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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 (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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Lin, Z., Jiang, C., Wang, P., Chen, Q., Wang, B., Fu, X., Liang, Y., Zhang, D., Zeng, Y., & Liu, X. (2023) · Theranostics · doi:10.7150/thno.85843 · Cited by 19
“Assuming that two drugs, A and B, both have the ability to inhibit tumor growth, with drug A inhibiting Ya percent of tumor growth at a dose a, and drug B inhibiting Yb percent of tumor growth at a dose b, the combination of inhibition percent Yab,P can be estimated by the complete additivity principle of probability…”
Altering microtubule dynamics is synergistically toxic with spindle assembly checkpoint inhibition
Schukken, K. M., Lin, Y., Bakker, P. L., Schubert, M., Preuß, S. F., Simon, J. E., van den Bos, H., Štorchová, Z., Colomé‐Tatché, M., Bastians, H., et al. (2020) · Life Science Alliance · doi:10.26508/lsa.201900499 · Cited by 18
“The combined effects of aneuploidy and ZLN005 act synergistically as assessed by a Bliss independence test (50% stronger effect than additive, P = 3.2E-3, [Zhao et al, 2014]).”
BackgroundZhang, C., Ding, J., Lim, K. S., Zhou, W., Miao, W., Wu, S., Liu, H., Huang, D., Chen, C., He, H., et al. (2025) · Cancer Research · doi:10.1158/0008-5472.can-23-2796 · Cited by 18
Mukherjee, D., Wang, P., Hooi, L., Sandhu, V., You, K., Blasiak, A., Chow, E. K., Ho, D., & Ee, P. L. R. (2022) · Theranostics · doi:10.7150/thno.73078 · Cited by 18
“The data set was subsequently uploaded to SynergyFinder to perform Bliss independence model analysis [53, 54, 71].”
MethodMasilamani, A. P., Dettmer‐Monaco, V., Monaco, G., Cathomen, T., Kuckuck, I., Schultze-Seemann, S., Huber, N., & Wolf, P. (2020) · Cancers · doi:10.3390/cancers12061648 · Cited by 18
“was used to determine synergistic cytotoxicity of the immunotoxin in combination with ABT-737 on the target cells [37].”
BackgroundMethodFotio, Y., Alaoui, A. A. E., Borruto, A. M., Acciarini, S., Giordano, A., & Ciccocioppo, R. (2019) · Frontiers in Pharmacology · doi:10.3389/fphar.2019.00711 · Cited by 18
Rollin‐Pinheiro, R., Borba-Santos, L. P., Xisto, M. I. D. D. S., de Castro-Almeida, Y., Rochetti, V. P., Rozental, S., & Barreto‐Bergter, E. (2021) · Journal of Fungi · doi:10.3390/jof7100803 · Cited by 16
“Bliss independence model was performed according to Meletiadis and colleagues and Zhao and colleagues [50,51].”
MethodBell, H. L., Blair, H. J., Gosling, S. J. J., Galler, M., Astley, D. J., Moorman, A. V., Heidenreich, O. T., Veal, G. J., van Delft, F. W., Lunec, J., et al. (2024) · Leukemia · doi:10.1038/s41375-024-02241-7 · Cited by 16
“Drug combination effects and synergy scores were analyzed using the Bliss independence model [20, 21].”
Vassileva, V., Rajkumar, V. S., Mazzantini, M., Robson, M. P., Badar, A., Sharma, S. K., Årstad, E., Hochhauser, D., Lythgoe, M. F., Boxer, G. M., et al. (2015) · Journal of Nuclear Medicine · doi:10.2967/jnumed.115.157362 · Cited by 16
Sriskandarajah, P., Brandon, A. D. H., Macleod, K., Carragher, N. O., Kirkin, V., Kaiser, M., & Whittaker, S. R. (2020) · BMC Cancer · doi:10.1186/s12885-020-06735-2 · Cited by 14
“Synergy was assessed using the Bliss Independence model, where values greater than 0 indicated synergy [30] (Fig.”
MethodSynergistic cytotoxicity of dual PI3K/mTOR and FLT3 inhibition in FLT3-ITD AML cells
Darici, S., Zavatti, M., Braglia, L., Accordi, B., Serafin, V., Horne, G. A., Manzoli, L., Palumbo, C., Huang, X., Jørgensen, H. G., et al. (2021) · Advances in Biological Regulation · doi:10.1016/j.jbior.2021.100830 · Cited by 16
Rossi, F., Santonicola, S., & Colavita, G. (2025) · Antibiotics · doi:10.3390/antibiotics14111106 · Cited by 17
Nakhjavani, M., Smith, E., Palethorpe, H. M., Tomita, Y., Yeo, K. K. L., Price, T. J., Townsend, A. R., & Hardingham, J. E. (2021) · Pharmaceuticals · doi:10.3390/ph14070633 · Cited by 16
Guillen, V. S., Ziegler, Y., Gopinath, C., Kumar, S., Dey, P., Plotner, B. N., Dawson, N. Z., Kim, S. H., Katzenellenbogen, J. A., & Katzenellenbogen, B. S. (2023) · Breast Cancer Research and Treatment · doi:10.1007/s10549-023-06878-3 · Cited by 15
Smith, M. L., Chyla, B., McKeegan, E. M., & Tahir, S. K. (2016) · Cytometry Part B Clinical Cytometry · doi:10.1002/cyto.b.21383 · Cited by 15
“The Bliss independence model was used to assess combination responses (25).”
MethodPredicting Drug Synergism by Means of Non-Negative Matrix Tri-Factorization
Pinoli, P., Ceddia, G., Ceri, S., & Masseroli, M. (2021) · IEEE Transactions on Computational Biology and Bioinformatics · doi:10.1109/tcbb.2021.3091814 · Cited by 15
Sastré-Velásquez, L. E., Dallemulle, A., Kühbacher, A., Baldin, C., Alcázar‐Fuoli, L., Niedrig, A., Müller, C., & Gsaller, F. (2022) · PLoS Pathogens · doi:10.1371/journal.ppat.1011066 · Cited by 15
“Independence Model [36] was used to analyze the potential synergistic interactions among the 455”
MethodSchaf, J., Shinhmar, S., Zeng, Q., Pardo, O. E., Beesley, P. W., Syed, N., & Williams, R. S. B. (2023) · Cell Death Discovery · doi:10.1038/s41420-023-01462-6 · Cited by 16
“4H) which provided synergistic inhibition of mTORC1 signalling [28].”
BackgroundMethodEnzenmüller, S., Niedermayer, A., Seyfried, F., Muench, V., Tews, D., Rupp, U., Tausch, E., Groß, A., Fischer‐Posovszky, P., Walther, P., et al. (2024) · Cell Death and Disease · doi:10.1038/s41419-024-06864-7 · Cited by 16
“Combination effects and synergy scores were analyzed (Synergy fi nder, https://synergy fi nder. fi mm. fi /synergy/20240318114830462623/) using the Bliss independence model [22 – 24].”
Gray, M., Lee, S., McDowell, A. L., Erskine, M., Loh, Q. T. M., Grice, O., Argyle, D. J., & Bergkvist, G. T. (2016) · Veterinary and Comparative Oncology · doi:10.1111/vco.12230 · Cited by 14
“Potential synergistic effects of dual targeting of the receptors was investigated in accordance to the Bliss Additivism model.(33) Here we report that EGFR and ERBB2 combined targeting by siRNAs produced a synergistic effect.”
MethodResultLadumor, Y., Seong, B. K. A., Hallett, R. M., Valencia-Sama, I., Adderley, T., Wang, Y., Kee, L., Gont, A., Kaplan, D. R., & Irwin, M. S. (2022) · Molecular Cancer Research · doi:10.1158/1541-7786.mcr-21-0425 · Cited by 14
The potential of PARP as a therapeutic target across pediatric solid malignancies
Keller, K. M., Koetsier, J., Schild, L. G., Amo-Addae, V., Eising, S., van den Handel, K., Ober, K., Koopmans, B., Essing, A. H. W., van den Boogaard, M. L., et al. (2023) · BMC Cancer · doi:10.1186/s12885-022-10319-7 · Cited by 13
“To this end, we performed a similar method and calculated three outcome metrics for each combination: 1) fold change in maximum effect at the highest library drug concentration (∆Emax), 2) fold change in IC50 value (∆IC50) and 3) average synergy score according to the bliss independence model [22].”
MethodZhao, D., Huang, P. C., Yu, L., & He, Y. T. (2024) · Clinical Pharmacokinetics · doi:10.1007/s40262-024-01391-2 · Cited by 14
“Bliss and his associates introduced the Bliss independence model to evaluate the efficacy of drugs using the independence criterion, which notably disregards the nonlinearity of dose–response relationships [139].”
Zaharieva, M. M., Trochopoulos, A., Dimitrova, L. L., Berger, M. R., Najdenski, H. M., Konstantinov, S., & Kroumov, A. D. (2018) · International Journal Bioautomation · doi:10.7546/ijba.2018.22.2.87-106 · Cited by 13
King, A. J., Kohler, J. N., Fung, C., Jiang, Z., Quach, A., Kumaraswamy, P., Chertow, G. M., & Rosenbaum, D. P. (2020) · American Journal of Physiology-Renal Physiology · doi:10.1152/ajprenal.00137.2020 · Cited by 13
“on the observed effect of each individual agent administered alone, with the observed effect of combination treatment (37).”
BackgroundMethodXisto, M. I. D. D. S., Rollin‐Pinheiro, R., de Castro-Almeida, Y., dos Santos, G. M. P., Rochetti, V. P., Borba-Santos, L. P., Fontes, Y. D. S., Ferreira‐Pereira, A., Rozental, S., & Barreto‐Bergter, E. (2023) · Journal of Fungi · doi:10.3390/jof9020187 · Cited by 12
“The Bliss independence model calculation was performed according to Meletiadis and colleagues and Zhao and colleagues [22,23].”
MethodSong, S., Xia, X., Qi, J., Hu, X., Chen, Q., Liu, J., Ji, N., & Zhao, H. (2021) · Drug Delivery · doi:10.1080/10717544.2021.2000677 · Cited by 12
“The new bliss independence model calculation formula (Zhao et al., 2014) was used to calculate the combined inhibition rate of the two drugs.”
MethodNorethindrone suppress the germ cell development via androgen receptor resulting in male bias
Long, X.-B., Shi, W., Yao, C.-R., Li, S., Zhang, J., Lu, Z., Ma, D.-D., Jiang, Y., & Ying, G. (2023) · Aquatic Toxicology · doi:10.1016/j.aquatox.2023.106604 · Cited by 12
Krais, J. J., Virani, N. A., McKernan, P., Nguyen, Q. D., Fung, K., Sikavitsas, V. I., Kurkjian, C. D., & Harrison, R. G. (2017) · Molecular Cancer Therapeutics · doi:10.1158/1535-7163.mct-16-0263 · Cited by 12
“Assessment for synergism of combination therapies was performed using the Bliss independence model on primary tumor growth inhibition (47, 48).”
MethodLight-activated quantum dot potentiation of antibiotics to treat drug-resistant bacterial biofilms
Stamo, D. F., Nagpal, P., & Chatterjee, A. (2021) · Nanoscale Advances · doi:10.1039/d1na00056j · Cited by 12
Murphy, R. A., Coates, M. S., Thrane, S., Sabnis, A., Harrison, J., Schelenz, S., Edwards, A. M., Vorup‐Jensen, T., & Davies, J. C. (2022) · Microbiology Spectrum · doi:10.1128/spectrum.00813-22 · Cited by 11
“Synergy between the activities of glatiramer acetate and tobramycin was tested for each 182 strain from colony counts, as previously described (37).”
MethodEleveld, T. F., Vernooij, L., Schild, L. G., Koopmans, B., Alles, L. K., Ebus, M. E., Dandis, R., van Tinteren, H., Caron, H. N., Köster, J., et al. (2022) · Frontiers in Oncology · doi:10.3389/fonc.2023.1130034 · Cited by 11
“Bliss independence scores were calculated to measure synergy between trametinib and each of the tested concentrations of BCL-2 family inhibitors (17).”
MethodMetformin Suppresses Stemness of Non-Small-Cell Lung Cancer Induced by Paclitaxel through FOXO3a
Tang, Z., Zhang, Y., Yu, Z., & Luo, Z. (2023) · International Journal of Molecular Sciences · doi:10.3390/ijms242316611 · Cited by 14
“If the combination effect is higher than the predicted value, the interaction is synergistic; if it is lower than the predicted value, the interaction is antagonistic; otherwise, the effect is additive and there is no interaction [63].”
BackgroundMiltefosine: A Repurposing Drug against Mucorales Pathogens
Xisto, M. I. D. D. S., Rollin‐Pinheiro, R., Rochetti, V. P., de Castro-Almeida, Y., Borba-Santos, L. P., dos Santos, G. M. P., Cypriano, J. B. S., Abreu, F. D. Á., Rozental, S., & Barreto‐Bergter, E. (2023) · Journal of Fungi · doi:10.3390/jof9121166 · Cited by 11
“The Bliss independence model was performed according to Meletiadis and colleagues and Zhao and colleagues [29,30].”
MethodAzfar, M., Gao, W., den Haute, C. V., Xiao, L., Karsa, M., Pandher, R., Karsa, A., Spurling, D., Ronca, E., Bongers, A., et al. (2025) · Molecular Oncology · doi:10.1002/1878-0261.13789 · Cited by 11
“8B) [22].”
Nunes, C., Anckaert, J., Vloed, F. D., Wyn, J. D., Durinck, K., Vandesompele, J., Speleman, F., & Vermeirssen, V. (2024) · PLoS ONE · doi:10.1371/journal.pone.0296322 · Cited by 10
“Dose-effect based models work if monotherapy dose-response curves are well characterized, which, depending on the response of a cell line to a drug dose range treatment, might not be achievable [19, 20].”
BackgroundMethodKeller, K. M., Eleveld, T. F., Schild, L. G., van den Handel, K., van den Boogaard, M. L., Amo-Addae, V., Eising, S., Ober, K., Koopmans, B., Looijenga, L. H. J., et al. (2022) · Frontiers in Oncology · doi:10.3389/fonc.2022.929123 · Cited by 11
“Following combination treatment, cell viability was calculated and synergy was evaluated using the bliss independence model (29).”
MethodBiochemical reaction network topology defines dose-dependent Drug–Drug interactions
Babaei, M., Evers, T. M. J., Shokri, F., Altucci, L., de Lange, E. C. M., & Mashaghi, A. (2023) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2023.106584 · Cited by 11
Heffern, E., Ramani, R., Marshall, G. R., & Kyei, G. B. (2019) · Journal of Virus Eradication · doi:10.1016/s2055-6640(20)30057-1 · Cited by 11
“Bliss independence model and isobole analysis We used the Bliss independence model, which is one of the ways to differentiate between additive and synergistic effects of two combined compounds, which has been previously described [10,23].”
MethodGhosh, S., Fan, F., Powell, R. T., Roszik, J., Park, Y. S., STEPHAN, C. C., Sebastian, M. M., Tan, L., Sorokin, A. V., Lorenzi, P. L., et al. (2023) · Molecular Cancer Therapeutics · doi:10.1158/1535-7163.mct-23-0110 · Cited by 10
Valencia-Sama, I., Kee, L., Christopher, G., Ohh, M., Layeghifard, M., Shlien, A., Hayes, M. N., & Irwin, M. S. (2023) · Cancer Research Communications · doi:10.1158/2767-9764.crc-23-0234 · Cited by 10
In silico assessment on TdP risks of drug combinations under CiPA paradigm
Qauli, A. I., Marcellinus, A., Setiawan, M. A., Zain, A. F. N., Pinandito, A. M., & Lim, K. M. (2023) · Scientific Reports · doi:10.1038/s41598-023-29208-5 · Cited by 10
Hernández‐Patlan, D., Solís-Cruz, B., Latorre, J. D., Merino-Guzmán, R., Morales, M., Ausland, C., Hernández-Velasco, X., Holguin, O. O., Delgado, R., Hargis, B. M., et al. (2022) · Frontiers in Veterinary Science · doi:10.3389/fvets.2022.784387 · Cited by 10
“predicted responses (42, 43) and to identify synergistic, antagonistic, or additive effects (36, 37).”
BackgroundTransfer of IGF2BP3 Through Ara-C-Induced Apoptotic Bodies Promotes Survival of Recipient Cells
Gou, J., Li, H., Bi, J., Pang, X., Li, X., & Wang, Y. (2022) · Frontiers in Oncology · doi:10.3389/fonc.2022.801226 · Cited by 10
“Half maximal inhibitory concentration (IC50) was calculated from survival curves by Bliss method (18).”
MethodLi, X., Yu, Z., Ye, J., Wang, X., Lin, H., Lei, L., Hu, W., & Luo, Y. (2025) · Environmental Science & Technology · doi:10.1021/acs.est.4c13071 · Cited by 9
Paukovčeková, S., Valík, D., Štěrba, J., & Veselská, R. (2020) · International Journal of Molecular Sciences · doi:10.3390/ijms21186591 · Cited by 9
“Analysis of possible interactions of compounds included in this study was performed using the Bliss independence model [65].”
MethodCD155 promotes radioresistance and malignancy of esophageal cancer by regulating Hippo-YAP pathway
Xin, H., Liu, Y., Chen, P., Yin, T., Wang, M., Liu, T., Wen, Z., & Cheng, Y. (2022) · Discover Oncology · doi:10.1007/s12672-022-00515-z · Cited by 10
“The interaction between radiation and CD155 knockdown was analyzed using the Bliss independence model [22].”
MethodRollin‐Pinheiro, R., Xisto, M. I. D. D. S., de Castro-Almeida, Y., Rochetti, V. P., Borba-Santos, L. P., Fontes, Y. D. S., Ferreira‐Pereira, A., Rozental, S., & Barreto‐Bergter, E. (2023) · PLoS ONE · doi:10.1371/journal.pone.0280964 · Cited by 10
“Bliss independence model was performed according to Meletiadis and colleagues and Zhao and colleagues [32, 33].”
MethodLong, X.-B., Yao, C.-R., Li, S., Zhang, J., Lu, Z., Ma, D.-D., Chen, C.-E., Ying, G., & Shi, W. (2024) · Journal of Hazardous Materials · doi:10.1016/j.jhazmat.2024.133844 · Cited by 10
Meyer, L. K., Delgado-Martín, C., Sharp, P. P., Huang, B. J., McMinn, D. L., Vincent, T. L., Ryan, T. M., Horton, T. M., Wood, B. L., Teachey, D. T., et al. (2022) · British Journal of Haematology · doi:10.1111/bjh.18181 · Cited by 9
Masilamani, A. P., Huber, N., Nagl, C., Dettmer‐Monaco, V., Monaco, G., Wolf, I., Schultze-Seemann, S., Taromi, S., Gratzke, C., Fuchs, H., et al. (2023) · Frontiers in Pharmacology · doi:10.3389/fphar.2023.1211824 · Cited by 8
“The Bliss Independence Model was used to determine the Combination Index (CI) as a measure of synergism in cytotoxicity (Zhao et al., 2014).”
MethodReihani, N., & Ghourchian, H. (2025) · Journal of Molecular Liquids · doi:10.1016/j.molliq.2025.126957 · Cited by 11
Papp, O., Jordán, V., Hetey, S., Balázs, R., Kaszás, V., Bartha, Á., Ordasi, N. N., Kamp, S., Farkas, B., Mettetal, J. T., et al. (2024) · npj Systems Biology and Applications · doi:10.1038/s41540-024-00394-w · Cited by 8
“Therearemultiplereasonswhy using the Bliss independence model is preferred over other alternative synergy modelslikeapplicabilityonentiredoserangesandincaseofnon-standard ornotavailabledose-responsecurves,straightforwardprobabilistic interpretation 83,84 .”
MethodKumar, S., Ziegler, Y., Plotner, B. N., Flatt, K. M., Kim, S. H., Katzenellenbogen, J. A., & Katzenellenbogen, B. S. (2024) · Breast Cancer Research and Treatment · doi:10.1007/s10549-024-07420-9 · Cited by 8
Chen, M., Yiu, H. P., Wang, Y.-C., Liu, T.-Y., & Li, C. (2024) · Nanomaterials · doi:10.3390/nano15010037 · Cited by 8
“A popular approach to test the synergistic effect of a drug combination is to examine an average response of different combined doses to see whether the response value exceeds the Bliss prediction [27,32–40].”
Zheng, J.-Y., Wang, C., Teng, M.-M., Li, T., Jiang, J.-Z., Chen, X.-G., & Wu, F. (2026) · Aquatic Toxicology · doi:10.1016/j.aquatox.2026.107713 · Cited by 7
Sass, G., Marsh, J. J., Shrestha, P., Sabino, R., & Stevens, D. A. (2022) · Frontiers in Cellular and Infection Microbiology · doi:10.3389/fcimb.2022.817315 · Cited by 7
Rollin‐Pinheiro, R., de Moraes, D., Bayona-Pacheco, B. L., Curvelo, J. A. D. R., dos Santos, G. M. P., Xisto, M. I. D. D. S., Borba-Santos, L. P., Rozental, S., Ferreira‐Pereira, A., & Barreto‐Bergter, E. (2023) · Journal of Fungi · doi:10.3390/jof9111115 · Cited by 7
“Bliss independence model was performed according to Meletiadis and colleagues and Zhao and colleagues [30,31].”
MethodCooperative blockade of FLT3 and ALK synergistically suppresses growth of osteosarcoma
Zhang, W., Qi, L., Xu, H., Yin, C., Yu, Z., Xu, R., Feng, C., Ren, X., Tu, C., & Li, Z. (2024) · Oncogene · doi:10.1038/s41388-024-03205-y · Cited by 7
“The analysis and quanti fi cation of the wound closure percentage were performed utilizing the Image J software.”
Synergy across the drugs approved for the treatment of asthma
ROGLIANI, P., RITONDO, B. L., Cavalli, F., GIORGINO, F. M., GIROLAMI, A., Gloria, P. A. N. E., PEZZUTO, G., ZERILLO, B., PUXEDDU, E., & Ora, J. (2022) · Minerva Medica · doi:10.23736/s0026-4806.21.07266-9 · Cited by 7
Parris, J. L. D., Barnoud, T., Leu, J. I.-J., Leung, J. C., Ma, W., Kirven, N. A., Poli, A. N. R., Kossenkov, A. V., Liu, Q., Salvino, J. M., et al. (2021) · Cancer Research Communications · doi:10.1158/2767-9764.crc-21-0033 · Cited by 7
“Synergy was determined using an interaction index calculated using a dose–response surface model based on the Bliss independence principle (27, 28).”
Shi, W., Long, X.-B., Li, S., Ma, D.-D., Liu, F., Zhang, J., Lu, Z., & Ying, G. (2022) · Aquatic Toxicology · doi:10.1016/j.aquatox.2022.106177 · Cited by 7
Combination mTOR and SHP2 inhibitor treatment of lymphatic malformation endothelial cells
Wolter, J. K., Valencia-Sama, I., Osborn, A. J., Propst, E. J., Irwin, M. S., Papsin, B. C., & Wolter, N. E. (2022) · Microvascular Research · doi:10.1016/j.mvr.2022.104397 · Cited by 8
Catanzaro, D., Milani, G., Bozza, A., Bernardi, M., Chieregato, K., Menarin, M., Merlo, A., Celli, P., Belli, R., Peroni, D., et al. (2022) · British Journal of Cancer · doi:10.1038/s41416-022-01865-9 · Cited by 7
“This model is indeed based on the probability of obtaining a determined effect [35].”
BackgroundDeng, O., Dash, S., Nepomuceno, T. C., Fang, B., Yun, S. Y., Welsh, E. A., Lawrence, H. R., Marchion, D. C., Koomen, J. M., Monteiro, Á. N. A., et al. (2022) · Journal of Biological Chemistry · doi:10.1016/j.jbc.2022.102550 · Cited by 8
“Drug combination effects were assessed by the Bliss independence model (42).”
MethodFan, F., Ghosh, S., Powell, R. T., Roszik, J., Park, Y., Sobieski, M. M., Sorokin, A. V., STEPHAN, C. C., Kopetz, S., Ellis, L. M., et al. (2023) · PLoS ONE · doi:10.1371/journal.pone.0281063 · Cited by 8
“The theoretical additivity surface was then calculated using a Bliss independence model [40].”
MethodViana, P. H. L., Schvarcz, C. A., Danics, L., Besztercei, B., Aloss, K., Bokhari, S. M. Z., Giunashvili, N., Bócsi, D., Koós, Z., Benyó, Z., et al. (2024) · Scientific Reports · doi:10.1038/s41598-024-57659-x · Cited by 7
“…the average of tumor masses for each treatment group (Sham + Vehicle: 300.0 mg, mEHT + Vehicle: 237.0 mg, Sham + KRIBB11: 312.3 mg, and mEHT + KRIBB11: 160.3 mg), we calacu-lated the expected combined effect based on individual mEHT and drug effects based on the Bliss Independence model 63,64 .”
MethodInfluentialKumar, V. S. S., Pretorius, E., & Rajanikant, G. K. (2018) · Cellular and Molecular Neurobiology · doi:10.1007/s10571-018-0605-6 · Cited by 7
Pseudomonas aeruginosa Virulence Factors Support Voriconazole Effects on Aspergillus fumigatus
Sass, G., Shrestha, P., & Stevens, D. A. (2021) · Pathogens · doi:10.3390/pathogens10050519 · Cited by 7
Zhang, C., Martínez-Ledesma, E., Gao, F., Zhang, W., Ding, J., Wu, S., Li, X., Wu, J., Yuan, Y., Koul, D., et al. (2019) · PubMed Central · Cited by 7
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Suárez-Rozas, C., Jara, J. A., Cortés, G., Rojas, D., Araya-Valdés, G., Molina‐Berríos, A., González‐Herrera, F., Fuentes-Retamal, S., Aránguiz, P., Campodónico, P. R., et al. (2024) · Cancers · doi:10.3390/cancers16172980 · Cited by 6
“For this article, the first model was used, a mathematical model appropriate for assessing the combined effect of two drugs with different mechanisms of action [20].”
MethodPredicting drug combination response surfaces
Huusari, R., Wang, T., Szedmák, S., Aittokallio, T. A., & Rousu, J. (2025) · npj Drug Discovery. · doi:10.1038/s44386-024-00004-z · Cited by 9
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“Two-way ANOVA tests, the bliss-independent model [40], and Chou-Talalay method [41] were used to determine the synergistic effect.”
MethodBell, H. L., Blair, H. J., Singh, M., Moorman, A. V., Heidenreich, O. T., van Delft, F. W., Lunec, J., & Irving, J. A. E. (2023) · Cancer Cell International · doi:10.1186/s12935-023-03057-8 · Cited by 6
“Drug combination effects were determined after 96 h, synergy scores were analyzed using the Bliss independence model [24, 25] and visualized using a Python script.”
Sakamoto, Y., Yamagishi, S., Okusaka, T., & Ojima, H. (2019) · Cells · doi:10.3390/cells8091026 · Cited by 6
Synergistic Effects of PARP Inhibition and Cholesterol Biosynthesis Pathway Modulation
Rutkowska, A., Eberl, H. C., Werner, T., Hennrich, M. L., Sévin, D. C., Petretich, M., Reddington, J. P., Pocha, S. M., Gade, S., Martinez-Segura, A., et al. (2024) · Cancer Research Communications · doi:10.1158/2767-9764.crc-23-0549 · Cited by 5
“The effects of combining niraparib or olaparib with either lipophilic (atorvastatin, fluvastatin) or hydrophilic (pravastatin) statins on a matrix of combination ranges were assessed using the Bliss Synergy Score (63).”
Dai, L., Jiao, W., Li, J., He, Z., Lu, Q., Zheng, C., Li, H., Wang, S., Yan, B., Lv, Y., et al. (2025) · Advanced Healthcare Materials · doi:10.1002/adhm.202501617 · Cited by 5
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Polynucleotide Mixture Attenuates Ultraviolet B-Induced Skin Pigmentation
Oh, S., Jeon, H.-D., Rho, N., Son, K. H., & Byun, K. (2025) · International Journal of Molecular Sciences · doi:10.3390/ijms26136399 · Cited by 6
“To determine whether the effect of PNM exceeds the combined effects of PN and AM, that is, to assess the presence of a synergistic effect when PN and AM are combined, we employed the Bliss independence model, which is widely used for evaluating drug synergy [49].”
Response envelope analysis for quantitative evaluation of drug combinations
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GPR15LG binds CXCR4 and synergistically modulates CXCL12-induced cell signaling and migration
Albers, D., Novikova, S., Vieyto‐Nuñez, J., Almeida‐Hernández, Y., Pastorio, C., Klassen, F., Weiss, D., von Maltitz, P., Jaikishan, J., Datta, M., et al. (2025) · Cell Communication and Signaling · doi:10.1186/s12964-025-02231-x · Cited by 4
“Values of 0 indicate no interaction, while negative values indicate antagonism and positive values synergistic effects [42].”
Yu, C., Kuo, Y.-H., Chang, T.-T., & Liao, V. H. (2025) · Journal of Hazardous Materials · doi:10.1016/j.jhazmat.2025.140499 · Cited by 4
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“To explain the combination therapies, a combination index (CI) based on the effective doses obtained by IC 50 was calculated according to the following equation [12]: CI= Where, C A,X and C B,x are the concentrations of drug A and B used in combination to achieve x% drug effect.”
Friedman, C. A., Saha, A., Hackman, G. L., Lu, X., Lodi, A., Tiziani, S., & DiGiovanni, J. (2024) · Molecular Carcinogenesis · doi:10.1002/mc.23674 · Cited by 4
“22 No samples or animals were excluded from the reported analysis.”
BackgroundBollmann, L. M., Lange, F., Hamacher, A., Biermann, L., Schäker‐Hübner, L., Hansen, F. K., & Kassack, M. U. (2024) · Cancers · doi:10.3390/cancers16193374 · Cited by 4
“Data were analyzed according to Chou-Talalay [57] (Table 3) and according to the Bliss model [58] (Figure 3).”
MethodSchurdak, M. E., Pei, F., Lezon, T. R., Carlisle, D. L., Friedlander, R. M., Taylor, D. L., & Stern, A. M. (2018) · Methods in molecular biology · doi:10.1007/978-1-4939-7847-2_16 · Cited by 4
The polyamine transporter ATP13A3 mediates DFMO-induced polyamine uptake in neuroblastomaPreprint
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Detecting bliss synergy in in vivo combination studies with a tumor kinetic model
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“I t ð Þ 1⁄4 yAB t ð Þ − yA t ð Þ − yB t ð Þ þ yA t ð Þ*yB t ð Þ (5)”
Self-citationNanocellulose synthesis via synergistic application of solid acid and cellulase
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Preventing Preterm Birth: The Search for Tocolytic Synergism
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“The HSA and Bliss Independence models follow an effect-based strategy that compares the effect of a combination (observed response) directly to the effects of its constituent drugs (expected additive effect), which con - stitutes efficacy-driven synergy [ 38, 39, 43].”
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A comparative study of in vitro dose–response estimation under extreme observations
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“Robust estimation of the dose–response curve can play a critical role in the investigation of adequate drug combinations (García-Fuente et al., 2018; Lee et al., 2007; Zhao et al., 2014).”
BackgroundHsp70‐Bim incoherent feedforward loop contributes to cell‐fate heterogeneity and fractional killing
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Bioactives in Disease Prevention and Health Promotion: Exploiting Combinatorial Effects
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“31 By comparing the empirically determined drug effect to the Bliss independence model, the interactions between each pair of drugs were characterized as antagonistic, additive, or synergistic.”
Synergy Assessment for Plant Growth by Independent Joint Action Theory
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Background
Metadata
- 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
- Life Sciences › Pharmacology, Toxicology and Pharmaceutics › Drug Discovery › 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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