:10.1111/php.12735 · Cited by 25 · see citing works
“This model used the probability theory of complete additive effect (39), where the observed (Yo) and expected (YE) responses of mixtures were compared.”
BackgroundMethodInhibiting casein kinase 2 overcomes paclitaxel resistance in gastric cancer
Jung, M., Park, K. H., Kim, H. M., Kim, T. S., Zhang, X., Park, S.-M., Beom, S., Kim, H. S., Cheong, J., Chung, H. C., et al. (2019) · Gastric Cancer · doi:10.1007/s10120-019-00971-7 · Cited by 25 · see citing works
Coates, J. T. T., Rodríguez‐Berriguete, G., Puliyadi, R., Ashton, T. M., Prevo, R., Wing, A., Granata, G., Pirovano, G., McKenna, G. W., & Higgins, G. S. (2020) · Cell Death Discovery · doi:10.1038/s41420-020-00343-6 · Cited by 23 · see citing works
Deusenbery, C. B., Carneiro, O., Oberkfell, C., & Shukla, A. (2023) · ACS Infectious Diseases · doi:10.1021/acsinfecdis.3c00239 · Cited by 24 · see citing works
Venetoclax-based Rational Combinations are Effective in Models of MYCN -amplified Neuroblastoma
Dalton, K. M., Krytska, K., Lochmann, T. L., Sano, R., Casey, C. E., D'Aulerio, A., Khan, Q. A., Crowther, G. S., Coon, C. M., Cai, J., et al. (2021) · Molecular Cancer Therapeutics · doi:10.1158/1535-7163.mct-20-0710 · Cited by 24 · see citing works
“The Bliss excess is demonstrated for each datum as the difference between the Bliss expectation and the observed growth inhibition induced by each combination (26, 27).”
BackgroundSynergistic activity of combined inhibition of anti-apoptotic molecules in B-cell precursor ALL
Seyfried, F., Stirnweiß, F. U., Niedermayer, A., Enzenmüller, S., Hörl, R. L., Münch, V., Köhrer, S., Debatin, K., & Meyer, L. H. (2022) · Leukemia · doi:10.1038/s41375-021-01502-z · Cited by 24 · see citing works
“5A) and determining synergy scores (Bliss independence model [23, 24]; Fig.”
Backgroundde Groot, E., Varghese, S., Tan, L., Knighton, B. G., Sobieski, M. M., Nguyen, N. H., Park, Y. S., Powell, R. T., Lorenzi, P. L., Zheng, B., et al. (2022) · Cancer & Metabolism · doi:10.1186/s40170-022-00281-0 · Cited by 23 · see citing works
“Rigor and reproducibility of the combinatorial drug screening assay was performed in accordance with the NCATS Assay Guidance Manual [19], and a bootstrapped bliss independence model was used to calculate drug synergy [20].”
MethodJensen, K. V., Hao, X., Aman, A. M., Luchman, H. A., & Weiss, S. (2020) · Neuro-Oncology Advances · doi:10.1093/noajnl/vdaa020 · Cited by 23 · see citing works
“The JAK2/STAT3 pathway is a potent pro-survival signaling pathway and activated STAT3 is expressed at high levels in more than 90% of GBMs 32,43 and patient-derived BTSCs. 44 This led us to investigate the effectiveness of a JAK2 inhibitor, pacritinib, in combination with afatinib.”
Sahler, J., Eade, C. R., Altier, C., & March, J. C. (2018) · Infection and Immunity · doi:10.1128/iai.00674-17 · Cited by 22 · see citing works
“Synergy calculations were performed in Microsoft Excel testing for Bliss independence (42, 43).”
MethodWu, C.-H., Yang, C., Wang, L., Gao, H.-X., Rakhshandehroo, T., Afghani, S., Pincus, L. B., Balassanian, R., Rubenstein, J. L., Gill, R. M., et al. (2020) · Journal of Investigative Dermatology · doi:10.1016/j.jid.2020.05.110 · Cited by 22 · see citing works
Asfaha, Y., Bollmann, L. M., Skerhut, A. J., Fischer, F., Horstick‐Muche, N., Roth, D., Wecker, M., Mammen, C., Smits, S. H. J., Fluegen, G., et al. (2023) · European Journal of Medicinal Chemistry · doi:10.1016/j.ejmech.2023.115907 · Cited by 22 · see citing works
Panov, V. G., & Вараксин, А. Н. (2016) · Toxicology Mechanisms and Methods · doi:10.3109/15376516.2016.1139023 · Cited by 22 · see citing works
“Determination of a combined toxicity type is usually based on one of two competing concepts: the additivity paradigm or the independence paradigm (Greco et al., 1995; Zhao et al., 2014).”
BackgroundSweeney, S., Collins, M., Pandey, R., Chiou, J., Lodi, A., & Tiziani, S. (2020) · Molecular Carcinogenesis · doi:10.1002/mc.23163 · Cited by 22 · see citing works
Epidermal growth factor receptor activation confers resistance to lenvatinib in thyroid cancer cells
Ohno, K., Shibata, T., & Ito, K. (2022) · Cancer Science · doi:10.1111/cas.15465 · Cited by 20 · see citing works
mTOR inhibition overcomes RSK3-mediated resistance to BET inhibitors in small cell lung cancer
Kumari, A., Gesumaria, L., Liu, Y.-J., Hughitt, V. K., Zhang, X., Ceribelli, M., Wilson, K. M., Klumpp-Thomas, C. A., Chen, L., McKnight, C. G., et al. (2023) · JCI Insight · doi:10.1172/jci.insight.156657 · Cited by 21 · see citing works
“The synergy of various drug combinations was assessed using the excess Highest Single Agent (HSA) method, the response heat map, and the Δ Bliss heat map (46, 47).”
MethodZhang, W., Qi, L., Liu, Z., He, S., Wang, C., Wu, Y., Han, L., Liu, Z., Fu, Z., Tu, C., et al. (2023) · MedComm · doi:10.1002/mco2.317 · Cited by 20 · see citing works
Pei, F., Li, H., Henderson, M. J., Titus, S. A., Jadhav, A., Simeonov, A. M., Çobanoğlu, M. C., Mousavi, S. H., Shun, T., McDermott, L. A., et al. (2017) · Scientific Reports · doi:10.1038/s41598-017-17378-y · Cited by 21 · see citing works
Wang, X., Zhang, G., Bian, Z., Chow, V., Grimaldi, M., Carivenc, C., Sirounian, S., Li, H., Sládeková, L., Motta, S., et al. (2025) · Nature Communications · doi:10.1038/s41467-025-56624-0 · Cited by 19 · see citing works
Chen, X., Zhuo, S., Xu, W., Chen, X., Huang, D., Sun, X., & Cheng, Y. (2020) · British Journal of Cancer · doi:10.1038/s41416-020-0852-4 · Cited by 20 · see citing works
“The interaction between radiation and IDH2 knockdown was analysed using the Bliss independence model.(19) Based on the inhibition rate (IR), the combined percentage inhibition, IRR+sh-IDH2, was predicted using IRR+sh-IDH2= IRR+ IRsh-IDH2− IRR × IRsh-IDH2 where IRR and IRsh-IDH2 were the IR of mono-treatment with radia…”
MethodKessler, B. E., Mishall, K. M., Kellett, M. D., Clark, E. G., Pugazhenthi, U., Pozdeyev, N. V., Kim, J., Tan, A. C., & Schweppe, R. E. (2018) · Oncogene · doi:10.1038/s41388-018-0617-1 · Cited by 20 · see citing works
Karsa, M., Kosciolek, A., Bongers, A., Mariana, A., Failes, T. W., Gifford, A. J., Kees, U. R., Cheung, L. C., Kotecha, R. S., Arndt, G. M., et al. (2021) · British Journal of Cancer · doi:10.1038/s41416-021-01332-x · Cited by 20 · see citing works
“The occurrence of synergy was determined with the Bliss Independence model.(18,19) Bliss Prediction curves indicate the predicted % viability of the cells when exposed to the combination of compounds if both compounds work additively together.”
Method
- Authors
- Zhao, W., Sachsenmeier, K., Zhang, L., Sult, E., Hollingsworth, R. E., & Yang, H.
- Affiliations
- AbbVie (United States) (US)
- Corresponding author
- Zhao, Wei
- Venue
- SLAS Discovery
- Publisher
- Elsevier BV
- Published
- 2014-06
- Volume
- 19
- Issue
- 5
- Pages
- 817-821
- ISSN
- 2472-5552 (ISSN-L)
- OpenAlex
- W1980181290
- Cited by
- 322
- References
- 14
- Citations by year
- 2026: 46 · 2025: 33 · 2024: 29 · 2023: 45 · 2022: 40 · 2021: 19 · 2020: 26 · 2019: 23 · 2018: 17 · 2017: 17 · 2016: 14 · 2015: 11 · 2014: 2
- FWCI
- 15.18
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- SLAS DISCOVERY (publishedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computational Drug Discovery Methods
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Keywords
- Bliss independence model, drug synergy, drug-drug interactions, false positive reduction, epidermal growth factor receptor, IGF-1 receptor, drug combination screening
- MeSH terms
- Algorithms, Antineoplastic Agents, Carcinoma, Non-Small-Cell Lung, Dose-Response Relationship, Drug, Drug Combinations, Drug Interactions, Drug Synergism, Humans, Lung Neoplasms, Models, Chemical, Neoplasms, Regression Analysis, Technology, Pharmaceutical, Signal Transduction, Receptor, IGF Type 1, Drug Resistance, Neoplasm, ErbB Receptors
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