Drug independence and the curability of cancer by combination chemotherapy

Describes and distinguishes between three noncompeting aspects of drug independence:•Bliss’ independence model describes how combination therapies decrease the fraction of cells that survive killing by one or more agents.•The Law independence model describes how combination therapies can overcome subpopulations of drug-resistant cells in a cancer.•The Frei independence model describes how combination therapies can increase the probability of tumor response in a population of patients without any drug additivity or synergy. A unified model of these drug independence principles quantitatively describes historical progress in curing pediatric acute lymphocytic leukemia. Combination chemotherapy can cure certain leukemias and lymphomas, but most solid cancers are only curable at early stages. We review quantitative principles that explain the benefits of combining independently active cancer therapies in both settings. Understanding the mechanistic principles underlying curative treatments, including those developed many decades ago, is valuable for improving future combination therapies. We discuss contemporary evidence for long-established but currently neglected ideas of how combination therapy overcomes tumor heterogeneity. We show that a unified model of interpatient and intratumor heterogeneity describes historical progress in the treatment of pediatric acute lymphocytic leukemia (ALL), in which increasingly intensive combination regimens ultimately achieved high cure rates. We also describe three distinct aspects of drug independence that apply at different biological scales. The ability of these principles to quantitatively explain curative regimens suggests that supra-additive (synergistic) drug interactions are not required for successful combination therapy. Combination chemotherapy can cure certain leukemias and lymphomas, but most solid cancers are only curable at early stages. We review quantitative principles that explain the benefits of combining independently active cancer therapies in both settings. Understanding the mechanistic principles underlying curative treatments, including those developed many decades ago, is valuable for improving future combination therapies. We discuss contemporary evidence for long-established but currently neglected ideas of how combination therapy overcomes tumor heterogeneity. We show that a unified model of interpatient and intratumor heterogeneity describes historical progress in the treatment of pediatric acute lymphocytic leukemia (ALL), in which increasingly intensive combination regimens ultimately achieved high cure rates. We also describe three distinct aspects of drug independence that apply at different biological scales. The ability of these principles to quantitatively explain curative regimens suggests that supra-additive (synergistic) drug interactions are not required for successful combination therapy. Several types of cancer are routinely cured by combination chemotherapy, and many incurable cancers can be controlled longer by combination therapy than by monotherapy. Why is combination therapy superior in these respects? In this review we consider this question from the perspective of three historical concepts used to explain the clinical benefits of combination therapy, and by reviewing the quantitative basis for the curability of childhood ALL. Our purpose is to examine these foundational principles of oncology in the light of contemporary evidence, and to better understand how more effective drug combinations might now be developed, including for more difficult-to-treat solid cancers that are only infrequently cured at present. The creators of the first curative combination regimens postulated that the probability of resistance to multiple mechanistically distinct drugs is lower than the probability of resistance to a single drug, and therefore combining multiple, individually effective chemotherapeutic mechanisms could overcome tumor heterogeneity, producing longer-lasting remissions – and perhaps even cures – in more patients [1.Bast R.C. Holland-Frei Cancer Medicine.9th edition. Wiley Blackwell, 2009Google Scholar, 2.László J. The Cure of Childhood Leukemia: Into the Age of Miracles. Rutgers University Press, 1995Google Scholar, 3.Frei E. Freireich E. Progress and perspectives in the chemotherapy of acute leukemia.in: Goldin A. Advances in Chemotherapy. Volume 2. Academic Press, 1965Crossref Google Scholar, 4.Pritchard J.R. et al.Understanding resistance to combination chemotherapy.Drug Resist. Updat. 2012; 15: 249-257Crossref PubMed Scopus (65) Google Scholar]. Modern research has also demonstrated the relevance of this idea to combinations including targeted therapies, while also emphasizing the challenge presented by mechanisms of multidrug resistance [4.Pritchard J.R. et al.Understanding resistance to combination chemotherapy.Drug Resist. Updat. 2012; 15: 249-257Crossref PubMed Scopus (65) Google Scholar, 5.Bozic I. et al.Evolutionary dynamics of cancer in response to targeted combination therapy.Elife. 2013; 2e00747Crossref PubMed Scopus (445) Google Scholar, 6.Bhang H.E. et al.Studying clonal dynamics in response to cancer therapy using high-complexity barcoding.Nat. Med. 2015; 21: 440-448Crossref PubMed Scopus (313) Google Scholar]. Pragmatic guidelines have defined much of the historical development of combination therapies: (i) each single agent should have antitumor activity, (ii) agents should have distinct mechanisms of action and thus distinct mechanisms of drug resistance, and (iii) the combination should be tolerable with few compromises in dosage. These guidelines led to combination regimens able to cure some hematological cancers and a few solid cancers, as well as to adjuvant and neoadjuvant combination therapies that improve cure rates in surgically resectable cancers. Despite the development of these successful combination regimens, many of which have been used to treat patients for decades, the mechanistic basis of treatment with curative intent remains incompletely understood. Relatedly, it is an open question why some of these regimens cure only a fraction of patients, and why many cancers still cannot be cured by combinations built according to these guidelines. A major complication in the treatment of cancer is that tumor heterogeneity and drug resistance are phenomena that manifest in multiple ways. At the most basic level, we can distinguish between intratumor heterogeneity (differences between cancer cells in one patient) and intertumor or interpatient heterogeneity (differences between the essential characteristics of cancers in different patients). Drug resistance can be present prior to the onset of therapy – whether in most cancer cells or in a rare subpopulation – or it can be acquired over time. Consequently, there are multiple ways in which tumor heterogeneity can limit therapeutic efficacy, and multiple ways in which combination therapy might overcome the challenges posed by tumor heterogeneity. The first of three quantitative principles which describes the probability of death when a cell (or organism) is treated with multiple toxins was developed by Chester Bliss in 1939 [7.Bliss C.I. The toxicity of poisons applied jointly.Ann. Appl. Biol. 1939; 26: 585-615Crossref Scopus (1593) Google Scholar]. The Bliss independence model is applied to combination therapy research in many diseases, and substantially overlaps with Loewe’s model of dose additivity [8.Gaddum J.H. Pharmacology.1st edn. Oxford University Press, 1940Google Scholar,9.Loewe S. The problem of synergism and antagonism of combined drugs.Arzneimittelforschung. 1953; 3: 285-290PubMed Google Scholar]. The two models are exactly concordant when dose response functions are exponential, which is common for chemotherapies [10.Blagoev K.B. et al.Therapies with diverse mechanisms of action kill cells by a similar exponential process in advanced cancers.Cancer Res. 2014; 74: 4653-4662Crossref PubMed Scopus (7) Google Scholar], since e–A × e–B (Bliss model) = e–(A+B) (Loewe model). The second principle describes a cancer cell’s probability of acquiring heritable multidrug resistance and was described by Lloyd Law in 1952 [11.Law L.W. Effects of combinations of antileukemic agents on an acute lymphocytic leukemia of mice.Cancer Res. 1952; 12: 871-878PubMed Google Scholar]. The third principle describes a patient’s probability of response when treated with multiple therapies, and was described by Emil Frei III et al. in 1961 [12.Frei E. et al.Studies of sequential and combination antimetabolite therapy in acute leukemia: 6-mercaptopurine and methotrexate.Blood. 1961; 18: 431-454Crossref Google Scholar], and then updated for progression-free survival data by Palmer and Sorger in 2017 [13.Palmer A.C. Sorger P.K. Combination cancer therapy can confer benefit via patient-to-patient variability without drug additivity or synergy.Cell. 2017; 171e13Abstract Full Text Full Text PDF PubMed Scopus (369) Google Scholar,14.Palmer A.C. et al.Predictable clinical benefits without evidence of synergy in trials of combination therapies with immune-checkpoint inhibitors.Clin. Cancer Res. 2022; 28: 368-377Crossref PubMed Scopus (29) Google Scholar]. Although these principles have similar mathematical structures, they describe biologically distinct phenomena, and their analysis requires different types of data. However, the three principles are mutually compatible and can all apply to a particular combination therapy, although their relative importance will depend on context. The development of combination regimens to cure the majority of children with ALL is among the greatest successes of cancer research. This success required solutions to both therapeutic and toxicological challenges [2.László J. The Cure of Childhood Leukemia: Into the Age of Miracles. Rutgers University Press, 1995Google Scholar]. In this review we focus on understanding the cancer-killing effect of combination therapy. With ALL, it was observed that increasingly intensive combination regimens improved clinical outcomes from low rates of remission and no cures to a high rate of cure. Remarkably, calculations to estimate the clinical efficacy of combination therapy were used in the 1960s by Emil Freireich and Emil Frei, as part of their development of the four-drug regimen VAMP – vincristine, doxorubicin hydrochloride (Adriamycin), methotrexate and prednisone – which they correctly predicted would provide the first cures of ALL. Based on clinical and experimental data, they described two calculations, one concerning interpatient heterogeneity and chance of remission [12.Frei E. et al.Studies of sequential and combination antimetabolite therapy in acute leukemia: 6-mercaptopurine and methotrexate.Blood. 1961; 18: 431-454Crossref Google Scholar], and one concerning intratumor heterogeneity and duration of remission [3.Frei E. Freireich E. Progress and perspectives in the chemotherapy of acute leukemia.in: Goldin A. Advances in Chemotherapy. Volume 2. Academic Press, 1965Crossref Google Scholar]. Their first calculation suggested that drug combinations would provide patients with multiple chances of complete response, since single drugs induced responses in a limited fraction of patients (where ‘complete response’ means no detectable amount of leukemia). When more than one drug was used, the fraction of patients whose leukemia responds to treatment would therefore increase even if no single patient benefited from more than one drug [2.László J. The Cure of Childhood Leukemia: Into the Age of Miracles. Rutgers University Press, 1995Google Scholar,12.Frei E. et al.Studies of sequential and combination antimetabolite therapy in acute leukemia: 6-mercaptopurine and methotrexate.Blood. 1961; 18: 431-454Crossref Google Scholar]. This was sufficient to explain the higher remission rates observed with two-drug combinations [15.Frei E. et al.The effectiveness of combinations of antileukemic agents in inducing and maintaining remission in children with acute leukemia.Blood. 1965; 26: 642-656Crossref PubMed Google Scholar]. However, increasing the chance of a response to one drug was not a sufficient basis for cure. Their second calculation concerned duration of remission and the prospects of complete eradication of leukemic cells within a single patient [3.Frei E. Freireich E. Progress and perspectives in the chemotherapy of acute leukemia.in: Goldin A. Advances in Chemotherapy. Volume 2. Academic Press, 1965Crossref Google Scholar]. Skipper et al. [16.Skipper H.E. et al.Experimental evaluation of potential anticancer agents. XIII. On the criteria and kinetics associated with “curability” of experimental leukemia.Cancer Chemother. Rep. 1964; 35: 1-111PubMed Google Scholar] had demonstrated in mouse models of leukemia that the duration of drug-induced remission was proportional to the logarithmic reduction in the number of leukemia cells (‘log-kills’). For example, killing 99.99% of cancer cells (4 log-kills) should produce a remission approximately twice as long as killing 99% (2 log-kills). Freireich and Frei applied this principle to clinically measured durations of remission from various chemotherapies. They sought to estimate the fraction of leukemic cells killed (and the fraction left alive) when a single drug produces a complete response. Next, informed by Lloyd Law’s experiments on combination chemotherapy in mouse models of leukemia [11.Law L.W. Effects of combinations of antileukemic agents on an acute lymphocytic leukemia of mice.Cancer Res. 1952; 12: 871-878PubMed Google Scholar], they hypothesized that the fraction of cancer cells surviving multiple drugs would be the product of the fractions that survive exposure to each of the drugs used individually. For example, if each of two drugs produced 3 log-kills (one in 103 cancer cells survive), then the combination of drugs is expected to produce 6 log-kills (one in 106 cancer cells survive). The disease burden in human leukemia was estimated to be ~1012 cells, based on counting the numbers of cancer cells in different organs. These calculations suggested that at least 12 log-kills would be required for treatment to eradicate cancer cells and achieve a cure [3.Frei E. Freireich E. Progress and perspectives in the chemotherapy of acute leukemia.in: Goldin A. Advances in Chemotherapy. Volume 2. Academic Press, 1965Crossref Google Scholar]. Based on these calculations, Freireich and Frei estimated that whereas two and three drug combinations were incapable of curing ALL, the four-drug VAMP regimen should be able to cure some patients. The VAMP regimen was famously controversial because of the near-lethality of a regimen involving simultaneous treatment of children with four toxic agents, but cures were ultimately observed in a fraction of patients with ALL [17.Freireich E.J. et al.Quadruple combination therapy (VAMP) for acute lymphocytic leukemia of childhood.Proc. Am. Assoc. Cancer Res. 1964; 5: 20Google Scholar], although many experienced relapse, often in the central nervous system. The landmark achievement of cures by VAMP had radical implications and raised the question of whether even more intensive combination regimens (including treatment of the brain) might deliver a higher cure rate. Motivated by the same logic as Frei and Freireich [18.Sides H. Childhood leukemia was practically untreatable until Dr Don Pinkel and St. Jude Hospital found a cure.47. Smithsonian Magazine, 2016: 108Google Scholar], this idea was pursued by Donald Pinkel with an approach that he named ‘total therapy’ [19.Pinkel D.P. et al.“Total therapy” of childhood acute lymphocytic leukemia.Pediatr. Res. 1971; 5: 408Crossref Google Scholar]:We said, “Let’s put it all together. Let’s attack the disease from different directions, all at once.” My hypothesis was that there were some leukemia cells that were sensitive to one drug and other cells that were sensitive to another. But if we use all these drugs at once and hit them along different pathways, we would permanently inhibit the development of resistant cells. Pinkel’s approach was so successful that his results were at first considered unbelievable by many oncologists. Ultimately, ‘total therapy’ became an ever-improving series of regimens which raised the 10-year survival for pediatric ALL patients from ~10% to over 90%, while also reducing toxicity to tolerable levels [20.Pui C.-H. Evans W.E. A 50-year journey to cure childhood acute lymphoblastic leukemia.Semin. Hematol. 2013; 50: 185-196Crossref PubMed Scopus (233) Google Scholar]. The quantitative principles developed by Bliss, Frei, Freireich, Law, and others provides a remarkably accurate description of trial results in pediatric ALL over the years 1948–1988, during which time patient outcomes improved from infrequent remissions to high rates of cure (defined as 10-year disease-free survival). What follows is a revival of Frei and Freireich’s calculations [3.Frei E. Freireich E. Progress and perspectives in the chemotherapy of acute leukemia.in: Goldin A. Advances in Chemotherapy. Volume 2. Academic Press, 1965Crossref Google Scholar], using the power of modern computation to describe response distributions in patient populations. This computation involves two parts. First, the fractions of cancer cells that resist multiple independently acting drugs is modeled as the product of the fraction of cells that resist each single drug; this is equivalent to addition of the log-kills achieved by each drug. Second, patients experience different magnitudes of response to individual drugs, due to intrinsic drug resistance; this can be described by drawing samples from single empirically determined drug response distributions. Such distributions can be obtained from early trials by the Acute Leukemia Group B (ALGB) that measured the distribution of remission times achieved by various single chemotherapies (Figure 1A ). As demonstrated by Skipper et al. [16.Skipper H.E. et al.Experimental evaluation of potential anticancer agents. XIII. On the criteria and kinetics associated with “curability” of experimental leukemia.Cancer Chemother. Rep. 1964; 35: 1-111PubMed Google Scholar], relapse occurs from the growth of cancer cells that survived treatment. Thus, response durations in ALL can be approximately modeled as being proportional to the log-kills achieved by a given course of therapy (Figure 1B) [3.Frei E. Freireich E. Progress and perspectives in the chemotherapy of acute leukemia.in: Goldin A. Advances in Chemotherapy. Volume 2. Academic Press, 1965Crossref Google Scholar]; note this idea is not universally true, as evidenced by the general failure of overall response rates to predict survival times in solid tumors. From this principle we can infer that the monotherapies used in early ALL regimens produced log-kill distributions that are approximately normal, having a median of ≈2 log-kills and a standard deviation of ≈2 log-kills. (Most survival distributions in oncology are close to log-normal [21.Plana D. et al.Cancer patient survival can be parametrized to improve trial precision and reveal time-dependent therapeutic effects.Nat. Commun. 2022; 13: 873Crossref PubMed Scopus (8) Google Scholar].) The ALGB’s ‘Protocol 2’ trial tested sequential monotherapy and observed no correlation between a patient’s response to their first and second therapies (Figure 1A); in our previously described formulation of independent action this corresponds to a correlation of zero [12.Frei E. et al.Studies of sequential and combination antimetabolite therapy in acute leukemia: 6-mercaptopurine and methotrexate.Blood. 1961; 18: 431-454Crossref Google Scholar]. Thus, a patient treated with n independently active chemotherapies can be modeled by drawing n responses from the observed distribution of log-kills, and adding them up (Figure 1C). This simple model lacks kinetic detail, instead approaching the problem by counting the proportion of leukemic cells that survive the full course of therapy. As described in the original calculations of Frei and Freireich, cure is presumed to require 12 or more log-kills, and a ‘complete response’ >3 log-kills (99.9% of leukemia cells killed) [3.Frei E. Freireich E. Progress and perspectives in the chemotherapy of acute leukemia.in: Goldin A. Advances in Chemotherapy. Volume 2. Academic Press, 1965Crossref Google Scholar]. When this model is used to estimate the proportion of pediatric ALL patients experiencing complete response or a cure when treated with different numbers of chemotherapies used in combination (Figure 1D), we find close agreement with clinically observed rates over a 40-year period (1948–1988) (Figure 1E) [1.Bast R.C. Holland-Frei Cancer Medicine.9th edition. Wiley Blackwell, 2009Google Scholar]. This analysis spans early trials of sequential monotherapy and two-drug combinations, the four-drug VAMP regimen that achieved the first cures, and subsequent progress to higher cure rates with Pinkel’s total therapy regimens. The match between model and data is striking given that the calculations omit many biologically and therapeutically important details, such as intrathecal chemotherapy and radiation to treat the brain and spinal cord, and the use of different drugs not all at once, but distributed across multiple phases of therapy (remission induction, consolidation, and maintenance). Thus, at a high level, these calculations provide a quantitative illustration of the value of classical concepts about the role of multiagent chemotherapy in addressing interpatient and intratumor heterogeneity. More specifically, the simulation’s workings provide two key insights. First, in a patient population exhibiting a typical level of heterogeneity in responses to monotherapy, ‘drug additivity’ represents a different sum of effects in every patient, such that the most efficacious drug differs by patient (Figure 1C). Second, synergistic drug interaction, or supra-additive activity in general, is not required to overcome tumor heterogeneity. Moreover, with reference to the diagram in Figure 1C, supra-additive activity – if it can be achieved in some cases – is likely to be an enhancement of only one of the multiple arrows contributing to overall activity. Indeed, supra-additive efficacy was never a rationale for the design of these regimens, and their clinical efficacy does not demonstrate it. Instead, the simulation shows that the additive effect of individually potent drugs is a quantitatively sufficient basis for the progressive development of curative therapies. These ideas have conceptual and practical value in the design of contemporary combination therapies and clinical trials [22.Chen C. et al.Independent drug action and its statistical implications for development of combination therapies.Contemp. Clin. Trials. 2020; 98106126Crossref Scopus (8) Google Scholar]. In particular, interpatient variation in response to drugs within combinations has significance for precision oncology, as reviewed in Plana et al. [23.Plana D. et al.Independent drug action in combination therapy: implications for precision oncology.Cancer Discov. 2022; 12: 606-624Crossref PubMed Scopus (37) Google Scholar]. In solid tumors, responsiveness to single agents is generally less frequent than in liquid tumors, and drug additivity within a patient is less impactful. Instead, combination therapy in these cases appears to rely on what we refer to here as Frei independence. Thus, patients with solid tumors are likely to receive one or more drugs that are ineffective against their tumors. Were reliable pretreatment biomarkers of sensitivity or on-treatment pharmacodynamic assays available for more drugs, then inactive agents could be omitted for specific patients to reduce toxicity without compromising therapeutic efficacy. A tangible demonstration of this principle was recently provided for combination chemoimmunotherapy for gastric cancer [24.Zhao J.J. et al.Low programmed death-ligand 1-expressing subgroup outcomes of first-line immune checkpoint inhibitors in gastric or esophageal adenocarcinoma.J. Clin. Oncol. 2022; 40: 392-402Crossref PubMed Scopus (51) Google Scholar]. The case study of pediatric ALL demonstrates that three different manifestations of independent drug action are relevant to thinking about combination chemotherapy; these originate with Bliss, Law, and Frei. They are not competing theories (in contrast to Loewe additivity versus Bliss independence [25.Berenbaum M.C. What is synergy?.Pharmacol. Rev. 1989; 41: 93-141PubMed Google Scholar]), but rather they describe distinct phenomena occurring at different biological scales that can be applied simultaneously to understanding the impact of tumor heterogeneity on drug response. These principles share a common mathematical basis in the addition law of probability (Figure 2A ), which is that the probability that either of two events (A and B) will occur is:PAorB=PA+PB–PAandB[1] This simply states that the probability that either event A or event B occurs (which includes A and B both happening) is the sum of their individual probabilities, minus the probability that both events occur (otherwise this would be counted twice). If events A and B are uncorrelated, PA and B = PA x PB and the equation can be rearranged to read:PAorB=PA+PB1–PA[2] However, if events A and B are correlated, PA and B is greater than PA × PB and the overall benefit is therefore less. In the case of chemotherapy, correlations in response arise from partial or complete cross-resistance between drugs, and it is therefore logical that the benefit of combining drugs will be less. The Bliss independence model applies to the probability of cell death and describes how combinations of therapies kill a larger fraction of cancer cells. This applies even before explicit consideration of heritable intratumor heterogeneity, which is the purview of Law’s independence model. Chester Bliss’s research on combinations of chemical agents predated cancer chemotherapy and concerned insecticides. Bliss used the addition law to analyze the proportion of animals killed by multiple toxins, and his versatile theory has been widely applied to analyzing the proportion of cancer cells killed by cytotoxic drugs or bacteria killed by antibiotics (Figure 2B). Bliss’s 1939 article [7.Bliss C.I. The toxicity of poisons applied jointly.Ann. Appl. Biol. 1939; 26: 585-615Crossref Scopus (1593) Google Scholar] actually described three different models of ‘joint action’ of which the widely used concept of ‘Bliss independence’ is only one. The ‘independent joint action’ model postulated that, when two toxins cause death in distinct ways, and have no correlation in susceptibility (thus P(A and B) = PA × PB), the proportion of individuals killed by the combination of toxins is:PCombination=PA+PB1–PA[3] where PA and PB are the proportion of individuals killed by single therapies (this is the simplest case of the addition law). Bliss also considered the case of correlated susceptibility, such that some individuals are more resistant to both agents, and some more sensitive to both. With a correlation in drug sensitivity equal to ρ, the expected combination effect is:PCombination=PA+1–PA×PB×1–ρ[4] where PA is the larger of the two probabilities (A is more cytotoxic). When applied to killing cancer cells, Bliss independence is one generally accepted definition of ‘drug additivity’ [25.Berenbaum M.C. What is synergy?.Pharmacol. Rev. 1989; 41: 93-141PubMed Google Scholar,26.Roell K.R. et al.An introduction to terminology and methodology of chemical synergy – perspectives from across disciplines.Front. Pharmacol. 2017; 8: 158Crossref PubMed Scopus (156) Google Scholar] such that 90% killing by drug A plus 90% killing by drug B = 99% killing by the combination. When cytotoxicity is quantified as log-kills, or reduction in the logarithm of tumor cell number, Bliss independence corresponds to the addition of effects (e.g., 1 + 1 log-kills = 2 log-kills). If cytotoxicity is greater than expected by Bliss independence, this satisfies a quantitative definition of synergistic drug interaction, and is evidence that one or more drugs has become more effective in combination [25.Berenbaum M.C. What is synergy?.Pharmacol. Rev. 1989; 41: 93-141PubMed Google Scholar]. Quantitative evidence of synergy – an effect that is ‘more than the sum of its parts’ – implies some mechanism of positive drug–drug interaction. Mechanisms of synergistic drug interaction are so diverse as to defy categorization, but the general outcome is that one drug enhances the effect of another [25.Berenbaum M.C. What is synergy?.Pharmacol. Rev. 1989; 41: 93-141PubMed Google Scholar]. However, synergy, in the rigorous meaning of positive drug–drug interaction, is not synonymous with efficacy, nor alone sufficient to make a clinically effective regimen. A consequence of Bliss independence is that combining ‘weak’ drugs (small log-kills) is expected to provide small benefit, and combining ‘strong’ drugs is expected to provide large benefit. For example, if two uncorrelated therapies individually produce 50% kill, their combination is expected to produce 75% kill (the surviving fraction drops from 50% to 25%, so tumor reduction is twofold greater than monotherapy). If the combination exceeded an additive effect and achieved 90% kill it would be classified as synergistic (the surviving fraction drops from 50% to 10%, so tumor reduction is fivefold greater than monotherapy). However, consider a different pair of more active therapies that individually produce 99% kill; an additive combination effect would result in 99.99% kill (from 1% to 0.01% survival is a 100-fold greater tumor reduction than monotherapy). This illustrates that a co