1 Introduction
Determining cell-death modes is critical in developing a combined cancer therapy: the combination may deactivate cells via a mode differed from that in the single regimen, or via more than one mode. Most single therapies deactivate cancer cells via the apoptosis pathway, and the apoptotic malfunction results in therapeutic resistance (Liu et al., 2025; Yue et al., 2025). Therefore, that a combined therapy can induce nonapoptotic death is a specific merit, for having a potential to combat resistance (Yu et al., 2016; Liu et al., 2022; Yu and Li, 2023; Swords et al., 2024; Moyer et al., 2025). Whether there is nonapoptotic death should be decided at an early state of a therapeutic trial.
Of those cell-death modes, apoptotic cells (i.e., the apoptosis percentage) can be directly and accurately quantified using easy methods (e.g., annexin V, terminal nick end labeling or sub-G1 assay). Indeed, the apoptosis percentage is calibrated in most therapeutic trials. However, the death percentages due to other modes (e.g., necrosis, necroptosis, ferroptosis or autophagy) can only be detected qualitatively or semi-quantitatively: nonapoptotic death is demonstrated by determining the bio-chemical biomarkers related to a specific death mode or observing a reduction in the death percentage after inhibiting a specific death mode (Hu et al., 2021; Kari et al., 2022; Liu et al., 2022; Khalef et al., 2024).
2 Determining nonapoptotic death based on the ratio of combination indexes
The effect-based combination index (CI) is used to assess a combined therapy (Equation 1).
EA or EB is the effect of a single therapy, and EA+B is the effect of the combination. The dose of A in EA+B is equal to that in EA, so is the dose of B in EA+B and EB. A CI of <0.85, 0.85–1.15, or >1.15 indicates antagonism, addition, or synergy, respectively (Yu et al., 2025). CI can be calculated using the percentages of dead cells (i.e., CIDea) or other effects (He et al., 2014). CIDea reflects the ultimate effect, because induction of death of cancer cells is the primary efficacy endpoint. A combined therapy can be further developed only when CIDea shows addition or synergy (He et al., 2012).
Each death mode contributes to a fraction of cell death when death results from multiple modes, and the sum is the percentage of dead cells (Equation 2). Thus, each death mode can be considered as a specific effect, i.e., having a corresponding CI (e.g., CIApo is based on the percentages of apoptotic cells). CIDea is the gross effect (Equation 3).
CIi is for a specific death mode, and Wi is the weight of that mode in overall cell death. However, the percentage of nonapoptotic death cells cannot be quantified directly and accurately, i.e., CIi except CIApo cannot be directly calculated. Theoretically, other CIi can be deduced by CIDea minus CIApo. These suggest that the ratio of CIApo to CIDea can provide info of the cell-death modes.
Here discussions are based on these premises: the identical therapeutic manner (doses and exposure duration of drugs) is employed in both cell-death and apoptosis trials, cell death and apoptosis are calibrated at the same time point, and CI
Deaindicates addition or synergy.
When apoptosis is the sole/determining death mode in the combined therapy, the number of dead cells is the sum of apoptotic cells. Accordingly, CIApo is nearly equal to CIDea, i.e., CIApo >F0×CIDea. F0 can be empirically set 0.8.
When there is a nonapoptotic death mode in the combination, the percentage of dead cells is partly due to that of apoptotic cells. Therefore, CIApo contributes to only a fraction of CIDea, i.e., CIApo <F0×CIDea.
In rare cases, the combination deactivates cells via a nonapoptotic mode although apoptosis is the mechanism for the single therapy (Ma et al., 2016; Liu et al., 2017; Silva et al., 2017). Consequently, the apoptosis percentage in the combination is not increased in comparison with the single therapy, i.e., CIApo <F1×CIDea. F1 can be set 0.4–0.5 (depending on cell type) (Figure 1).
FIGURE 1
The ratio of CIApo to CIDea can indicate the occurrence of nonapoptotic death in a combined therapy. F0 and F1 are cell-type dependent; the empirical values are 0.8 and 0.4–0.5, respectively. CIDea, combination index based on death percentages; CIApo, combination index based on apoptosis percentages.
These deductions were tested in 2 datasets. The agreement was 77.6% (111/143) when using the death mode stated in the trial as the reference (κ = 0.40 [95% confidence interval: 0.23–0.57], p < 0.0001) (noticeably, data can be extracted from 39/198 papers released in 2016–2017, but from 37/308 papers released in 2022–2024). The accuracy for apoptosis was 81.4% (92/113), and that for nonapoptosis was 63.3% (19/30), respectively (Supplementary Tables S1, S2). These findings suggest that the CIApo/CIDea ratio can be used to preliminarily determine the death mode in a combined therapy.
Based on the present data, an inquiry about the role of autophagy arises. Autophagy was considered a death mechanism in certain trials, but CIApo>CIDea indicated that apoptosis was the determining death mode (Wang et al., 2016; Zhang et al., 2017). A reasonable interpretation is that the increase in autophagy is an accompanying response, or that autophagy is the switch to apoptosis. There arise similar concerns when necrosis is deemed as a death mechanism based on only propidium iodide-positive cells in flow cytometry but CIApo is not inferior to CIDea (Shirvalilou et al., 2024).
3 Improving the accuracy
CIDea has high accuracy, since available assays for cell viability are with high selectivity, specificity and stability. Therefore, the accuracy of the present method relies on accurate CIApo which is determined by accurate apoptosis percentages. The apoptosis percentage in control cells (receiving no therapy) was >10% (even >20%) in certain trials, demonstrating a high background level (Yadav et al., 2022; Zheng et al., 2023; Camero et al., 2024). Such a high background level suggests biases in apoptosis percentages in cells receiving therapies, which will distort CIApo. An apoptosis percentage of <5% in control cells indicates that data are with high quality for evaluations.
One dose for each single therapy is commonly used in an apoptosis trial. In certain cases, the dose may not be the optimum one to determine apoptosis in the combination, thereby underestimating CIApo and eventually leading to misjudgments. A preferred method is to adopt 2–3 doses in each single therapy to catch the apoptosis property better, particularly when the CIApo/CIDea ratio is 0.7–0.8. Doses for the apoptosis trial can be set according to the death percentage vs. dose curve, and should be up to the half-maximum effective dose. A higher dose may lead to saturation, thereby covering up apoptosis synergy (Yu et al., 2025).
Apoptosis does not necessarily synchronize with cell death. In certain cases, the apoptosis pattern of a regimen in the combination differs from that of being administrated alone, i.e., alterations of apoptosis percentages in two single and the combined therapies are nonsynchronous. The apoptosis percentage in the combined therapy can be lower than the actual level, thereby distorting CIApo and eventually resulting in misjudgments. The apoptosis kinetics may be a solution. Apoptosis percentages in a definite duration (t1–tlast) are quantified at multiple time points. RAUC (relative area under the apoptosis percentage vs. time curve) is used to calculate CIApo, where integration utilizes the trapezoidal method (Figure 2; Equations 4, 5) (Yu et al., 2024).
FIGURE 2
![Graph depicting the relationship between apoptosis percentage and time. The graph includes a piecewise linear function with points labeled \(A_i\), \(A_{i+1}\), \(A_{i+2}\), and \(A_{i+3}\) over time intervals \(t_i\), \(t_{i+1}\), \(t_{i+2}\), and \(t_{i+3}\). An equation for RAUC (Relative Area Under the Curve) is shown above: \[RAUC = \frac{\int_{t_1}^{t_{\text{last}}}Adt}{k(t_{\text{last}}-t_1)} = \frac{\sum_{i=1}^{n}\frac{(A_i + A_{i+1})(t_{i+1} - t_i)}{2}}{k(t_{\text{last}} - t_1)}.\]](https://www.frontiersin.org/files/Articles/1737170/xml-images/fphar-17-1737170-g002.webp)
AUC is integrated using the trapezoidal method, and then RAUC is calculated. The coefficient k outlines the panorama of apoptosis, and the default value can be 1.0. AUC, area under the apoptosis percentage vs. time curve; RAUC, relative AUC.
tlast should be identical to the time point of determining the cell-death percentage. Ai is the apoptosis percentage at the i-th time point. The coefficient k (depending on cell type) outlines the apoptosis panorama, and should be biologically and mathematically logical (i.e., RAUC complies with the rule of calculating CI). Thus, k should be 0.8–1.0, and the default value can be 1.0 (i.e., with an apoptosis percentage of 100%). CIApo based on RAUC is the preferred method when apoptosis percentages indicate that nonapoptotic death is the sole mechanism for the combination, but either single therapy deactivates cells via apoptosis. This manner can avoid false negative.
4 Conclusion
The CIApo/CIDea ratio provides a preliminary indicator of cell-death modes. A higher ratio confirms apoptosis and a lower ratio suggests the involvement of nonapoptotic death, which can be used to assess the potential of a combined therapy. Individually optimizing F0 or F1 may be needed in specific cases. The accuracy of this method is reliant on accurate CIApo that is determined by accurate apoptosis percentages. Using RAUC to calculate CIApo can improve the accuracy when apoptosis does not synchronize with cell death.
Statements
Author contributions
TY: Formal Analysis, Writing – original draft. YD: Formal Analysis, Writing – original draft. XL: Formal Analysis, Validation, Writing – original draft. TY: Conceptualization, Formal Analysis, Validation, Writing – review and editing.
Funding
The author(s) declared that financial support was not received for this work and/or its publication.
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The author TY declared that they were an editorial board member of Frontiers at the time of submission. This had no impact on the peer review process and the final decision.
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Supplementary material
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphar.2026.1737170/full#supplementary-material
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Summary
Keywords
apoptosis, apoptosis kinetics, combination index, combined therapy, nonapoptosis
Citation
Yu T, Dong Y, Li X and Yu T (2026) The ratio of effect-based combination indexes can indicate nonapoptotic cell-death in a combined cancer therapy. Front. Pharmacol. 17:1737170. doi: 10.3389/fphar.2026.1737170
Received
01 November 2025
Revised
27 December 2025
Accepted
06 January 2026
Published
22 January 2026
Volume
17 - 2026
Edited by
Raghuram Kandimalla, James Graham Brown Cancer Center, United States
Reviewed by
Purushoptham Pothula, University of Louisville, United States
Mahendar Kadari, University of Louisville, United States
Updates
Copyright
© 2026 Yu, Dong, Li and Yu.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Tinghe Yu, yutinghe@hotmail.com, yutinghe@cqmu.edu.cn
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.