Translating the dose response into risk and benefit

Abstract

When choosing a medicine two aspects determine the balance between benefit and harm (risk–benefit), matching the medicine to the individual and the choice of dose. Knowing the relationship between dose and response allows a calculation of the dose that causes 50% of the maximal effect, the ED₅₀. Rational drug dosing depends on defining the ratio of the dose to the ED₅₀. The ED₅₀ of each drug has two scales, whether the effect measured is for efficacy, or safety. Quantifying efficacy is comparatively straightforward. A fall in blood pressure, combined with a statistical and clinically significant reduction in cardiovascular events, might justify the efficacy of an antihypertensive. Measuring a drug's effect on safety is more complex, as this is so often a subjective assessment of a collection of adverse events. Though a science‐based therapeutic window defined from in vitro efficacy and safety dose response curves is reassuring, this review discusses how to translate this into dose‐dependent risk–benefit based on clinical trial data. Some of the limitations of our knowledge about the choice of dose that optimizes an individual's risk–benefit, or whether no drug is a better option, are discussed. It is important to define these limitations when educating the consumer/patient about the clinical pharmacology that justifies their treatment dose options.

1. INTRODUCTION

In this issue we discuss the clinical pharmacology behind the choice of dose, based on a British Pharmacology Society Symposium held in December 2018.

The sigmoid dose–response curve is a foundation of pharmacology. The in vitro logarithmic interaction between a drug and its receptor conforms reassuringly to the law of mass action. The half‐maximal point of the curve, the effective dose‐50%, or ED₅₀, can predict the likely effective tissue concentration and dose needed when the drug is given in vivo.

Translating bench‐derived neat curves into a favourable risk–benefit loses precision as the phases of clinical development progress. Often questions remain whether the morbidity, or even mortality, associated with the treatment are less than those of the disease. Whether a better choice of dose would improve clinical outcome can only be addressed by the availability of sufficient dose‐dependent efficacy and safety data.

The aim of any medicine is to deliver the optimal active drug concentration to the therapeutic target, taking into account individual variability, a central tenet of pharmacokinetics. Pharmacokinetic data aid the choice of doses that enable the benefit to the patient to be defined in clinical trials. This is balanced against the complex assessment of safety. Drug safety is handicapped in multiple ways: the lack of predefined endpoints, the lack of predefined statistical analyses, descriptive summaries of data sets, a dearth of composite safety endpoints, or an imbalance in the weighting of safety and efficacy signals. These points are discussed further in relation to the information available to guide the consumer/patient in their choice of treatment dose.

2. THE DOSE–RESPONSE CURVE

2.1. Types of curve

The sigmoid dose–response curve describes the pharmacology of antagonists, inhibitors or blockers. With an agonist some pharmacodynamic effects plateau, whereas others do not at the highest clinical doses. Constriction of the pupil by an opioid will plateau with dose, whereas respiratory depression with the same drug will not. A pure beta 1 blocker acting as an antagonist cannot reduce heart rate more than a sympathectomy and plateaus at higher doses. In contrast, a sympathomimetic drug, acting as an agonist, increases heart rate with increasing dose until fatal, with no plateau in the response. Both efficacy and safety pharmacology can arise from either antagonism or agonism. These may also be mixed, such as one side effect caused by blocking an enzyme and another by stimulating a receptor.

2.2. Therapeutic window

Illustrating the therapeutic window by plotting two curves, of efficacy as Effect A and safety as Effect B, with effect on the vertical axis against log dose on the horizontal axis, puts opposing outcomes on the same Y‐axis scale. Restricting efficacy to the positive scale above the horizontal axis and re‐plotting harm in the opposite direction below the X‐axis, as negative benefit, allows the integration of the efficacy and safety curves, generating a single curve to summarize net risk–benefit. Such an integration is only possible if the Effects A and B can be weighed on the same scale. Mortality data can summarize risk–benefit as a single line. This can be flat with no effect, reduced or increased. There is no therapeutic window, unless mortality is reduced with lower doses and increased with higher doses to give a U‐shaped curve. For most drugs we do not know the optimal dose for survival benefit, even if this is the primary objective of treatment. There is no commonly used drug where sufficient clinical data are available to plot a curve of the effect of dose on mortality.

2.3. The complexity of the plot of safety

Efficacy in clinical trials is usually measured as a single primary endpoint. This can be a pharmacodynamic marker, such as blood pressure, cholesterol, HbA1c, spirometry or viral load that are considered biomarkers of clinical outcome. When a drug improves multiple aspects of a disease, or condition, such as a range of psychiatric symptoms, statistically insignificant individual benefits can be combined into a single composite endpoint that shows statistical significance. In contrast, the safety assessment is usually a soup of minor signals that are individually not significant yet are insufficient evidence that potential risk is outweighed by the benefit.1 The plot of safety against dose is no longer a single curve, more a collection of adverse events with a small proportion of patients associated with each event classification category. This prevents the evaluation of risk–benefit on one scale.

3. RISK–BENEFIT ON ONE SCALE

For most drugs, single scales of risk–benefit are not an option. Some exceptions are discussed below, where a single mechanism may underlie both efficacy and safety.

3.1. Coagulation

For anti‐coagulants and pro‐coagulants, risk–benefit depends mainly on the coagulation scale. Inhibition of coagulation reduces the incidence of thrombosis at the cost of an increased risk of haemorrhage. The therapeutic window for anti‐coagulants defines doses that maximize the prevention of thromboembolic events while minimizing the incidence of haemorrhage, though what severity grade of thrombosis is equivalent to a minor or major haemorrhage is arbitrary. Heparin can reduce the risk of thrombosis postoperatively for a patient who has been co‐administered aprotinin, a pro‐coagulant with the opposite effect on coagulation. Only a summary of risk–benefit using a single coagulation scale will determine if a combination of heparin and aprotinin can ever be justified. Even small numbers of deaths will add to the validity of this approach, particularly the strength of the evidence for an absence of harm as a confidence interval around the number of deaths observed, allowing a calculation of the potential magnitude of harm.

3.2. Vasoconstriction

A topical alpha agonist spray for nasal congestion is another example of a single scale being useful, in this case vasoconstriction. The therapeutic window is defined by the drug's pharmacokinetic distribution; the concentration in the nose should be high enough to vasoconstrict locally, whereas the systemic concentration should be low enough not to be detrimental to blood pressure.

3.3. Mortality

The ultimate endpoint for risk–benefit assessment is mortality; the patient is entitled to ask whether they are more likely to die of the disease or the treatment. Such information is rarely available. Aspirin, in use for over a century, is a good example as it still attracts debate on potential survival benefit.2 Whether another old drug, paracetamol (acetaminophen), can inhibit cyclooxygenase‐2 sufficiently to increase cardiovascular mortality is not clear.3 Metformin, introduced in the 1950s and now widely used as first line treatment for type‐2 diabetes, has a better survival profile than sulphonylureas, though it is still debated whether it reduces mortality.4, 5, 6, 7, 8 How the significant increase in mortality with typical and atypical antipsychotics should be considered against their benefit is difficult to assess.9, 10

Adequately powered mortality trials are usually thought to be too costly as they require large populations, unless the mortality rate is high enough during the trial to sufficiently power a smaller trial. This view was not accepted in the past when the International Studies of Infarct Survival (ISIS) trials revolutionized the treatments of myocardial infarction, despite being relatively cheap to carry out. The ISIS mega‐trials11, 12, 13, 14 collected only one page of data per subject, deaths did not require a monitoring committee to adjudicate events, and there was little commercial pressure on the outcome.15 Because large numbers of patients were randomized and the outcomes were not subject to bias, the results are considered valid.

Most deaths are caused by cardiovascular disease and cancer; for these common diseases therapeutic survival benefit is disappointing. For cholesterol drugs, fibrates as a class tend to decrease survival; statins for primary prevention show little survival benefit.16 A meta‐analysis of angiotensin II inhibitor trials showed a small non‐significant increase in mortality.17 In a review of recently approved oncology drugs, only 35% showed survival benefit, with a median increase in life expectancy of 2.7 months.18 Such data should inform patient‐orientated decisions as to whether to start treatment, let alone at what dose.

Broad spectrum cytotoxic drugs for oncology are both effective and dangerous because of the single mechanism of the inhibition of cell division. The therapeutic window is a fine balance between killing tumour cells before they develop resistance and the toxicity of killing healthy cells. The complexity of their adverse event profile reaffirms the need for survival impact data.

3.4. Excluding harm on the cardiovascular scale

In the past an absence of significant harm was determined by collecting adverse effects, or comparing adverse event rates, in populations considered sufficiently large to ensure the capture of important safety signals. More recently, safety has been quantified as the evidence for an absence of a predefined level of harm based on a single cardiovascular scale. This arose in response to the cardiovascular safety profiles of oral type 2 diabetes agents, particularly rosiglitazone.19

When a drug lowers a biomarker of circulating glucose, such as HbA_1c, it might be presumed that improved glycaemic control will reduce the cardiovascular complications of diabetes. The unexpected possibility that diabetes treatment increases cardiovascular events led the US Food and Drug Administration (FDA) to review the requirements for proof of an absence of harm and issue guidance in 2008,20 followed by similar requirements from the European Medicines Agency.21 The absence of harm is quantified by the upper limit of a two‐sided 95% CI, limited to an estimated risk ratio of <1.8. For agents whose 95% CI upper limit are between 1.3 and 1.8 in premarketing analysis, completion of a post‐marketing trial or continuation of a premarketing trial after approval may be needed to conclusively show that the upper limit of the two‐sided 95% CI is <1.3.

This requirement raises important issues. Risk–benefit has switched from an expectation of efficacy associated with reduced cardiovascular risk, to one of an absence of a predefined level of harm. The benefit of “you will not be made much worse by this medicine” is a difficult concept to promote to a patient compared to “this medicine will make you better and live longer”. The magnitude of a 30–80% increase in cardiovascular risk is not zero risk and considerably beyond the magnitude of benefit of most cardiovascular drugs.

3.5. Mortality as an additional consideration

When toxic chemotherapy is given for a cancer which is rapidly fatal if untreated, then mortality is the obvious primary consideration. In other scenarios mortality data may be taken into consideration, particularly when an absence of harm cannot be excluded. The rofecoxib (Vioxx) withdrawal and the subsequent controversy about cyclooxygenase‐2 inhibitors introduced mortality data as a safety concern late in the lifecycle of the product.

Using osteoarthritis an example, ideally neither the treatment nor the disease would reduce life expectancy. Efficacy based on standard arthritis scales might show benefit. A safety profile might be consistent with the general properties of non‐steroidal anti‐inflammatory drugs, or simple analgesics, to give a clear indication of the appropriate dose. Tramadol is an example of an analgesic originally promoted as having little abuse potential. Though the potential for addiction, or respiratory depression, is now known, the adverse event label does not describe an increased mortality risk. A recent paper22 describes how tramadol was associated with an increased mortality risk over a year when compared to naproxen (hazard ratio [HR] 95% CI, 1.41–2.07), diclofenac (HR 95% CI, 1.51–2.35), celecoxib (HR 95% CI, 1.33–2.17]) and etoricoxib (HR 95% CI, 1.37–3.03), but not compared with codeine (HR 0.94). These are substantial increases in mortality considering that it is such a challenge to show any benefit in mortality with any drug. How this should affect the choice of dose of common drugs such as tramadol or codeine is not known.

4. UNBALANCED SCALES

Once different scales are used for risk and benefit then sources of bias should be considered.

4.1. Publication bias

Clinical trials that show efficacy are positive for the patient, the academic and the sponsor. Negative trials that show no effect, or harm, are less likely to be funded or published and will depress commercial return. Several aspects of trial design can bias the assessment of risk–benefit in favour of finding efficacy.

4.2. Statistical methodology

One bias in favour of efficacy is the statistical method used in the design and analysis. Statistics can quantify if a result may have arisen by chance. A null hypothesis is set that the result would be found if the active does not differ from control. The probability that the null hypothesis is incorrect can be described by P‐values and confidence intervals. This requires predefined efficacy endpoints and the power of the trial is increased if the number of efficacy endpoints is restricted, preferably to a single primary endpoint. Such an analysis is unsuitable for the adverse event profile. Showing no difference from control is a given if there are insufficient data, the smaller the trial the less likely a safety signal will be detected. The safety hypothesis to disprove is not that the drug is no different from control, but to disprove that it is no different from a toxin. As a safety concern may not be identified before the trial, then a safety endpoint cannot be prespecified, weakening the value of statistical tests of significance. If a multitude of safety signals are found, then statistical testing is corrected for multiplicity, for example, with a Bonferroni correction, to compensate for the chance of a false positive. For the final analysis the evidence for efficacy may be a highly significant P‐value, measured on a single predefined endpoint in an intention‐to‐treat population. This outweighs the validity of the evidence of non‐statistically significant signals from multiple safety endpoints on post‐hoc analyses from a per protocol population. The balance is then in favour of treatment, even though a future larger trial may show more people died from the treatment than the disease.

4.3. Biomarkers

Another imbalance in risk–benefit assessment occurs with the use of biomarkers. A fall in blood pressure, cholesterol, HbA1c or viral load may be considered a therapeutic goal, even when the boundary between abnormal and normal values is debated. For a safety parameter, such as a rise in liver enzymes, an adverse event has to meet a definition of abnormality, such as three times or five times the upper limit of a normal range.

Minor changes in biochemistry which are omitted from the safety evaluation can still be relevant. The incidence of a statin adverse event using a creatinine kinase of >10 times the upper limit has been reported as 0.01%. Other estimates of statin adverse events, including muscle biopsies, report them as common.23

Not only are potassium blood concentrations outside the normal range of 3.5–5.0 mmol/L associated with increased mortality in heart failure, those at the ends of the normal range of 3.5–4.1 and 4.8–5.1 mmol/L are also associated with higher mortality.24 This is an important consideration, particularly as mortality is considered too difficult an endpoint for most cardiovascular trials.

4.4. Composite endpoints

In cardiovascular trials it is common to use a composite of stroke, myocardial infarction and cardiovascular death as a single efficacy endpoint. This is complex, as each component may require adjudication as to whether it meets a protocol definition. The majority of the components of the composite, hence those with most statistical power in the outcome, are those considered to be of lesser importance to the patient.25 A reduction in cardiovascular death supports the mechanism of action, though it is total deaths that count for risk–benefit. It is not good news that a relative did not die of cardiovascular disease, but died of another disease instead. These trials are usually insufficiently powered to detect a mortality benefit, despite cardiovascular disease being the commonest cause of death in the trial populations. Using a composite endpoint for efficacy and not for safety distorts the analysis.1 Of many examples is the largest ezetimibe trial, with over 1200 deaths in each arm.26 A meta‐analysis of all ezetimibe trials confirms no mortality benefit27; with over 30 000 patients in the trials we can be confident that there was no significant mortality difference, RR: 1.003, 95% CI 0.954–1.055.27

Even when endpoints are matched, a safety signal may be undervalued compared to a comparable efficacy signal. Until a revision of the requirements for the cardiovascular safety of diabetes drugs by the FDA,20 it was considered that if a safety signal was less than double that with a control, that this was not significant.28 At the same time small falls in cardiovascular events, such as a 15% reduction, were considered as sufficient evidence of efficacy.28

Perhaps the greatest concern for unfair assessment lies with psychiatry. Most diagnoses listed in the Diagnostic and Statistical Manual of Mental Disorders (DSM‐5) depend on composite scales of symptoms. These composites are also used to evaluate treatment because individual symptoms are inadequately powered to detect significant change. For schizophrenia, depression, attention deficient hyperactivity disorder (ADHD) and other major conditions, some 17–30 symptom scores are added together to make an efficacy composite. The analysis of safety rarely uses composites, making any safety signal comparatively invisible.1 This is like using a microscope to detect efficacy and merely glancing at safety.29 The Columbia Suicidality Rating Scale is a rare exception as it uses a composite safety endpoint, establishing a safety signal with many drugs where the signal from individual components was not appreciated.30

Given the widespread use of composite scales for measuring the efficacy of antidepressant drugs and their historical absence for safety,1 a case can be made for the suicidality scale being both a safety and an efficacy endpoint. If antidepressants are effective, they might be expected to decrease the incidence of suicidality. The adverse event profile of antidepressants is poorly documented in trials and much of the negative efficacy data are overlooked.31 Antidepressant withdrawal is a problem for the more than seven million people in the UK who take these drugs long‐term. More than half of those who attempt to come off antidepressants experience withdrawal, nearly half of whom describe these symptoms as severe and withdrawal symptoms can last for months.32 For all psychiatric drugs, not just antidepressants,33 there is almost no clinical trial evidence for optimal dosing, despite an increase in dose being standard practice for a lack of effectiveness.

5. DOSING IN CLINICAL TRIALS

5.1. Starting dose and Phase 1

A starting dose for Phase 1 first‐in‐human (FIH) clinical trials will refer to an estimate of the therapeutic window from non‐human data. Pharmacodynamic and pharmacokinetic activity are used to find a dose low enough to avoid toxicity, yet high enough to allow the reasonably rapid attainment of Phase I trial objectives. A No Observed Adverse Effect Level (NOAEL), calculated from three species, allows a default safety factor to be set. A Minimum Anticipated Biological Effect Level (MABEL) is more appropriate in that the emphasis can be any biomarker, not just a safety concern.34 Fixed conversion factors between species are published, such as dividing the animal dose by precise factors, such 12.3 or 1.1.35, 36 Any sense of precision this implies should be tempered by the precautionary principle of first do no harm. The aim of any FIH study is to guarantee no effect with the first dose. A dose can always be increased, whereas harm from too high an initial dose may be irreversible for the subject, the investigator and the future of the drug. As a default position, investigators should be confident why additional logarithmic reductions of the first dose below the MABEL level are unnecessary. Rapid 10‐fold increments in dose towards the MABEL dose are possible with minimal delay to the development programme. There may be marked differences between subjects in absorption, metabolism, excretion or protein binding. If all of these differences go the same way, together with previously undetected major differences between non‐human species and humans, then the proposed MABEL‐based margin of safety will be too small.

5.2. Pharmacokinetics

With so many advances in drug assays, pharmacokinetic data can provide an additional safety net for Phase 1 trials. If a drug concentration is suspected to be toxic in vitro, or in preclinical models, a maximum drug concentration can be pre‐set to prevent dosing beyond this limit, irrespective of any lack of safety signals in early human exposure.

5.3. The pyramidal approach

For subsequent doses a pyramidal approach to how dose and subject exposure are increased makes sense. At each stage either the dose can be increased, or the number of subjects increased, though not both at the same time. Increments in either should be limited to ten‐fold changes in dose, or the number exposed, reducing to a three‐fold increment once potential pharmacodynamic effects are recorded. Increments should be reduced when dealing with narrow therapeutic index drugs.

5.4. Phase 2

The main aim of Phase 2 studies is to identify doses that might be taken into larger Phase 3 trials. This is facilitated by reliable biomarkers such as blood pressure, cholesterol, HBA1c, spirometry, viral load or symptom scales. Mechanism of action data, such as enzyme inhibition matched to pharmacokinetic profiles, can justify the choice of dose needed to reach the target tissue concentration. A pattern of adverse events becomes recognizable from the safety data, though in Phase 2 the concept of a therapeutic window often loses definition as it is unusual for safety to be captured by one pharmacodynamic marker. The importance of safety biomarkers within the normal range should also be considered, such as changes in potassium concentrations in heart failure,24 or heart rate changes with a sympathomimetic weight loss agent.37

5.5. Phase 3

Phase 3 trials rarely use more than three doses, usually two, sometimes only one. Most development programmes underestimate the logarithmic aspect of the dose response; small increments in dose are less informative, unless the drug has a narrow therapeutic index. The consequence of this is evident in the abundance of small dose increment recommendations in any formulary. Trials with a tenfold difference between the top and bottom dose, with an intermediate three‐fold difference in dose usually generate useful Phase 3 data. By the time a drug is marketed, it is unusual to have dose response mortality data, partly explaining why consensus opinion on the merit of a drug can erode in proportion to the length of time it is on the market.

6. THE PATIENT/CONSUMER PERSPECTIVE

The final arbiter of any treatment decision is the consumer/patient. Even when the science behind a prescriber's recommendation is impeccable, only about half of long‐term medication is taken. Regulatory authorities increasingly welcome patient representatives' views and it may be time to reconsider the clinical pharmacology information provided to the consumer. When prescribing drugs for fatal diseases, treatment dose‐related mortality data are invariably absent. A cancer patient is entitled to ask whether they are likely to live longer with chemotherapy, yet these data are not known for the majority of treatments, let alone the optimal dose. The international guideline recommendations to treat much of the adult population for primary prevention with statins still has counter‐arguments that are difficult to dismiss23; few prescribers know the benefit of statins on survival in target populations. If some 7.5 million people in the UK take long‐term antidepressants, can the general population rely on the evidence used to justify this? There is no trial evidence to support increasing antidepressant doses for non‐responding patients. The patient/consumer perspective can illustrate shortfalls in the evidence used to justify dose. A case can be made for increased transparency of the limitations of data being made more publicly available.

7. CONCLUSIONS

The best estimates of the efficacy and safety ED₅₀ are a rational basis for dose selection. For most drugs, elucidating the safety dose response is more of a challenge than the efficacy dose response. The safety profile may be a collection of diverse adverse events where the lack of prespecified analysis excludes an assessment of their statistical significance. Translating a pharmacodynamic in vitro therapeutic window into a risk–benefit calculation of the right dose for a patient is complex. Too often there is an imbalance in handling of the scales used for the assessment of safety and efficacy. Mortality data can simplify decisions, though for most drugs used to treat potentially fatal diseases, proof that they increase the chance of survival is absent. This has implications for patients who wish to make informed decisions about treatments for diseases such as cancer or cardiovascular disease.

There is pressure to demonstrate efficacy in drug development which is not matched by the vigour of the safety assessment. A conclusion will be distorted if composite endpoints are used to determine efficacy and these are absent for safety data; this applies to nearly all drugs used for psychiatry. The case for efficacy can be reinforced by favourable changes in biomarkers, whereas safety biochemical markers are only listed when substantially beyond the normal range.

The case for a positive risk–benefit is a strengthened when a drug reduces disease‐related mortality. This approach guided the internationally accepted guidelines for most treatments used for myocardial infarction following the success of the ISIS trials. In contrast, international guidelines for blood pressure, cholesterol and diabetes are based on large and expensive trials where mortality was not a primary endpoint. For oncology the recommended treatments of many tumours have poor evidence of improved survival as progression‐free survival is often used as a surrogate.

For a fair assessment of the risk–benefit of a choice of dose, the patient should be aware of the limitations of the data on which decisions are made. For cardiovascular, oncology and psychiatry drugs, as highlighted in this issue of the Journal, not all the evidence is clear. It is difficult to define the comparative merits of doses, unless the dose–response can be summarized on one scale. The optimal dose of many drugs is a best guess based on limited data on benefit and harm.

COMPETING INTERESTS

The author has no competing interests for this paper. He receives personal dividends from Medicines Assessment Ltd; is Executive Editor of the British Journal of Clinical Pharmacology; and is member of the Joint Speciality Committee for Clinical Pharmacology and Therapeutics at the Royal College of Physicians, London.

Warren JB. Translating the dose response into risk and benefit. Br J Clin Pharmacol. 2019; 85: 2187–2193. 10.1111/bcp.13949