Clinical pharmacology = disease progression + drug action

Abstract

Clinical pharmacology is concerned with understanding how to use medicines to treat disease. Pharmacokinetics and pharmacodynamics have provided powerful methodologies for describing the time course of concentration and effect in individuals and in populations. This population approach may also be applied to describing the progression of disease and the action of drugs to change disease progress. Quantitative models for symptomatic and disease-modifying effects of drugs are valuable not only for describing drugs and diseases but also for identifying criteria to distinguish between types of drug actions, with implications for regulatory decisions and long-term patient care.

The population approach

Following the pioneering work of Sheiner and colleagues over 40 years ago [1] the science of quantitative clinical pharmacology has been guided by a methodology known as the population approach. This methodology is often associated with pharmacokinetic studies [2–7] but it is also used to describe pharmacodynamics [8–12]. Its application to describe the natural history of disease and the response to treatment was first used quite early in the history of the population approach [13]. This use of the population approach follows fundamentally the same principles as those used for pharmacokinetics and pharmacodynamics but also provides more rigorous ways of describing disease and its progression over time.

Disease progression

In the context of clinical pharmacology, the use of the population approach for studies of disease progression refers to describing the natural history of disease reflected in repeated measures of disease status. Disease status is a general term that refers to any quantifiable variable describing disease at a particular point in time. Observations of disease status, like those of drug concentration or drug effect, can often be made repeatedly in the same patient. Disease status is used to identify the trajectory of the disease using a disease progression model in a way analogous to the use of drug concentrations for a pharmacokinetic model and drug effects for a pharmacodynamic model. Disease progression is used within this review to refer to the time course of the changes in disease without influence of drug or other treatments.

Disease progress

It is often hard to obtain repeated measure of disease status in the absence of treatment because there is usually a clinical imperative to offer treatment to patients with disease, e.g. a PubMed search using ‘disease’, ‘progression’ and ‘natural’ and excluding ‘killer’ produced only 54 references, many to rather rare diseases without effective treatment. In practical terms, this means that the combined effects of natural disease progression and those of treatment, whether active or placebo, are the most commonly available observations. Disease progress is used in this review to refer to the time course of the changes in disease under the influence of drug or other treatments. The distinction between disease progression and disease progress is not important but can be useful when trying to emphasize the additional effects of treatment on disease.

The challenge of separating out natural disease progression, active drug effects and placebo response lends itself to the population-modelling approach. Models are necessarily simplifications of reality [14] but even though they may not describe every detail of what is observed they can be useful for describing the main features of disease progression and for testing hypotheses about the effect of interventions on disease progress.

A very simple disease progress model was used a long time ago to help understand the time course of drug effects [15]:

(1)

The terms E_max and C₅₀ are the pharmacodynamic parameters defining the efficacy and potency of the drug. The parameter E₀ was used to describe the time (t) course of the effect [E(t)] when drug concentration at its effect site [Ce(t)] was zero. It should be obvious that this is a misuse of the term ‘effect’, which is usually applied in pharmacology to refer to the action of a drug. The effect of a drug when Ce(t) is zero must obviously be zero. Equation 1 requires renaming of its elements in order to describe the response when Ce(t) is zero correctly.

(2)

Here, S₀ refers to the baseline disease status, conventionally assumed to occur when time is zero, but could also apply if there is no disease progression, and S(t) is now the time course of disease status determined by both the underlying disease and drug action. Disease in this context is used in a general sense to include biomarkers, such as blood pressure.

When the observation period is short it may not be unreasonable to use Equation 2, which assumes that there is no time course of disease status independent of the time course of drug action. Even if there is no direct evidence of natural progression of the disease status it is nevertheless important to try to describe the baseline parameter S₀ and not be tempted to subtract the baseline in order to see the ‘pure drug effect’. An obvious reason not to do this is because subtracting two observations can only increase the measurement error associated with the result. A more subtle reason is that the baseline may be correlated with other parameters, such as E_max. This correlation can be estimated when there are disease status profiles available from several subjects (the examples are part of this review). Ignoring the correlation will lead to biased simulations based on the model and its parameters [16].

More broadly, S₀ can be thought of as the disease progression part and the drug action expression as the pharmacology part, which together define a view of clinical pharmacology.

Figure 1 shows a simple model that assumes disease progression and drug action are additive to produce the overall response that is described as the clinical pharmacology of a drug. This assumption of additivity is a simple starting place on which to build more complex models that may involve interaction between disease and drug.

Figure 1.

Clinical pharmacology defined as the sum of disease progression and drug action

Natural history

An obvious extension to Equation 2 to account for changes of disease status over time that are unrelated to drug action is to propose a linear model (Equation 3). The rate of disease progression is defined by the slope parameter α starting at time zero with a disease status S₀. This is the simplest case for a practical model of disease progression.

(3)

Figure 2 shows the predicted disease progression using a linear model. The disease status could be the Unified Parkinson's Disease Response Scale (UPDRS) followed over 52 weeks. Over this period, the change is relatively small and can be adequately described by a straight line [17].

Figure 2.

Disease progression describing the natural history using a linear model. The baseline disease status at time zero is 20 units (S₀). The slope of the line (α) defines the rate of progression (12 units per year)

Drug action

For simplicity and generality the E_max model of drug action in Equation 2 has been replaced in the following section by the expression E[Ce(t)]. This expression indicates the time course of effect arising from any pharmacodynamic model predicting drug action, as a function of the time course of drug concentration at its effect site.

Symptomatic effects

The most widely known type of drug action is additive to the disease progression model. It produces an offset from the disease progression curve. Drug action is usually delayed, and this is shown in Figure 3. Treatment starts at time zero and builds up to reach a constant drug action. The delay in effect may be due to pharmacokinetic accumulation, distribution to the site of action, binding to receptors or to the turnover of a physiological process underlying the observed effect [15]. The combined additive effect of treatment on disease progression shows this delayed onset of action as well as continuing progression without any change in the rate of progress once a steady-state drug effect is reached. This kind of drug action may be described as an offset effect because it does not change the underlying disease progression. When treatment is stopped at 40 weeks, the drug effect washes out. In the figure, the washout is assumed to occur at the same rate as the wash in of effect, which may be plausible on mechanistic grounds in many cases but is not always the case when the mechanism of delayed onset and offset of effects is not well understood [17].

Figure 3.

The time course of symptomatic drug action influencing disease progression. The long-dashed blue line shows linear disease progression. The short-dashed green line shows the time course of drug action, with a delayed onset and slow washout after withdrawal of treatment at 40 weeks. The continuous red line shows the sum of the disease progression and drug action lines. , natural history; , total response; , offset effect

When the disease progression is linear, it is expected that the disease status will return to the same value as the nontreated progression curve once all drug effects have dissipated. This kind of reversible and temporary drug action is often called symptomatic because the benefit is transient and occurs only during treatment or while treatment effects are washing out.

The symptomatic effects of drug treatment on disease status can be predicted using Equation 4. All symptomatic effects can be described in terms of an additive effect of drug action on the baseline disease status S₀.

(4)

The term Ce(t) is used to indicate that drug concentration is at the site of drug effect. As noted above, drug actions are usually delayed, and the use of an effect compartment concentration is one way to describe this.

Disease-modifying effects

A second kind of drug action on disease progression occurs when the drug influences the rate of progression. If disease progression is linear, this may be described as a slope effect. More generally, this kind of effect is known as a disease-modifying action. The onset of changes in disease status is typically slow and it is difficult to distinguish the delay attributable to drug reaching its site of action, which is usually visible with symptomatic effects. Figure 4 illustrates a disease-modifying effect on a linear progression curve. The rate of progression is effectively zero during drug treatment, but when treatment stops at 40 weeks the disease continues to progress. Note, however, that the rate of progression returns to the same value seen in the natural disease progression curve but the disease status curve stays separate. The drug action is seen to be persistent because a treatment benefit continues after drug effects have ceased. Observing the response after washing out treatment effects is valuable in order to confirm a true disease-modifying effect.

Figure 4.

The time course of disease-modifying drug action influencing disease progression. The long-dashed blue line shows linear disease progression. The short-dashed green line shows the time course of drug action, with a rapid onset and washout after withdrawal of treatment at 40 weeks. The continuous red line shows the sum of the disease progression and drug action lines. , natural history; , total response; , slope effect

Combined symptomatic and disease-modifying effects

There is no intrinsic reason to classify drug effects on disease progression as either symptomatic or disease modifying. Both kinds of effect may occur, and the ability to distinguish the relative contribution of each effect can be challenging. Figure 5 shows this kind of combined behaviour. Several trial designs have been proposed for trying to identify disease-modifying effects. These include a parallel group design, a washout design and a delayed start design. The parallel group design might be used to test whether a treatment has a disease-modifying effect, but without a further intervention it is not possible to distinguish a slow-onset symptomatic effect from a disease-modifying effect. The response to treatment with a lead chelating agent appeared to change the rate of diminishing glomerular filtration rate [18] but given the slow turnover of lead it cannot be concluded that changes were not due to a slow symptomatic effect. This is the major weakness of a parallel trial design. Clinical trial simulation has been used to investigate more informative trial designs to separate symptomatic and disease-modifying effects quantitatively. The power of the washout design is clearly superior to the delayed start design [19], although in practice both designs have led to inconclusive results because of oversimplistic data analysis and restrictive assumptions (see below in Parkinson's Disease section).

Figure 5.

The time course of combined symptomatic and disease-modifying drug action influencing disease progression. The long-dashed line shows linear disease progression. The continuous red line shows the sum of the disease progression and drug action lines, with a slow onset and washout after withdrawal of treatment at 40 weeks. , natural history; , both offset and slope effect

Disease process and disease progress

A particular case of disease-modifying behaviour is when the disease is cured and there is no further progression after treatment ends. Both disease-modifying effects and curative effects of treatment can be understood in terms of changes in disease process [20]. Disease progression can be understood in some cases as arising from a difference between input and output of factors which, when balanced, lead to constant disease status.

A simple example is to consider the processes involved with bone formation and loss, which are thought to underlie the development of osteoporosis.

(5)

Bone mass (usually measured indirectly using bone mineral density) typically increases during childhood and early adult life, then declines around the age of 40 years and later. The decline is usually more rapid in women around the time of the menopause. It is thought that loss of ovarian hormones, such as oestrogen, leads to an increased rate of loss of bone. This is the basis of oestrogen supplementation treatments to slow or prevent further bone loss. In this case, the rate of loss of bone is a disease process, which is accelerated by endogenous reduction in oestrogen exposure or decelerated by treatment with oestrogen.

Cure of disease, e.g. viral infection, can be understood with the same basic model. Using viral load as a measure of disease status, the number of virus particles will depend on their rate of formation (typically by replication) and their rate of loss (typically by white cell activity). Treatments which inhibit viral replication can reduce the rate of formation to zero, with loss of viral particles from the body. Once the last particle is removed, the disease is cured. Models for viral dynamics based on these ideas have been very helpful in drug development [21–24].

Placebo response

A common challenge when describing disease progress is to distinguish the underlying disease progression from the response to placebo treatment. As noted previously, it is unusual to be able to observe the natural history of progression without some kind of treatment intervention. In the setting of a well-designed clinical trial, there is often a placebo treatment group, which can be helpful in understanding both the response to placebo and the progression of the disease. Given that the two effects are confounded in the observed disease status, it is necessary to make some assumptions in order to distinguish the two factors. When the disease does not change rapidly over the period of observation, e.g. <30% change from baseline, then any disease progression curve can be reasonably well approximated by a straight line. Deviations from the straight line can then be ascribed to the response to placebo treatment. This is illustrated in Figure 6, which shows the separate placebo effect and disease progression curves that, when combined, give the observed disease progress curve.

Figure 6.

Disease progression describing the natural history using a linear model with the transient effect of an ongoing treatment with placebo. The long-dashed blue line shows progression without placebo. The short-dashed purple line shows the time course of the placebo effect. The continuous red line shows the combined disease progress curve. , natural history; , total response; , placebo component

Some assumptions are also useful when describing the response to placebo treatment. The effect of placebo treatment is expected to be transient, with an initial improvement (or worsening) followed by disappearance of the effect, so that eventually the placebo-treatment curve is indistinguishable from the natural progression curve [see next section (Placebo response) for examples].

Disease examples

Some illustrative examples of disease progression and drug action will be discussed. This is not intended to be a comprehensive review of the diseases that are mentioned but is aimed to show how the theoretical concepts and quantitative models described above may be translated into practice.

Obstructive airways disease

Patients with an acute exacerbation of obstructive airways disease, whether due to asthma or chronic disease, can usually expect the attack to resolve and return to their baseline state without treatment. Episodic attacks of obstruction, whether triggered by allergy or infection, then followed by recovery are characteristic of disease progression. The acute response to treatment of an episode of severe airways obstruction requiring hospital admission was described in the setting of a randomized concentration-controlled trial of theophylline [25]. The time course of improvement in airways obstruction could be assigned in part to a rapid effect of theophylline, with an E_max pharmacodynamic model driven by plasma concentration. In addition, there was a time-related recovery that was independent of theophylline treatment [13] but was related to the current status compared with the eventual fully recovered state.

Large-scale trials have been mounted to try to demonstrate disease-modifying effects of inhaled treatments in patients with chronic obstructive airways disease [26,27]. There is no evidence that corticosteroids change the rate of progression [28]. A meta-analysis which tried to look at the problem looked only at the change from baseline over 2 years. Simply looking at the change from baseline alone cannot cannot distinguish symptomatic from disease-modifying effects [26,29]. This is illustrated by comparing Figure 3 (symptomatic offset effect) with Figure 4 (disease-modifying slope effect). The change from baseline at time 40 is the same in both cases, but the effect on disease progression is quite different. Tiotropium, an anticholinergic bronchodilator, showed symptomatic improvement but no change in rate of progress despite a large trial size (nearly 6000 patients) and long follow-up (4 years) [30]. The same trial demonstrated that an inhaled β-agonist gave better symptomatic benefit than tiotropium.

Osteoporosis

The natural history of disease progression in postmenopausal osteoporosis appears to be relatively linear over a 5 year period. Attempts to distinguish a disease-modifying effect from a symptomatic effect of combined oestrogen and progestin treatment were unsuccessful despite the relatively long follow-up [31]. This is because the time course of change in bone mineral density is rather slow and it is hard to establish when the full treatment effect is reached. A similar study in a larger population showed that the peak effects of hormone replacement therapy were achieved earlier in the cancellous bone of the lumbar spine than in the denser cortical bone at the hip, but the study was also not able to distinguish symptomatic from disease-modifying effects clearly [32]. When the effects of drug treatment are slow in onset, as they are for effects on bone, it may be practically impossible to distinguish a slow-onset effect of drug from a disease-modifying effect because the initial phases of onset of drug action will show a change in slope as illustrated in Figure 3. Studies wishing to demonstrate disease-modifying effects must recognize the finite time horizon and understand the limitations when any symptomatic effects are relatively slow in onset.

Diabetes

Type II diabetes is a complex disorder, with a variety of biomarkers that can be used to define disease status, e.g. fasting plasma glucose, serum insulin, haemoglobin A_1c. A descriptive model of the onset of action of gliclazide on fasting plasma glucose showed that the drug action was delayed by several weeks but then remained with a constant offset to a linear progression model [33]. A positive correlation was noted between the baseline glucose and the subsequent rate of increase of glucose due to natural progression. Gliclazide appears to have the properties of a symptomatic treatment, but the reversibility was not tested by observing the glucose response after withdrawal.

The underlying disease processes include decreasing sensitivity to the action of insulin and diminishing secretory capacity of the pancreas to produce insulin. An empirical model for the time course of fasting plasma glucose and serum insulin was coupled with a plausible physiological feedback mechanism to try to identify the effects of different oral hypoglycaemic agents on the progress of insulin sensitivity and insulin secretion [34]. The effects of gliclazide (a stimulator of insulin secretion) were assumed to be symptomatic, and a disease-modifying effect was not tested. Pioglitazone (an insulin sensitizer), in contrast, showed some indication of a disease-modifying effect by slowing the rate of decline in insulin sensitivity. A more mechanistic model for insulin and glucose turnover confirmed the disease-modifying effects of pioglitazone, with no evidence of a disease-modifying effect for metformin (insulin sensitizer) or a variety of sulphonylurea insulin secretion stimulators [35].

Alzheimer's disease

There have been many clinical trials of drug treatments seeking benefit for patients with Alzheimer's disease. Only the cholinesterase inhibitor class of drugs have shown any statistical advantage compared with placebo, and these effects are relatively small and not widely accepted as valuable in clinical practice. Tacrine was the first of these agents to be approved. A pooled population analysis from several trials identified linear disease progression, with offset drug action taking more than 6 weeks to reach a constant value [36,37]. The effect was linearly related to the daily doses that were evaluated. The baseline disease status (Alzheimer's Disease Assessment Scale cognitive subscale; ADASC) was positively correlated with the rate of progression. These results were confirmed in a subsequent analysis of five trials, which also showed that lecithin had an additional small benefit and identified responder and poor responder groups for tacrine effect.

Meta-analyses of clinical trials in Alzheimer's disease using the population approach have confirmed the linear progression of the disease and shown that there has been no change in the typical rate of progression over two decades of clinical trials [38,39]. This confirms the robustness of ADASC as a measure of the status of Alzheimer's disease in the face of changing standards of care and other environmental factors. It is possible that with much longer observation, particularly prior to development of established disease, the shape of the progression curve might be shown to be deviate from linearity, but this awaits the experimental evidence.

Some patient factors, such as age, sex and apolipoprotein E4 expression, have been shown to account for some of the variability in progression, and this may be useful for clinical trial analysis and simulation models [39–41].

A promising methodological advance based on item response theory has been described, which may make global clinical scales, such as ADASC, more effective for designing and evaluating clinical trials [42].

Parkinson's disease

The application of the population approach to the description of disease progress in Parkinson's disease has been particularly fruitful because of the existence of a database of patients with long-term follow-up and the use of drug treatments with pronounced beneficial effects. The Parkinson Study Group undertook a trial called DATATOP, which tested whether antioxidant treatments could delay the need for use of dopaminergic agents, such as levodopa [43]. No evidence was found to support the effectiveness of antioxidant treatment, but a later report showed evidence for a disease-modifying effect of selegiline, which slowed the rate of decline of the UPDRS disease status marker, although this was not recognized at the time [44]. Subsequent analysis of these data and follow-up data in the DATATOP cohort confirmed the beneficial disease-modifying action of selegiline and also revealed the previously unrecognized disease-modifying action of levodopa, which appears to be potentiated when combined with selegiline [17]. The disease-modifying effects of levodopa alone were confirmed in a relatively short-term (9 months) randomized trial [45] by using a population approach to analyse the data [46].

The disease progress based on UPDRS and its subscales (tremor, rigidity, bradykinesia, postural instability and gait disturbance) can be separated into progression and drug action components with a combined symptomatic and disease-modifying pharmacodynamic model for several drug treatments [47]. The progression component is best described by initial slow progression followed by a more rapid phase, then slowing to approach an asymptote. This shape was modelled using a Gompertz growth model that has been used elsewhere to describe tumour growth [48].

Rasagiline is in the same mechanism class as selegiline (a monoamine oxidase B inhibitor), and a large-scale clinical trial has been conducted specifically looking for a disease-modifying effect [49]. The results were difficult to interpret because the analysis method concluded that a dose of 1 mg day⁻¹ was just disease modifying, while 2 mg day⁻¹ was only symptomatic. The problems associated with the design and analysis of this trial have been debated elsewhere (e.g. [50–52]). Key issues were the use of a delayed start design, which is known to be less powerful than a washout design [19], and the assumption that any symptomatic effects of rasagiline would be complete at 12 weeks after starting treatment [53].

Renal function

Markers of renal function, such as serum creatinine, creatinine clearance and glomerular filtration rate, are readily available disease status measures that can be used to describe disease progression and the response to treatment. Some prediction methods, such as the Modification of Diet in Renal Disease formula for glomerular filtration based on serum creatinine [54], are methodologically flawed because of their empirical basis that does not explicitly recognize obvious factors, such as body size and the directly inverse relationship of clearance with serum creatinine. The Cockcroft and Gault method [55] is theoretically correct and practically useful. It can be used with models for predicting normal glomerular filtration rate from age and weight to calculate a renal function value that has the value 1 when the predicted creatinine clearance is the same as that predicted from the age and weight normal value [56].

Both a calcium channel blocker (nifedipine) and an angiotensin-converting enzyme inhibitor (captopril) have been shown to slow the rate of decline of predicted creatinine clearance in patients with high blood pressure [57].

The effect of calcium disodium EDTA on the progression of glomerular filtration rate (predicted from serum creatinine) has shown what appears to be a rapid symptomatic effect followed by a disease-modifying effect, reducing the rate of progression almost to zero for the 2 years of follow-up [58]. There was no withdrawal phase to this study and it possible that the symptomatic improvement develops more slowly because of tight binding of lead to bone. This is another example where the distinction between slow-onset symptomatic effects and disease-modifying effects may be impractical to separate.

The placebo response

As noted above, studies of disease progress can give insights into the placebo response. The assumption that the response to placebo treatment is transient has been modelled using a two-exponential model known as the Bateman function. It is analogous to the first-order absorption and first-order elimination model used in pharmacokinetics. The Bateman function describes the input and washout of the response in terms of two half-lives and the magnitude of the response related to the response predicted at the time of the peak. It was first applied to describe the placebo response in Alzheimer's disease and identified that the magnitude of the placebo response was markedly larger in studies conducted in France [36]. The disease progression model was assumed to be linear.

The Bateman function and a Weibull model with a broadly similar shape have been used to describe the placebo response in clinical trials of major depression [59–61]. The disease progression model was implicitly assumed to be constant, with no change over time.

The response to placebo treatment may be beneficial (placebo response) or harmful (nocebo response). Both placebo and nocebo responses have been reported in trials of antidepressants and also identified in newly diagnosed patients with Parkinson's disease [62,63]. The population approach is particularly helpful here for identifying subpopulations with mixture models.

Why is the study of disease progress useful?

A framework for describing disease progress and distinguishing natural disease progression from drug action and response to placebo has been described. This framework provides a mechanism for testing quantitative hypotheses about the magnitude of drug benefits and also for qualitative claims of disease-modifying effects. Disease-modifying effects are especially needed in long-term progressive diseases associated with a poor prognosis after many years.

The ability to describe disease progress, including the responses to treatment, in a quantitative fashion allows the use of disease status to predict clinical outcome events, such as death [64] and bone fractures [32]. Interest in methods of time-to-event analysis is expected to lead to many more practical applications for predicting clinical outcome events [65,66].

Disease progress models incorporate both pharmacokinetics and pharmacodynamics to describe drug action. Natural history progression models incorporate the clinical and pathophysiological features of disease. By combining them, a more complete picture can be created of the roles of disease and treatments in understanding clinical pharmacology and improving patient care.

Competing Interests

The author provides consulting advice to pharmaceutical companies on disease progress and other pharmacometrics issues. No conflict of interest has been identified in writing this review.