The rationale of dose–response curves in selecting cancer drug dosing

Abstract

Drug development for cancer chemotherapy has an interesting history. A mix of serendipity, animal, cell line, and standard pharmacological principles of dose, dose‐response, dose‐concentration, dose intensity and combination therapies have been used to develop optimal dosing schedules. However in practice, significant gaps in the translation of preclinical to clinical dosing schedules persist, and clinical development has instead moved to new drug development. A older chemotherapies are still the backbone of most solid tumour schedules, therapeutic drug monitoring has emerged as a method for optimising the dose for individual patients.

1. BACKGROUND

The development of dose scheduling in chemotherapy goes back over 100 years, from early work in infectious diseases and antibiotic development to the development of animal models with transplantable tumour systems. Although dichloroethylsulfide (mustard gas) was used experimentally both topically and intratumourally prior to the 1930s, the origins of routine human use of alkylating chemotherapy derives from the observant pharmacological skills of Goodman and Gilman. These noted from the medical records that soldiers exposed to mustard gas in either World War I or II had lymphopenia and hypothesised that mustard gas might also therefore kill malignant lymphoid cells. After mouse experiments, trials on a human of a second‐generation nitrogen mustard termed synthetic lymphocidal chemical occurred in 1942.1

The positive clinical response from this human study led to the clinical development of the first chemotherapeutic agent for clinical use,2 and subsequent synthesis and testing of several related alkylating molecules such as cyclophosphamide and chlorambucil. Around the same time, hormonal therapy in prostate cancer was seen to decrease acid phosphatase concentrations,3 a known correlate of tumour size and activity, and the effects of folate deficiency on haematological maturation were being acknowledged. Subsequently, antifolate compounds in leukaemic children were trialled and in 1948 published data showing remissions.4 Thiopurine discovery followed and the subsequent fluorine attachment to the 5‐position of the uracil pyrimidine base enabled synthesis of the fluoropyrimidines, still the backbone of many epithelial cancer treatments. The use of plant alkaloids in solid and haematological tumours, and discovery of the activity of procarbazine for Hodgkin's disease occurred in the late 1950s.

However, despite this blossoming of new cancer treatments and apparent tumour regression, overall survival did not appear to improve significantly for most epithelial cancers using chemotherapy alone. Clinicians noted that although new agents were being developed, there was a lack of focus on the dose, on the synergistic effect of combination therapies (including with radiation therapy) and the dosing regimen, although mathematical biologists were experimenting with animals on such observations to predict dosing regimens to improve survival. For example, in 1956, Goldin et al. noted that chemotherapy for in vivo transplanted tumours induced cell death inversely proportional to the volume of tumour.5 Skipper later (1978) confirmed this in experimental in vivo limb systems where the primary limb tumour was amputated, and the cure rate often significantly increased with the use of chemotherapy.6 Skipper et al.'s earlier predictions (1964) based on the work of Goldin had shown that a given dose of cytotoxin killed a constant fraction (not number) of tumour cells, and he therefore proposed that chemotherapy success would depend on the number of cells present at the beginning of each treatment.7 His in vitro work was used to cure L1210 (a genetically homogenous mouse leukaemic cell line), suggesting that eradication of every tumour cell could be considered, and more aggressive and frequent use of chemotherapy in humans. This idea was supported by animal data showing that the relationship between drug dose and fractional tumour cytoreduction was linear for several alkylating agents in an in vivo murine lymphoma model and other cell lines.8

However, the assumed translation of the steep and nonplateauing dose–response curve seen in animals to humans would require that increased numbers of cancer cells were consistently killed when drug doses were increased. This is different to other therapeutics where a sigmoidal dose–response relationship is the norm, with a linear relationship between dose and response over a range of drug doses and a response plateau at higher doses.9 In fact, although seen in cell lines and a mouse lymphoma model, albeit in alkylating agents, there is overall a paucity of animal studies showing the existence of a steep and persistent dose–response relationship for the majority of the chemotherapy agents used in human solid tumours, particularly those commonly used at high dose as conditioning agents (reviewed in8, 10). As a specific example, preclinical studies have failed to show a log‐linear dose–response relationship over a broad range of doses in solid tumours for mitoxantrone, paclitaxel, topotecan and vinblastine; however, many of these were chosen for use in the initial high dose therapy in solid tumour studies in the 1990s, such as the then ground‐breaking Scandinavian Breast Cancer Study Group 9401.11 In humans, it appears therefore that an initial proportional tumour cell kill with dose increments is followed by a kill‐plateau as doses are further increased (reviewed in12).

It is noted that some of the clinical difficulties in knowing how to translate information from cell culture to preclinical models to animal and then human studies is the apparent interchangeable use of the term dose when the original paper describes log‐dose, dose is sometimes reported as mg per unit size or as an actual amount, as a cumulative (particularly in human studies) or a single dose. Response in earlier preclinical work usually documents cell kill, but maybe log‐cell kill. Further, in animals, response appears to be related to reduction in tumour size. Whilst this response surrogate is also measured in human response endpoints, as seen in the use of response evaluation criteria in solid tumours, as an endpoint in clinical trials, overall survival and progression‐free survival are used for registration and reimbursement purposes, based on the fact that a smaller tumour may be harbouring multidrug‐resistant mutations.13 This temporal change in the use and definition of terms behoves a consideration of the original definitions when translating basic research into human drug development.

2. COMBINATION STUDIES AND HIGH VS LOW DOSE

In spite of the lack of preclinical evidence for steep dose–response relationships with some alkylating agents, combination cytotoxicity of certain drug combinations, chosen because of complementary mechanisms of action did achieve steep dose–response relationships in a variety of cultured and implanted animal tumours including solid tumours (including thiotepa and cyclophosphamide, cyclophosphamide plus nitrosourea or melphalan, and melphalan plus nitrosourea combinations).14

In humans, however, little improvement was seen in overall survival in a variety of human epithelial tumours with either increased dose, or combination therapies. For example, in a study of high dose combination therapy and conventional combination therapy for metastatic breast cancer15 there was no significant benefit of high dose therapy over standard therapy in overall or progression‐free survival. The final report of the CALGB 9082 Study16 also in breast cancer (high risk) found similar results in patients randomised to high‐dose combination therapy vs an intermediate dose regimen as did the Scandinavian Breast Cancer Study Group 9401.11 Overall, high‐dose therapy may not offer any additional survival benefit compared to conventional therapy, in fact in the long‐term follow‐up, there may be worse survival, at least for breast cancer. It should be noted that the high dose combination regimens in these studies included cytotoxic therapies (etoposide, mitoxantrone, carboplatin and cisplatin) where a steep dose–response relationship, albeit in single drugs, over a wide concentration range in human tumours had not been established.12

3. MAXIMUM TOLERATED AND METRONOMIC DOSING

A development of the log‐kill hypothesis was to design drug regimens to kill as many tumour cells as possible, by treating with the maximum tolerated doses (MTDs) of these cytotoxic agents. Toxicity entailed reducing the dose for the next cycle. However, significant and persisting adverse effects e.g. cardiac, skin and neurotoxicity and various injury to proliferating cells in healthy tissues were beginning to be seen. Episodic dosing schedules were then developed, with application of the chemotherapy at or near MTD followed by intervals to allow nonmalignant tissues such as the bone marrow to recover. Although such chemotherapy regimens initially often appeared to diminish tumour or impede growth, relapses often appeared aggressive and treatment resistant, probably due to mutations in DNA and mismatch repair genes.13 It is therefore noted that the translation of effect, or response, starts to include not just cell death but tumour size, growth rate, relapse rate, drug resistance and the variety of organ toxicities.

Awareness that solid tumours display heterogeneous biology, that cancer cells are in various phases of the cell cycle during treatment and that tumour growth rate decreases as they increase in size resulted in a paradigm shift in dosing, from the log‐kill and MTD practice, dictating spaced out but high dose chemotherapy, to de‐intensified dosing. However, toxicity remained a significant cause of morbidity. This toxicity concern was the likely experimental basis for the choice of the majority of regimens used in the high dose chemotherapy treatments for solid tumours. Whether this choice was the cause of the lack of comparative efficacy seen in high‐dose studies in solid tumours remains unclear.17

The dosing literature and clinical practice subsequently followed the metronomic dosing chemotherapy concept whereby frequent but low dose chemotherapy was given. This concept was based on the biology of noncancer cell factors that appeared to support tumour growth, such as inhibition of aspects of tumour growth assumed to be angiogenesis‐dependent. The angiogenesis hypothesis specifically was supported by 2 older preclinical studies (reviewed in18). These both suggested a potentially synergistic strategy of rescheduling the administration of chemotherapy drugs dosed at well below the MTD, metronomically (either continuous infusion or frequent administration without extended rest periods) rather than episodically in order to concurrently target tumour endothelial cells. The metronomic method aimed to target the more slowly proliferating tumour endothelial cells and attenuate their apparent capability to repair and recover during the off‐treatment periods. Preclinically, metronomic (once every 6 days) dosing of cyclophosphamide significantly impaired tumour growth compared to conventional MTD.18

This metronomic dosing schedule has more recently moved into other dosing concepts, including an adaptive therapy concept where varying doses and schedules of chemotherapy are given based on patient response or tolerability (reviewed in19). Further, computer driven, genetic supported, covariate‐ or plasma exposure‐based chemotherapy has been considered as a potential therapeutic option to improve personalisation of cancer drug choice and dose, subject to clinical trial and evidence‐based testing. However, dosing in such ways is not always evidence based and therefore sometimes off guidelines. Off‐guideline dosing can leave oncologists vulnerable to perceived concerns about under or overdosing.20

More recently, we have witnessed the explosion of new cancer chemotherapies, synthesised against a tumour expressed gene or against an immune cell receptor. Interestingly these new drugs tend to be marketed as a single flat dose (as with the small molecules and with the immune therapies); others such as monoclonal antibodies (e.g. trastuzumab) have been marketed as a mg/kg dose. Many other current cancer therapies, if not a flat dose, are often dosed as a mg/m² of body surface area (BSA). Based on what we know about the difference in pharmacokinetic parameters across populations, dosing on these rules appears to be too variable to ensure that the patient is getting the optimal dose for them, for their tumour biology and for the anatomical disposition of the malignancy. Further concerns about this dosing are raised when it becomes apparent that data have been extrapolated from experimental to clinical setting, or from blood to solid tumours, or from response to actual clinical improvement or toxicity, from primary tumour response to how a tumour would respond at relapse. Therefore, the current practices raise concerns around the pharmacological assumptions of dosing chemotherapy, particularly the evidence behind dose–response.

The pharmacological assumptions underlying current practice in chemotherapeutic dosing, particularly regarding dose–response relationships, are therefore founded upon evidence of uncertain clinical relevance.

4. DOSE INTENSITY

The principles of dosing based on dose intensity are derived from in vitro studies in experimental homogenous tumour cell lines, animal xenograft models, and mathematical modelling of the tumour response. However, in humans we have to include extra variables such as dose, frequency, route and rate of administration.

As discussed, the classic experiments of Skipper7 using tumour models/cell lines show that some cytotoxic agents have a steep dose–response curve; and a logarithmic relationship between drug dose and percentage tumour cell death. However, most human tumours, or at least parts of the heterogenous solid tumours, do not follow such first‐order kinetics, and the rate may depend on the organ involved, the blood supply, cell type and location kinetics, which are also variable at different cell density. Further, solid tumours are heterogenous, not homogenous. Post‐Skipper, human tumour growth was then modelled by a version of Gompertzian kinetics—where both the proportion of cells killed, and tumour regrowth is greater when there is a low cell number.

Clinically, in the 1960s and early 1970s, it became apparent that there were relationships between delayed or incomplete doses and suboptimal outcome. Animal tumour models also illustrated effects of dosage reduction relevant to the clinical effects of suboptimal dose intensity and cure rates.

Hryniuk and Bush then defined a new concept of dose intensity as the amount of drug delivered per unit of time (mg/m²/week) and applied it retrospectively to show a clear relationship between dose intensity and outcome in patients with breast cancer.21 Dose intensity was subsequently shown to correlate with outcome in prospective clinical studies in various tumour types, including breast and ovarian, acute myeloid leukaemia (AML) and in multiple retrospective studies (reviewed in22). In the classic and well cited study of Bonadonna (1976), breast cancer patients received cyclophosphamide, methotrexate and 5‐fluorouracil. Dose reduction was used routinely in the case of toxicity or for older patients. Over a 20‐year follow‐up, patients receiving <85% of the intended dose had a poorer survival.

Other studies subsequently demonstrated that dose intense chemotherapy improves the outcome of patients with AML, multiple myeloma, and relapsed non‐Hodgkin's lymphoma although conflicting results were seen in solid tumours (reviewed in,23 discussed above). More recently, although the majority of studies had shown a slightly higher numerical response rate for the dose intense arm vs the conventional arm, in a large node‐positive breast cancer study,24 2305 women randomised to dose‐escalated or dose‐intensified cyclophosphamide plus doxorubicin arms showed no statistically significant differences in disease‐free or overall survival between dose intense regimens and conventional therapy up to 5 years of follow‐up. This work shows the importance of using actual clinical endpoints such as toxicity and efficacy to measure the impact of a new dosing regimen.

Similarly, although work with the earlier Ridgeway osteosarcoma models showed worse outcomes with reduced dose intensity,25 some of the human studies based on these models could not demonstrate that higher dose intensities correlated with better outcomes.26 Whether less than normal dose intensity and worse outcomes is a different issue than the fact that supra‐normal dose intensity does not increase survival is of interest. This is supported by the high dose therapy trial data from the breast and other tumours which also failed to show increased survival.

Hryniuk and Levine22 subsequently proposed the relative dose intensity (RDI) concept—the amount of drug administered per unit of time expressed as the fraction of that used in the standard regimen. However, concern arose over using RDI alone as a measure of therapy adequacy, over drug dose, specifically around the ability (or benefit) from equal weighting of different drugs in the chemotherapy regimen, the lack of focus on importance of schedule and assumptions that drug doses with different mechanisms of action combine to give linear increases in percentage of tumour cell death.

5. CLINICAL PHARMACOLOGY AND BSA

It is interesting to recall that BSA was only introduced into oncology to guide safe starting doses for phase I studies from preclinical animal toxicology data. It is “not clear as to why dosing by BSA was extended to the routine dosing of antineoplastic agents”.27 It has long been recognised that dose calculation for chemotherapy using BSA can be variable due to significant interpatient variation in pharmacokinetics leading to differences in toxicity and efficacy (summarised in28). However, it is the standard dosing method, despite the fact that there can be up to a 10‐fold variation in the clearance of cancer chemotherapy due to, for example, up to 50‐ fold difference in CYP3A activity and eight‐fold variation of activity in dihydropyrimidine dehydrogenase, the enzyme that inactivates 5FU, along with variation in drug resistance genes and other efflux pumps, reviewed in.29 In addition to genetics, other factors include variation in renal function, important for the many drugs that are, in part, renally cleared, e.g. with methotrexate.

Hepatic and renal function, body size and composition disproportionate to estimated BSA (e.g. obesity, sarcopenia), age, sex, coadministered drugs, food and recreational drugs are also important for relative clearance of other drugs. Little of this is accounted for when BSA alone is used to calculate drug dose leading to large interpatient variation in plasma concentration and response.28 The likelihood of implementing individualised dosing recommendations for therapies is affected by many key factors. These include historical factors, where dosing has always been done in a specific way and change is not perceived to be helpful or even possible in some cases; the costs of research and drug development, which often do not include analysis of drug behaviour in specific population groups; the fact that it is often more simple for industry to market a single dose of a drug than an algorithm based on BSA or drug exposure; and the cost and difficulties of setting up, validating and funding assays for pharmacokinetic analysis.

6. CLINICAL PHARMACOLOGY AND FLAT DOSING

The preference for flat dosing, one dose fits all, and the resultant significant toxicity, poor compliance and lack of efficacy seen in some patient groups30 merits closer scrutiny.

As discussed by Ferner et al. in this issue of the Journal,31 factors contributing to observed pharmacological variability when dosing in oncology (as they do for other therapeutic areas) should include obesity, genetic variants, age, hepatic and renal function, smoking, alcohol and coadministered drugs. Diet is a long‐recognised variable,32 for example, some diets increase exposure of oral tyrosine kinase inhibitors by more than double. This variability is of clinical concern, particularly as these factors affect the dose–exposure relationship and as for most therapies there are clearer relationships between exposure and outcomes than dose and outcomes.

7. DOSE–RESPONSE RELATIONSHIPS IN CANCER CHEMOTHERAPY

By its very nature, efficacy dose–response for most drugs eventually plateau. The dose causing 50% of maximum effect (ED50) is often chosen as the start dose for many therapeutics, as is it on the steep part of the sigmoid shaped dose–response curve. Even when manufacturer dose–response work provides an estimate of a population ED50 for a particular cytotoxic agent, this provides only a guide to starting dosage, which should be adjusted to the factors outlined above.

Further, variation between individual ED50 depends on body composition, pharmacokinetics and pharmacodynamics, along with drug interactions and their effects on different outcomes, all difficult to ascertain with each patient. Importantly also, dose finding studies and hence dosage guidelines are often based on surrogate measures such as reduction in tumour size rather than major long‐term outcomes such as mortality or quality of life.

This raises the issue of being clear around the specific outcome the treatment is aiming for and how the literature to date addresses this. What is the outcome of interest for the patient specifically—is it cure, tumour response or morbidity benefit, for example? What is the dose–response for toxicity, all clinical efficacy outcomes or lethality? On what endpoint is ED50 best based? Endpoints can include surrogate measure such as reduction in tumour size, human efficacy or human equivalent dose taken from animal data, and how does the ED50 change in combination therapy or with concomitant radiation?

Dose–response may also be affected by tumour cell heterogeneity.33 Apart from molecular characteristics, tumour factors such as tumour cell kinetics, tumour size, and duration of tumour growth, and drug features such as dose, schedule and delivery are all likely to contribute to varying extent to determine the outcome of a particular treatment. This makes the whole area of how to predict the best dose for an individual patient very complex. Some centres have used therapeutic drug monitoring, where there is a verified relationship between plasma concentration and cancer outcome.33 Others have used specimens obtained from cancer patients at surgical resection; however, the correlation between in vivo drug levels and human cancer response has been little studied. Despite extensive study in drug development, correlation of individual dose to drug sensitivity, resistance and patient survival is complicated due to many confounding factors and not commonly considered for an individual patient in practice.

One more common issue confusing the dose–response area in chemotherapy is the effects on the immune system of chemotherapy. Significant immune toxicity has been seen with radiation therapy to patients also having standard (i.e. mg/kg) doses of checkpoint inhibitor therapy. Significant toxicity has been reported in patients with human immunodeficiency virus on standard doses of chemotherapy for non‐Hodgkin's lymphoma,34 although this work has been criticised as ignoring the function of the immune system and the power to detect outcome differences.35 Although the latter toxicity may have been a consequence of high drug exposure (possibly from CYP3A4 drug interactions of the human immunodeficiency virus and other required therapies), identified by the concomitant haematological toxicity, additional immune factors might be involved, and excessive dose is likely to affect functions of various immune cells. Similarly, retrospective studies of bowel cancer patients with toxicity,36 known to be associated with high drug concentrations, but similar efficacy outcomes despite dose reduction would be consistent with a drug exposure theory.

8. DISCUSSION

There are clear historical reasons for dosing in cancer, particularly that derived from animal and in vitro work. It appears that experimental dose–response curves are available for some responses, from which ED50 could be estimated to help guide practitioners. However, dose–response is complex, particularly when moving from homogenous cells to heterogeneous tumours whose biology changes over time. The issues of comparative efficacy and toxicity of the combination, acquired drugs resistance stage of disease, type of tumour and anatomical locations need to be considered.

Further issues around interpreting older dose–response curves of single agents are that in the combinations some doses of individual drugs may well need to be higher than ED50 e.g. doxorubicin. Dose intensity and RDI are important for outcomes, although increasing dose intensity supranormally does not improve outcomes further in solid tumours based on the data to date.

While preclinical models do not accurately predict clinical outcome, it may still be useful to employ such models to select agents that display a relationship between dose and desired response over a wide range of achievable concentrations in the target tumours. Further, response to immune therapies may be related to complex additional factors and a signal or information relating to this may be seen in the animal model, particularly around toxicity and immune effects.

9. FUTURE DIRECTIONS

From first principles, and confirmed by the early pharmacology work above, it appears likely that neither a weight‐based metric nor a body surface metric should correlate well with tissue concentrations, with both methods likely to give a different exposure and therefore a different dosing recommendation. The difference in exposure can be understood in terms of the lean/fat ratio and the drug's distribution, influenced by drug physicochemical properties such as the log P value and drug penetration of the tumour and blood brain barrier permeability (reviewed in37). A commonly used pharmacological methodology—therapeutic drug monitoring (TDM) whereby actual concentrations are measured, as a surrogate of the tissue concentration can overcome the known and unknown factors and degree of effect contributing to observed pharmacological variability when dosing chemotherapy. For example, TDM takes into account hepatic and renal function, dose, obesity, genetics, age, diet, smoking, alcohol and drugs, sex, coadministered drugs, and other factors that affect plasma concentration, and it is often the concentration (rather than dose) that is associated with clinical outcomes. Even minor changes in organ function, or addition/removal of a drug can change the concentrations, altering dose to a target concentration can therefore provide more individualised dosing recommendations. This is particularly relevant as the use of the therapies move from a relatively homogenous non‐comorbid middle‐aged population to using the drug in the elderly, or in children and adolescents.38 Although there is usually little knowledge on the exact relationship between plasma and tumour concentrations of drug for a patient, especially over time, data suggest that, for many therapies, plasma exposure is a better surrogate for outcome than just dosing.39

It is, however, a surprise that as we increasingly acknowledge the PK variability in populations, doses with the same amount of drug that dosing recommendations from the pharmaceutical industry adopted by regulators favour flat dosing and TDM is not mentioned.

Although tumour cell heterogeneity may also affect response to dose, intense regimens and knowledge of cancer biology and heterogeneity, greater knowledge on the weighting of these complex factors could lead to a more personalised method of treatment. Gene testing of tumours at diagnosis to predict drug is therefore unlikely to help predict drug response in later disease and ignores the crucial aspect of dose and dose–response, particularly if a target concentration is needed.

Before employing therapies, thorough review of earlier registration data and evidence on which dosing is based, including the definitions of dose, and response are important. Transparent process and incentives are key to ensuring appropriate basic and clinical pharmacology are in place for all new therapies, in particular evidence‐based recommendations on dosing to support marketing, counter detailing and education and training of prescribers and regulators.

COMPETING INTERESTS

J.M. gave expert clinical pharmacology testimony to the New South Wales Government Inquiry into off‐protocol prescribing of chemotherapy in NSW in 2016 (https://www.parliament.nsw.gov.au/lcdocs/submissions/56585/0050%20Professor%20S%20Ackland%20and%20Professor%20J%20Martin,%20University%20of%20Newcastle.pdf). J.M. was a member of the NSW Health Inquiry into Cancer Dosing in NSW led by the Cancer Institute https://www.health.nsw.gov.au/patients/cancertreatment/Documents/section‐122‐final‐report.pdf. J.M. is the Director of the 2018–2023 Cancer Council NSW Program Grant ‐ The PREDICT programme in cancer pharmacology (2018–2023) – PW18–01.

Martin JH, Dimmitt S. The rationale of dose–response curves in selecting cancer drug dosing. Br J Clin Pharmacol. 2019; 85: 2198–2204. 10.1111/bcp.13979