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Cited by 27Statistical Methods in Clinical TrialsComputational Drug Discovery MethodsMathematical Biology Tumor Growth

Statistical Assessment of Drug Synergy from In Vivo Combination Studies Using Mouse Tumor Models

Open access
Mao, Binchen, Guo, Sheng·2023·Cancer Research Communications
DOI 10.1158/2767-9764.crc-23-0243PMC PMC10591909

Published version of a preprint

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Abstract

Drug combination therapy is a promising strategy for treating cancer; however, its efficacy and synergy require rigorous evaluation in preclinical studies before going to clinical trials. Existing methods have limited power to detect synergy in animal studies. Here, we introduce a novel approach to assess in vivo drug synergy with high sensitivity and low false discovery rate. It can accurately estimate combination index and synergy score under the Bliss independence model and the highest single agent (HSA) model without any assumption on tumor growth kinetics, study duration, data completeness and balance for tumor volume measurement. We show that our method can effectively validate in vitro drug synergy discovered from cell line assays in in vivo xenograft experiments, and can help to elucidate the mechanism of action for immune checkpoint inhibitors in syngeneic mouse models by combining an anti-PD-1 antibody and several tumor-infiltrating leukocytes depletion treatments. We provide a unified view of in vitro and in vivo synergy by presenting a parallelism between the fixed-dose in vitro and the 4-group in vivo combination studies, so they can be better designed, analyzed, and compared. We emphasize that combination index, when defined here via relative survival of tumor cells, is both dose and time dependent, and give guidelines on designing informative in vivo combination studies. We explain how to interpret and apply Bliss and HSA synergies. Finally, we provide an open-source software package named invivoSyn that enables automated analysis of in vivo synergy using our method and several other existing methods. Significance: This work presents a general solution to reliably determine in vivo drug synergy in single-dose 4-group animal combination studies.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper introduces invivoSyn, an eGR-based statistical method for assessing in vivo drug synergy in standard 4-group mouse tumor combination studies under the Bliss independence and HSA models. It reports improved sensitivity over single-day methods, provides design guidance, and releases an open-source R package.

Key findings

  • In reanalysis of three colon xenografts, invivoSyn detected Bliss synergy where CombPDX did not: SW837 P = 0.032, CI = 0.672, SS = 15.0; SNU-81 P = 0.016; LS-1034 borderline P = 0.083. CombPDX reported no Bliss synergy for SW837 (global P = 0.253) or SNU-81 (P = 0.944) and missed LS-1034.
  • In anti-PD-1 plus tumor-infiltrating leukocyte depletion syngeneic models, strong antagonism was common with anti-CD8 in all four models; MC38 showed significant synergy with CD4+ T-cell, Treg, and TAM depletion, while Hepa1–6 showed antagonism with CD4+ T-cell, NK-cell, and TAM depletion.
  • Simulations showed high power and low FDR: strong Bliss synergy had >80% power with 2 mice per group and complete power at 6 mice per group; weak synergy reached high power at 8–10 mice per group; delayed treatment effect needed 40–50 days for power >0.8; tumor regrowth scenarios had low FDR when study duration was sufficiently long.
  • Under the Bliss model, CI and SS are both time and dose dependent; the P value is unchanged across days and is therefore recommended as a more meaningful indicator of synergy.

Methods

  • eGR is calculated from log-transformed tumor volume using trapezoidal AUC net gain over the study duration, with no assumption on tumor growth kinetics; group mean eGR is used to compute relative survival and CI/SS under Bliss and HSA models, with t = 21 days as a convention.
  • Significance is assessed by stratified bootstrap with 1,000 resamples with replacement, using bias-corrected and accelerated (BCa) 95% confidence intervals and P values for CI and SS.
  • Simulation used an exponential tumor growth model with parameters including TV0, k, TGItr21, Tobs, TVmax = 3,000 mm3, Tki, Prt, Tir, CV0, CVk, and σ; 100 datasets per scenario; power was the proportion with P < 0.05. Case studies included colon PDX CR1197 treated with cetuximab 15 mg/kg and palbociclib 10 mg/kg, reanalysis of published xenograft studies, anti-PD-1 syngeneic studies, and comparison with CombPDX.

Limitations

  • Stated: CI and SS under the Bliss model are time and dose dependent, so they should be interpreted cautiously when comparing xenograft models or drug combinations; P value may be a better indicator. HSA is described as not based on probability theory and as somewhat abusing the synergy terminology.
  • Stated: the 4-group in vivo design limits applicable synergy models; Loewe additivity and ZIP/response-surface methods require multiple doses and are not applicable. Bliss clinical validation is generally not possible due to ethical regulations and cost.
  • Evident from the text: eGR is an equivalent exponential growth rate, and the simulations rely on exponential growth assumptions; the paper does not provide a formal Limitations section, and performance under non-exponential or otherwise irregular tumor growth is not fully established beyond the simulated scenarios.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1158/2767-9764.crc-23-0243

Cites

38 of 38 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

37 of 43 cited sources checked · 8 supported · 0 flagged · accuracy not yet measured

  • Premisecitation

    Existing 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”
    Quote in the paperSubstantial claim3 of 3 sources checked
    • cites [24] Wu, 2012, Assessing interactions for fixed-dose drug combinations in tumor xenograft studies, J Biopharm Stat source

      The Introduction (page unavailable) says there is little literature on assessing fixed-dose drug combinations in tumor xenograft experiments, but it does not say existing methods impose unrealistic assumptions. Searches for limitations and assumptions about tumor growth or tumor-volume data found no passage addressing that criticism. (LLM, conf=0.72)

      Experimental — accuracy not yet measured
    • cites [25] Wu, 2013, Assessing interactions for fixed-dose drug combinations in subcutaneous tumor xenograft studies, Pharm Stat source

      The Introduction says some existing methods are inapplicable to fixed-dose studies or assess superiority rather than drug interaction. Section 2 describes incomplete longitudinal tumor-volume data. Neither passage says those methods impose unrealistic assumptions about tumor growth or tumor-volume data, so the stated reason for their limitations is not supported. (LLM, conf=0.73)

      Experimental — accuracy not yet measured
    • cites [29] Demidenko, 2019, Statistical determination of synergy based on Bliss definition of drugs independence, PLoS One source

      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
  • Premisecitation

    CI 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.”
    Quote in the paperSubstantial claim3 of 3 sources checked
    • cites [24] Wu, 2012, Assessing interactions for fixed-dose drug combinations in tumor xenograft studies, J Biopharm Stat source

      Section 2 (Interaction Index; page unavailable) defines an index using tumor-volume measurements from a control group, but does not discuss whether it can be calculated after control mice are euthanized. Section 5 (Actual Tumor Xenograft Data Analysis; page unavailable) says mice were euthanized after two weeks of treatment, without describing a tumor-size threshold or earlier euthanasia of controls. Searches for those conditions found no supporting passage. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
    • cites [25] Wu, 2013, Assessing interactions for fixed-dose drug combinations in subcutaneous tumor xenograft studies, Pharm Stat source

      Section 2 (page unavailable) says mice are euthanized when tumors reach four times their initial volume, leaving incomplete longitudinal tumor-volume data. Section 6 reports that control tumors reached this endpoint earlier than treated tumors in the examples. The paper does not say that CI cannot be calculated after a particular day when most or all control mice have been euthanized; Section 4 instead describes a confidence interval based on tumor-quadrupling times. (LLM, conf=0.85)

      Experimental — accuracy not yet measured
    • cites [29] Demidenko, 2019, Statistical determination of synergy based on Bliss definition of drugs independence, PLoS One source

      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 measured
  • Premisecitation

    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”
    Quote in the paperSubstantial claim3 of 3 sources checked
    • cites [24] Wu, 2012, Assessing interactions for fixed-dose drug combinations in tumor xenograft studies, J Biopharm Stat source

      Section 2 analyzes observed tumor volumes at the end of the study, and Section 3 examines confidence-interval coverage in small samples. Searches for missing or unbalanced tumor-volume data, interpolation, and uncertainty from interpolated values found no passage addressing the claim. (LLM, conf=0.72)

      Experimental — accuracy not yet measured
    • cites [25] Wu, 2013, Assessing interactions for fixed-dose drug combinations in subcutaneous tumor xenograft studies, Pharm Stat source

      Section 2 (page not available) says that euthanizing mice produces incomplete longitudinal tumor-volume data and describes interpolation to estimate the time of tumor quadrupling between measurements. It does not say that interpolation patches missing tumor-volume measurements, that existing methods struggle with unbalanced data, or that the uncertainty is unmeasurable. (LLM, conf=0.84)

      Experimental — accuracy not yet measured
    • cites [29] Demidenko, 2019, Statistical determination of synergy based on Bliss definition of drugs independence, PLoS One source

      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
  • Premisecitation

    Combination therapies using two or more therapeutic agents can be superior to single-agent therapies in the treatment of cancers.

    “Combination therapies using two or more therapeutic agents can be superior to single-agent therapies in the treatment of cancers (1–3).”
    Quote in the paperSubstantial claim1 of 3 sources checked
    • cites [1] Al-Lazikani, 2012, Combinatorial drug therapy for cancer in the post-genomic era, Nat Biotechnol source
    • cites [2] Lopez, 2017, Combine and conquer: challenges for targeted therapy combinations in early phase trials, Nat Rev Clin Oncol source
    • cites [3] Jin, 2023, Rational combinations of targeted cancer therapies: background, advances and challenges, Nat Rev Drug Discov source
  • Premisecitation

    Wu's alternative Bliss CI based on survival analysis parameters becomes undefined if tumors shrink in any group.

    “Subsequently, Wu defined an alternative Bliss CI based on parameters estimated from survival analysis; however, the index becomes undefined if tumors shrink in any group, which is often seen for efficacious drugs (25).”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [25] Wu, 2013, Assessing interactions for fixed-dose drug combinations in subcutaneous tumor xenograft studies, Pharm Stat source

      Sections 3 (Interaction Index) and 4 (Confidence Interval) define a Bliss-based interaction index using tumor-growth delays estimated from median tumor quadrupling times. The paper does not say the index becomes undefined whenever tumors shrink; Section 3 explicitly discusses treated tumors regrowing, while Section 2 treats tumors that do not quadruple during follow-up as censored. Page numbers are unavailable in our copy. (LLM, conf=0.87)

      Experimental — accuracy not yet measured
  • May combine two claims. 36
  • Classified as probably not a substantial claim. 14
  • The quote only partly states this claim. 1

  • May combine two claims.

    Premisecitation

    eGR makes no assumption on tumor growth kinetics and is invariant to starting TV.

    “We previously defined an efficacy readout called normalized AUC that makes no assumption on tumor growth kinetics and is invariant to starting TV (31).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [31] Guo, 2019, The design, analysis and application of mouse clinical trials in oncology drug development, BMC Cancer source

      The Methods section on continuous efficacy endpoints introduces an AUC ratio as a more general readout that reduces to the growth-rate ratio under exponential kinetics. It does not call the readout normalized AUC or eGR, or state that it is invariant to starting tumor volume. The latter part of the attributed claim is therefore unsupported by our copy. (LLM, conf=0.76)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Premisecitation

    Existing 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)”
    Quote in the paperSubstantial claim3 of 3 sources checked
    • cites [24] Wu, 2012, Assessing interactions for fixed-dose drug combinations in tumor xenograft studies, J Biopharm Stat source

      Section 2 (page unavailable) calculates an interaction index from tumor-volume measurements at the end of the study, supporting the single-day aspect. It does not report that the index fluctuates excessively or switches between synergy and antagonism on different days; it also calls the measure an interaction index, not CI. (LLM, conf=0.85)

      Experimental — accuracy not yet measured
    • cites [25] Wu, 2013, Assessing interactions for fixed-dose drug combinations in subcutaneous tumor xenograft studies, Pharm Stat source

      Section 2 (page unavailable) describes weekly tumor-volume measurements and a time-to-event endpoint; Section 3 (page unavailable) defines a local interaction index. Neither passage says that existing methods calculate a combination index from one day's tumor-volume data or that day-to-day fluctuations can switch its interpretation between synergy and antagonism. Searches for single-day calculations and fluctuating local indices found no such discussion. (LLM, conf=0.73)

      Experimental — accuracy not yet measured
    • cites [29] Demidenko, 2019, Statistical determination of synergy based on Bliss definition of drugs independence, PLoS One source

      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 measured

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Huang and colleagues established CombPDX as a statistical framework for Bliss independence, HSA, and response additive models, with Bliss CI equivalent to Wu and colleagues and HSA and RA newly introduced.

    “More recently, Huang and colleagues established CombPDX as a statistical framework for three synergy models: Bliss independence, HSA, and response additive (RA; ref. 27), their definition of Bliss CI is equivalent to that in Wu and colleagues (24), while HSA and RA were newly introduced.”
    Quote in the paperNot a substantial claim2 of 2 sources checked
    • cites [27] Huang, 2022, CombPDX: a unified statistical framework for evaluating drug synergism in patient-derived xenografts, Sci Rep source
    • cites [24] Wu, 2012, Assessing interactions for fixed-dose drug combinations in tumor xenograft studies, J Biopharm Stat source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Zhao and colleagues derived a Bliss independence index using differential equations to model tumor growth, which is equivalent to the interaction index in Wu and colleagues.

    “Zhao and colleagues used differential equations to model tumor growth and derived a Bliss independence index (26), which is equivalent to interaction index in Wu and colleagues (24).”
    Quote in the paperNot a substantial claim1 of 2 sources checked
    • cites [26] Zhao, 2019, Detecting bliss synergy in in vivo combination studies with a tumor kinetic model, Pharm Stat source
    • cites [24] Wu, 2012, Assessing interactions for fixed-dose drug combinations in tumor xenograft studies, J Biopharm Stat source

      Section 2 (INTERACTION INDEX; page unavailable) defines Wu and colleagues’ interaction index using a Bliss independence model, supporting the characterization of their index. Our copy does not discuss Zhao’s differential-equation model or establish that Zhao’s index is equivalent to Wu’s, so the equivalence is not verified by this source. (LLM, conf=0.82)

      Experimental — accuracy not yet measured

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    Demidenko 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).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [29] Demidenko, 2019, Statistical determination of synergy based on Bliss definition of drugs independence, PLoS One source

      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 measured

  • May combine two claims.

    Premisecitation

    Most in vivo synergy studies simply compare tumor volume at a single day using t test, or use survival analysis to compare time-to-event between groups.

    “Most studies simply compare TV at a single day using t test, or use survival analysis to compare the time-to-event (i.e., time for TV to reach a threshold) between groups (4–6, 23).”
    Quote in the paperSubstantial claim3 of 4 sources checked
    • cites [4] Jaaks, 2022, Effective drug combinations in breast, colon and pancreatic cancer cells, Nature source

      The Methods section ('In vivo tumour xenograft studies'; page not provided) reports Welch’s t-tests for endpoint comparisons and log-rank tests for survival experiments. It also defines a tumour-volume threshold for survival experiments. This supports the paper as an example of those approaches, but it does not establish that most in vivo studies use them; it also uses two-way ANOVA for tumour-volume changes during treatment. (LLM, conf=0.87)

      Experimental — accuracy not yet measured
    • cites [5] Holbeck, 2017, The National Cancer Institute ALMANAC: a comprehensive screening resource for the detection of anticancer drug pairs with enhanced therapeutic activity, Cancer Res source

      The Materials and Methods section (Human Tumor Xenografts; page unavailable) describes comparing groups with Kaplan–Meier and log-rank analyses of time to tumor-volume doubling. The Results section (Examination of Promising Anticancer Drug Combinations; page unavailable) says various methods have been used in xenograft studies, but it does not establish that most studies use these methods or report single-day tumor-volume comparisons using a t test. (LLM, conf=0.86)

      Experimental — accuracy not yet measured
    • cites [6] O'Neil, 2016, An unbiased oncology compound screen to identify novel combination strategies, Mol Cancer Ther source
    • cites [23] Turner, 2020, Identification of synergistic drug combinations using breast cancer patient-derived xenografts, Sci Rep source

      The Methods (Statistical analyses; page unavailable) report unpaired t tests for comparisons between in vivo treatment groups, and the Figure 8 caption (Results; page unavailable) displays endpoint significance. The paper does not establish that most studies use this approach; it also lists p-values for all measured timepoints. Its survival analysis concerns patients’ metastasis-free survival, not time for tumor volume to reach a threshold. (LLM, conf=0.83)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    In CombPDX, TV data at a single day are used to calculate a local CI, and the average of all local CI values is the global CI.

    “TV data at a single day were used to calculate a local CI, the average of all local CI values is the global CI (27).”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [27] Huang, 2022, CombPDX: a unified statistical framework for evaluating drug synergism in patient-derived xenografts, Sci Rep source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    The combination of palbociclib and cetuximab was proposed as a potential strategy to overcome cetuximab resistance by targeting cyclin D1 deregulation.

    “The combination of the CDK4/6 inhibitor palbociclib and the EGFR inhibitor cetuximab was proposed as a potential strategy to overcome cetuximab resistance by targeting cyclin D1 deregulation (28).”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [28] Demidenko, 2010, Three endpoints of in vivo tumour radiobiology and their statistical estimation, Int J Radiat Biol source

      The Introduction and Discussion describe statistical estimation of tumour-treatment endpoints, while the photodynamic radiotherapy example concerns a mouse prostate-tumour model. Searches for palbociclib, cetuximab resistance, and cyclin D1 found no passage addressing the proposed combination or its rationale in our copy. (LLM, conf=0.78)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Premisecitation

    In vivo validation studies of irinotecan and rabusertib only showed HSA synergy but not Bliss synergy.

    “However, such in vivo validation studies only showed that synergy exists under the HSA model but not the more stringent Bliss model.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [4] Jaaks, 2022, Effective drug combinations in breast, colon and pancreatic cancer cells, Nature source

      The ‘Irinotecan and CHEK1i synergize in colon’ section (page unavailable) reports that the combination reduced tumour growth more than irinotecan alone in two mouse xenograft models. That supports an in vivo benefit over a single agent, but the paper does not classify the in vivo results under HSA or test whether they meet Bliss synergy. Its Bliss-based classification is described for the cell-line screen in ‘Methods > Classifying synergy’ (page unavailable). (LLM, conf=0.85)

      Experimental — accuracy not yet measured

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    The MuSyC framework unifies a variety of synergy metrics and separates potency synergy and efficacy synergy such that the two synergies are objective metrics purely determined by the interactions of two drugs, and are neither dose nor time dependent.

    “The MuSyC framework unifies a variety of synergy metrics and separates potency synergy and efficacy synergy such that the two synergies are objective metrics purely determined by the interactions of two drugs, and are neither dose nor time dependent (13).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [13] Wooten, 2021, MuSyC is a consensus framework that unifies multi-drug synergy metrics for combinatorial drug discovery, Nat Commun source

      Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

      Experimental — accuracy not yet measured

  • May combine two claims.

    Findingown data

    invivoSyn has high sensitivity and low false discovery rate in detecting synergy.

    “Here, we introduce a novel approach to assess in vivo drug synergy with high sensitivity and low false discovery rate.”
    • Also stated in: § Introduction · boosted
      “We used simulation and case studies to show that our method has high sensitivity and low FDR in detecting synergy.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The SW837 study had an unbalanced design with different numbers of mice in the four groups and large variations of starting TVs in the irinotecan and combo groups.

    “This study has an unbalanced design with different numbers of mice in the four groups, with large variations of starting TVs in the irinotecan and combo groups.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning

    Under the nil synergy setting, invivoSyn has low statistical power, hence low FDR.

    “Under the nil synergy setting, the power is low so that we will not erroneously claim synergy (i.e., low FDR).”
    • Also stated in: § InvivoSyn Detects Synergy with High Statistical Power and Low FDR · plain
      “while for nil synergy, the power is always low”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In SNU-81, tumor grew fast in vehicle and rabusertib groups such that TV data were only available in first 15 days, while irinotecan and combo groups had TV data for 36 days.

    “Tumor grew fast in the vehicle group and the rabusertib group such that TV data were only available in the first 15 days after dosing started, while the irinotecan and the combo groups had TV data available for 36 days.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    In the LS-1034 xenograft, irinotecan+rabusertib combo was more potent but the Bliss synergy P value was only 0.083, even though the two drugs showed stronger in vitro efficacy in LS-1034 than in SNU-81 and SW837.

    “A real-world example is the combination study of irinotecan+rabusertib on the LS-1034 xenograft (Fig. 2I–L). Irinotecan has very strong efficacy by itself, so although the combo treatment is more potent, the P value for Bliss synergy is only 0.083, even though the two drugs showed stronger in vitro efficacy in LS-1034 than in SNU-81 and SW837.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In the CR1197 colon PDX study, some mice in the combo group exhibited a delayed response with tumor regression then regrowth at the late stage, while the vehicle group had a shorter study duration (49 vs. 24 days).

    “We noticed that some mice in the combo group exhibited a delayed response that resulted in tumor regression then regrowth at the late stage of the study, whereas the vehicle group had a shorter study duration (49 vs. 24 days).”
    Quote in the paperSubstantial claim

  • The quote only partly states this claim.

    Findingown data

    Under delayed treatment effect, invivoSyn power is insufficient if the study is terminated at day 30.

    “The power increases steadily by both sample size and study duration, but is insufficient if the study is terminated too early at day 30.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In SW837, the CI is 0.672, meaning observed TV under combo is 67.2% of expected TV under additivity.

    “The CI is 0.672, which means that under the combo treatment, the observed TV is only 67.2% of the expected TV when there is only additive effect.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    invivoSyn demonstrated superior performance in both real-world studies and simulated datasets.

    “Our method demonstrated superior performance in both real-world studies and simulated datasets, and it imposes no constraint on tumor growth kinetics and uses TV data from all days for all mice.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Both invivoSyn and CombPDX confirmed HSA synergy in all three xenograft studies.

    “We note that both invivoSyn and CombPDX confirmed HSA synergy in all three studies.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingnone given

    In an in vivo 4-group combination study, CI and SS values vary by day, but the P value is unchanged.

    “At different days, the values of CI and SS vary, but the P value is unchanged (It is therefore more meaningful to use P value to assess synergy.).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In LS-1034, irinotecan treatment was more effective such that the efficacy difference between irinotecan and combo treatments was not pronounced and evaded detection by CombPDX.

    “However, irinotecan treatment was more effective to LS-1034 such that the efficacy difference between the irinotecan and the combo treatments was not pronounced and evaded detection by CombPDX (Fig. 2J).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    CombPDX could not use TV data beyond day 15 and failed to account for the long-lasting effect of combo treatment in SNU-81 (P = 0.944).

    “The uneven TV data structure posed a challenge for CombPDX, which could not use TV data beyond day 15 and failed to account for the long-lasting effect of the combo treatment (Fig. 2F, P = 0.944).”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given

    Both Bliss and HSA combination indices theoretically assume log-normal distributions.

    “In particular, both Bliss and HSA combination indices theoretically assume log-normal distributions.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Premiseown data

    BCa bootstrapping is more appropriate for skewed distributions, as is the case here.

    “BCa bootstrapping is more appropriate for skewed distributions, as is the case here.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given

    Combination index, when defined via relative survival of tumor cells, is both dose and time dependent.

    “We emphasize that combination index, when defined here via relative survival of tumor cells, is both dose and time dependent”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisereasoning

    The dose-response curve and surface methods used for cell line assays are no longer applicable to in vivo combination studies because there is only a single dose for a drug, and Loewe and ZIP models are no longer applicable since both require dose-response curves for parameter estimation.

    “The dose–response curve and surface methods used for cell line assays are no longer applicable because there is only a single dose for a drug (as a result, Loewe and ZIP models are no longer applicable since both require dose–response curves for parameter estimation).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    In vitro and in vivo studies assess combination effects from different angles, each describing only part of the synergy landscape.

    “It is evident that in vitro and in vivo studies are assessing combination effects from different angles so that either only describe part of the synergy landscape.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    invivoSyn has low FDR for detecting synergy even if tumors regrow, as long as the combination study is well designed with enough mice and sufficiently long study duration.

    “Overall, our results suggest that invivoSyn has low FDR for detecting synergy even if tumors regrow, as long as the combination study is well designed with enough mice and sufficiently long study duration.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Interpretationown data

    CI is defined in essentially the same way for both in vitro and in vivo combination studies.

    “The CI is defined in essentially the same way for both in vitro and in vivo combination studies due to the parallelism shown in Fig. 7.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    Tumor-infiltrating leukocyte depletion experiments cannot be performed in cell lines.

    “Such tumor-infiltrating leukocyte (TIL) depletion experiments cannot be performed in cell lines”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    A parallelism exists between in vitro and in vivo combination studies such that terminologies can be defined conceptually the same way and synergy models can be applied equally.

    “In this work, we showed that a parallelism exists between in vitro and in vivo combination studies such that not only terminologies can be defined in conceptually the same way, but also synergy models can be applied equally (Fig. 7).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    Under the Bliss independence model, CI and SS are both time and dose dependent.

    “We now show that under the Bliss independence model, CI is both time and dose dependent by comparing the 4-group in vivo combination study with the fixed-ratio in vitro combination study.”
    • Also stated in: § Synergy Metrics are Both Time and Dose Dependent Under the Bliss Independence Model · plain
      “Jointly, we know that the CI, as well as the SS, is both time and dose dependent.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisenone given

    Existing methods for evaluating in vivo combination effects fall into two categories: ones using differential and kinetic equations to model tumor growth, and ones directly comparing TV at a single day.

    “Existing methods for evaluating in vivo combination effects fall into two categories, ones using differential and kinetic equations to model tumor growth, and ones directly comparing TV at a single day.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationnone given

    invivoSyn imposes no constraint on tumor growth kinetics and uses TV data from all days for all mice.

    “Our method demonstrated superior performance in both real-world studies and simulated datasets, and it imposes no constraint on tumor growth kinetics and uses TV data from all days for all mice.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    invivoSyn's detection of Bliss synergy in SNU-81 demonstrates its robustness and flexibility in handling uneven tumor growth data.

    “demonstrating its robustness and flexibility in handling uneven tumor growth data.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    The greater sample size needed for fast-growing tumors is likely due to larger variation in tumor volume between mice, and consequently in TV-based metrics such as eGR.

    “This is likely due to the larger variation of TV between mice for fast-growing tumors; therefore TV based metrics, such as eGR, also have larger variation.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    InvivoSyn power is not strongly affected by TV cutoff as long as there are enough measurement days to estimate eGR and the cutoff is not too small.

    “This is expected as long as there are enough datapoints (i.e., number of measurement days) to estimate eGR and the TV cutoff is not too small (e.g., only slightly larger than the initial TV).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    This study establishes a well-founded method to investigate in vivo combination studies and provides a unified view of in vitro and in vivo synergy under the Bliss independence model.

    “This study establishes a well-founded method to investigate in vivo combination studies and provides a unified view of in vitro and in vivo synergy under the Bliss independence model.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Interpretationreasoning

    A significant HSA synergy means a combo treatment is better than either single-agent treatment.

    “Nonetheless, a significant HSA synergy means a combo treatment is better than either single-agent treatment, which is often sufficient in the clinical treatment of patients with cancer.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    The lack of Bliss synergy detection by CombPDX in SW837 indicates a lack of statistical power and high fluctuation for single day-based synergy methods.

    “which indicates a lack of statistical power and high fluctuation for single day–based synergy methods.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given

    If two drugs have strong in vitro synergy, significant in vivo synergy can be observed with proper study designs.

    “Nonetheless, if two drugs have strong in vitro synergy, significant in vivo synergy can be observed with proper study designs, as we explain more in Discussion.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given

    A typical fixed-ratio in vitro combination study evaluates the combination effect at a single timepoint, while a typical 4-group in vivo combination study evaluates the combination effect at single-dose levels.

    “We further emphasize that synergy, when represented by CI, is both time and dose dependent; a typical fixed-ratio in vitro combination study evaluates the combination effect at a single timepoint, while a typical 4-group in vivo combination study evaluates the combination effect at single-dose levels.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    CI and SS depend on tumor growth rate and time.

    “The third one is to use combination indices and SSs cautiously, especially when comparing between different xenograft models or comparing drug combinations in the same xenograft model, because these two synergy measures depend on tumor GR and time.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    The quantitative invivoSyn analysis classified combination effects into additivity, synergism, and antagonism, giving a better understanding of how intrinsic tumor immunity affects immunotherapies in different syngeneic models.

    “The quantitative invivoSyn analysis unambiguously classified combination effects into additivity, synergism, and antagonism that gave us a better understanding of how intrinsic tumor immunity affects immunotherapies in different syngeneic models”
    Quote in the paperSubstantial claim
45 of 45

  • The authors state this as an assumption.

    TV is a measurement of the number of cells in a tumor.

    “We view TV as a measurement of the number of cells in a tumor.”

  • The authors state this as an assumption.

    Tumor growth can be represented by an equivalent exponential growth equation for the purpose of calculating eGR.

    “under an equivalent exponential kinetics assumption”
    “an average exponential growth curve, with the mean eGR as the rate constant, is drawn regardless of the shapes of actual individual growth curves”

  • The paper relies on this without support.

    In most in vivo combination studies, tumors exhibit regular growth patterns in the sense that all tumors in a treatment group either grow or shrink with variations in GR.

    “In most in vivo combination studies, tumors exhibit regular growth patterns in the sense that all tumors in a treatment group either grow or shrink with variations in GR (Fig. 4A).”

  • The paper relies on this without support.

    In practice, nearly all in vivo combination studies use the 4-group design for its simplicity and relatively low cost.

    “However, in practice, nearly all in vivo combination studies use the 4-group design for its simplicity and relatively low cost.”

  • The authors state this as an assumption.

    Exponential growth kinetics holds for both cell proliferation and tumor growth under drug treatment and well before reaching maximal values constrained by nutrient and space.

    “Specifically, we assume exponential growth kinetics for both cell proliferation (Fig. 7A) and tumor growth (Fig. 7D) under drug treatment and well before reaching maximal values constrained by nutrient and space.”

  • The paper relies on this without support.

    In practice, in vivo combination studies normally have only four groups.

    “while in practice, we normally have only four groups, not only to save cost but to focus on the selected drug dose levels.”

  • The paper relies on this without support.

    Clinical validation of Bliss synergy is generally not possible to conduct due to ethical regulations and cost.

    “However, its clinical validation is generally not possible to conduct due to ethical regulations and cost.”
7 of 7

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • eGR is described as preserving endpoint change but is calculated from area under the curve

    Major

    The stated eGR calculation uses the area under the entire log-volume trajectory. Two tumors can have the same starting and ending volumes but different intermediate trajectories, yielding different eGR values; an equivalent exponential curve therefore cannot, in general, preserve the stated net TV change.

  • Intrinsic-resistance simulation assigns resistance to different groups

    Minor

    The methods say intrinsic resistance was assigned to all three drug-treatment groups, including B. The Figure 6 caption says it was assigned to A and A+B only.

2 of 2

Cites

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Related

Authors
Mao, B., & Guo, S.
Affiliations
  • 1Crown Bioscience Inc., Suzhou, Jiangsu, P.R. China.
  • Crown Bioscience (China) (CN)
Corresponding author
Guo, Sheng
ORCID
Venue
Cancer Research Communications
Publisher
American Association for Cancer Research (AACR)
Published
2023-10-23
Volume
3
Issue
10
Pages
2146-2157
ISSN
2767-9764 (ISSN-L)
DOI
10.1158/2767-9764.crc-23-0243
PMC
PMC10591909
OpenAlex
W4387599688
Semantic Scholar
23c6e037f0b663cac87d1fb8a1586f39857ace37
Cited by
27
References
38
Citations by year
2026: 13 · 2025: 11 · 2024: 3
FWCI
5.28
Type
journal article
Language
en
Open access
Licence
Locations
  • Cancer Research Communications (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • PubMed Central (submittedVersion, cc-by)
Funders
Crown Bioscience, Inc.
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Computational Drug Discovery Methods
  • Physical Sciences › Mathematics › Modeling and Simulation › Mathematical Biology Tumor Growth
Keywords
drug synergy, combination index, Bliss independence model, syngeneic mouse model, immune checkpoint inhibitors, anti-PD-1, tumor growth kinetics, false discovery rate
MeSH terms
Animals, Disease Models, Animal, Drug Therapy, Combination, Humans, Cell Line, Tumor, Mice

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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-27.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-27.

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