Statistical determination of synergy based on Bliss definition of drugs independence
Open accessAbstract
Although synergy is a pillar of modern pharmacology, toxicology, and medicine, there is no consensus on its definition despite its nearly one hundred-year history. Moreover, methods for statistical determination of synergy that account for variation of response to treatment are underdeveloped and if exist are reduced to the traditional t-test, but do not comply with the normal distribution assumption. We offer statistical models for estimation of synergy using an established definition of Bliss drugs' independence. Although Bliss definition is well-known, it remains a theoretical concept and has never been applied for statistical determination of synergy with various forms of treatment outcome. We rigorously and consistently extend the Bliss definition to detect statistically significant synergy under various designs: (1) in vitro, when the outcome of a cell culture experiment with replicates is the proportion of surviving cells for a single dose or multiple doses, (2) dose-response methodology, (3) in vivo studies in organisms, when the outcome is a longitudinal measurement such as tumor volume, and (4) clinical studies, when the outcome of treatment is measured by survival. For each design, we developed a specific statistical model and demonstrated how to test for independence, synergy, and antagonism, and compute the associated p-value.
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Existing methods have limited power to detect synergy in animal studies.
“Existing methods have limited power to detect synergy in animal studies.”
From Statistical Assessment of Drug Synergy from <i>In Vivo</i> Combination Studies Using Mouse Tumor Models (2023) · cites this paper as [29]
The Discussion (page unavailable) says existing statistical tests for synergy are scarce and applies the proposed method to animal studies. The single-dose section also says traditional whole-curve approaches may overlook synergy at particular doses. These passages support limitations in existing methods, but do not establish that those methods have limited statistical power specifically in animal studies. (LLM, conf=0.82)
Experimental — accuracy not yet measuredExisting methods use only TV data from a single day to calculate CI, and local CI values may fluctuate excessively such that they may indicate synergy and antagonism at different days.
“or use only TV data from a single day to calculate CI (local CI values may fluctuate excessively such that they may indicate synergy and antagonism at different days)”
From Statistical Assessment of Drug Synergy from <i>In Vivo</i> Combination Studies Using Mouse Tumor Models (2023) · cites this paper as [29]
The “Tumor growth experiments in vivo” section (page unavailable) says several authors apply CI to tumor volume at a specific time point, supporting the single-day part of the claim. The Introduction says CI values can be affected by biological variation, but our copy does not say that local CI values fluctuate enough to indicate synergy on one day and antagonism on another. (LLM, conf=0.82)
Experimental — accuracy not yet measuredCI cannot be calculated after a day when most or all mice in the vehicle control group are euthanized because their tumors reach a size threshold faster than drug-treated tumors.
“or that CI cannot be calculated after a day when most or all mice in the vehicle control group are euthanized because their tumors reach certain size threshold faster than drug-treated tumors.”
From Statistical Assessment of Drug Synergy from <i>In Vivo</i> Combination Studies Using Mouse Tumor Models (2023) · cites this paper as [29]
The Introduction’s “Advantages and limitations of Loewe additivity and combination index” section says CI is difficult to generalize to longitudinal animal experiments, including tumor growth. The “Tumor growth experiments in vivo” section says CI has been applied to tumor volume at a specific time point. Neither passage says that CI becomes incalculable after control mice are euthanized at a tumor-size threshold; no page numbers are available in our copy. (LLM, conf=0.82)
Experimental — accuracy not yet measuredDemidenko and colleagues defined Bliss independence using tumor growth rates of the four groups by assuming exponential tumor growth kinetics, and devised a Z-test using estimated GRs from linear mixed models on log-transformed TV data.
“Specifically, Demidenko and Miller defined Bliss independence using tumor growth rates (GR) of the four groups by assuming exponential tumor growth kinetics, and devised a Z-test to assess whether Bliss synergy exists using estimated GRs obtained from fitting linear mixed models on log-transformed TV data (29).”
From Statistical Assessment of Drug Synergy from <i>In Vivo</i> Combination Studies Using Mouse Tumor Models (2023) · cites this paper as [29]
The “Tumor growth experiments in vivo” section defines Bliss independence using growth rates for four groups under an exponential-growth assumption. It also describes testing synergy with p-values calculated from slope estimates and variances obtained using linear mixed models on log-scale tumor-volume data. Our copy does not explicitly identify this procedure as a Z-test, so that specific characterization is not verified. (LLM, conf=0.82)
Experimental — accuracy not yet measuredExisting methods impose unrealistic assumptions for tumor growth and TV data.
“These methods, however, have inherent limitations because they either impose unrealistic assumptions for tumor growth and TV data”
From Statistical Assessment of Drug Synergy from <i>In Vivo</i> Combination Studies Using Mouse Tumor Models (2023) · cites this paper as [29]
In “Tumor growth experiments in vivo” (page unavailable), the paper says its tumor-volume analysis assumes exponential growth or decay and notes that a U-shaped trajectory after short or one-time treatment requires a different model. This supports a limitation of a tumor-growth assumption, but the paper does not characterize existing methods generally as imposing unrealistic assumptions. (LLM, conf=0.76)
Experimental — accuracy not yet measured
Existing methods have trouble dealing with missing and unbalanced TV data even though mathematical interpolation is used to patch missing data with unmeasurable uncertainty.
“or have trouble dealing with missing and unbalanced TV data even though mathematical interpolation is used to patch missing data with unmeasurable uncertainty”
From Statistical Assessment of Drug Synergy from <i>In Vivo</i> Combination Studies Using Mouse Tumor Models (2023) · cites this paper as [29]
The “Tumor growth experiments in vivo” section discusses modeling tumor-volume measurements over time, but does not address missing or unbalanced data. The Introduction discusses uncertainty in dose-response and combination-index methods, not uncertainty from interpolating missing tumor-volume measurements. Searches for missing or unbalanced tumor-volume data and interpolation found no passage supporting the attributed claim; page numbers were unavailable in our copy. (LLM, conf=0.75)
Experimental — accuracy not yet measured
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- Authors
- Demidenko, E., & Miller, T. W.
- Affiliations
- Dartmouth College (US)
- Corresponding author
- Demidenko, Eugene
- Venue
- PLOS ONE
- Publisher
- Public Library of Science (PLoS)
- Published
- 2019-11-25
- Volume
- 14
- Issue
- 11
- Pages
- e0224137
- ISSN
- 1932-6203 (ISSN-L)
- PMC
- PMC6876842
- OpenAlex
- W2989954637
- Cited by
- 187
- References
- 54
- Citations by year
- 2026: 53 · 2025: 26 · 2024: 22 · 2023: 27 · 2022: 28 · 2021: 27 · 2020: 4
- FWCI
- 11.51
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- PLoS ONE (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Figshare (submittedVersion, cc-by)
- Funders
- National Institutes of Health
- National Cancer Institute (U01CA196386, P30CA023108)
- U.S. National Library of Medicine (R56LM012371)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computational Drug Discovery Methods
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Keywords
- drug synergy, Bliss independence, antagonism, dose-response relationship, cell survival, tumor volume, survival analysis, treatment response variability
- MeSH terms
- Animals, Antineoplastic Agents, Cell Survival, Clinical Trials as Topic, Disease Models, Animal, Dose-Response Relationship, Drug, Drug Antagonism, Drug Evaluation, Preclinical, Drug Synergism, Humans, Models, Biological, Neoplasms, Treatment Outcome, Cell Culture Techniques, Cell Line, Tumor, Mice, Kaplan-Meier Estimate, Intention to Treat Analysis
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