Pain relief model for a COX-2 inhibitor in patients with postoperative dental pain

Abstract

AIM

To develop a pain relief model for a cyclooxygenase (COX)-2 inhibitor, CS-706, that permits prediction of doses for acute pain relief in Japanese and Western populations.

METHODS

A categorical response model was developed to describe the probability of pain relief (PR) over time for a Phase 2a study. Models were also developed to describe patient's use of rescue medication and onset of pain relief.

RESULTS

The placebo response was described by a first-order increase in PR that achieved a stable response after 4 h. The effect of CS-706 on PR was described using an E_max model; the plasma concentration of CS-706 producing 50% of the maximum response was estimated to be 87 ng ml⁻¹, the median peak plasma concentration achieved after a 50-mg oral dose. The probability of rescue medication (REMD) decreased over time and was a function of the last observed PR score. This probability was < 16% for patients with a PR score ≥2. The probability of experiencing meaningful PR was 98% in patients who did not require REMD and 47% in those who required REMD. For patients who did not require REMD, the median onset time of meaningful pain relief (TMPR) decreased with increasing doses. In patients who required REMD, there was a saturable decline in TMPR, with the greatest improvement occurring from placebo to 50-mg doses.

CONCLUSIONS

The set of models developed permitted compilation of multiple dose–response curves for dose selection of CS-706 in Westerners and facilitated scaling of doses to a Japanese population.

WHAT IS ALREADY KNOWN ABOUT THIS SUBJECT

• Modelling and simulation are being increasingly used to support decision-making in new drug development.

• Novel modelling methods are required to capture the complexity of multiple end-points for a disease and to address questions such as dose selection in various populations.

• The focus of this study was to present a novel pain relief model to address such questions.

WHAT THIS STUDY ADDS

• New contributions of this work to the literature include:

  1. application of pain relief models to COX-2 inhibitors
  2. modelling of the time to meaningful pain relief
  3. scaling pain relief data from Westerners to Japanese
  4. use of multiple dose–response curves to facilitate dose selection decisions.

Introduction

CS-706 is a new orally active, selective inhibitor of cyclooxygenase (COX)-2. Phase 1, single- and multiple-dose pharmacokinetic/pharmacodynamic (PK/PD) studies, a gastrointestinal tolerability study, and a Phase 2a safety and efficacy study in acute postoperative dental pain patients have recently been completed in the USA. A programme was initiated to utilize the clinical data collected in these studies to provide a framework to bridge to other subpopulations, especially the Japanese population, with a view to developing a global Phase 2 strategy for CS-706. Three key models were identified: a population PK model that describes changes in CS-706 plasma concentrations over time and identifies sources of intersubject variability in CS-706 pharmacokinetics, a PK/PD model that describes the effects of CS-706 on inhibition of COX-1 and COX-2 activity and identifies sources of intersubject variability in CS-706 pharmacodynamics, and an exposure vs. response model that describes the clinical efficacy and short-term safety profile of CS-706 and allows comparison of its performance with other selective COX-2 agents.

PK and PK/PD (biomarker) models have been described previously [1, 2]. The objective of the present analysis was to develop a set of models that describe the clinical effects of CS-706 on acute dental pain relief (PR). Multiple clinical end-points were evaluated, including the probability of pain relief over time, patient's use of rescue medication and onset time of pain relief. The analysis permitted compilation of dose vs. response curves for multiple end-points to facilitate dose selection decisions and to provide a framework to bridge Western PR data to the Japanese population. Thus, the model was utilized to anticipate the therapeutic dose range of CS-706 in Western and Japanese patients.

Methods

Data

Data were collected in a randomized, double-blind, placebo- and active comparator-controlled Phase 2a study to assess the analgesic efficacy and safety of CS-706 in acute, postoperative dental pain. A clinical study report has been published separately [3]. Briefly, at two sites in the USA, patients with moderate to severe pain intensity were included in the study within 6 h following completion of dental surgery to remove two or more third molars. Patients were randomized in approximately equal proportions to receive a single oral dose of one of six treatments (∼50 patients/treatment): 10, 50, 100 or 200 mg CS-706, placebo or 400 mg celecoxib.

Pain intensity (PI; categorical and visual analogue scales) was assessed at the time of dosing and PI and pain relief (PR; categorical scale) assessments were performed at 0.25, 0.5, 0.75, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 12 and 24 h postdose. Pain relief was measured on a five-point scale: 0, none; 1, a little; 2, some; 3; a lot; and 4, complete (100% PR). Time to onset of perceptible pain relief (defined as when the patient began to feel any pain relief) and time to onset of meaningful pain relief (defined as when the patient felt the pain relief was meaningful to them) were assessed by the patient using a separate stopwatch for each measurement.

In the event that a patient required oral rescue medication for relief of intractable pain, efficacy assessment was performed prior to administration of rescue medication. The patient then discontinued further pain assessments. According to protocol, any patient requiring rescue medication within 90 min of dose administration was excluded from the primary efficacy analysis and patients who received rescue medication prior to the end of the 24-h evaluation period were analysed using last observation carried forward.

Study participants remained in the study for all safety assessments over the 24-h postdose period and returned to the clinic after 5–9 days for follow-up assessment.

Approval of the study protocol and informed consent form were obtained from Quorum Institutional Review Board (Seattle, WA, USA) before subjects were enrolled. The nature and purpose of the study were explained to subjects before they provided their consent to participate.

Model development

Each patient in the study had a series of PR measurements over 24 h, or may have discontinued and received a rescue medication at the time of discontinuation (T). The joint probability (P) of pain relief measurements (PR) and the probability of rescue medication (REMD) given predictors (ϕ) and subject-specific random effects (η) was conceptualized as follows:

(1)

where φ includes plasma concentrations, baseline pain scores, and other relevant predictors, and η is a vector of subject-specific random effects assumed to be multivariate normal. Each term in the right-hand side of Equation 1 was modelled separately (as described below in the sections Pain relief model and Rescue medication model, respectively). The joint likelihood across all measurements and all patients was calculated using mixed-effects modelling, which integrates across the subject-specific random effects. Since taking rescue medication also defines the time of discontinuation, Equation 1 can also be used to compute T.

The probability of having onset of meaningful pain relief (MPR) was described as follows:

(2)

where ϕ includes dose and PR measurements, means no rescue occurs, and P(REMD) and P() are calculated from Equation 1. The probability of having MPR depended on whether or not the subject took rescue medication. Each MPR term on the right-hand side was modelled separately (as described below in the section Onset of meaningful pain relief model).

Given onset occurred, the likelihood of the time of meaningful pain relief (TMPR) was modelled as follows:

(3)

where ϕ includes dose, and σ is a normally distributed subject-specific random variable. The likelihood of TMPR taking a certain value depends on whether or not the subject took rescue medication. Each TMPR term on the right-hand side was modelled separately, as described below in the section Onset of meaningful pain relief model.

Exploratory analysis

An exploratory graphical analysis of the data was performed using S-PLUS version 6.1 (Insightful Corp., Seattle, WA, USA) to guide subsequent steps in the data analysis process. For example, pain relief scores vs. time plots, grouped by dose, were examined in order to evaluate the nature of the dose vs. response relationship and to ascertain whether the response was dose dependent. Subsets of these plots were examined further to evaluate onset and duration of pain relief. Bar plots of the number of patients vs. time, grouped by dose, were evaluated to provide an understanding of the nature of the model describing the rate of rescue medication.

Pain relief model

The pain relief model describes the probability that the response, Y, at time, t, is greater than or equal to the pain relief score, k. A standard categorical response model was used [4]:

(4)

where Y is the j^th pain relief score in patient i at time t_ij, k takes on the values of 1, 2, 3, or 4 with P(Y_ij ≥ 0) = 1, η_i accounts for intersubject variability, C_ij is the j^th concentration value in patient i at time t_ij, f_P is a function of time describing placebo effect, and f_D is the function describing the effect of CS-706 in pain relief. β_k are the logit of the probability of equalling or exceeding each pain score, k, extrapolated back to time = 0. The intercepts β_k were parameterized as follows:

(5)

Thus, the estimated parameters are q₁, q₂, q₃ and q₄. The model is parameterized this way because, with the exception of θ₁, θ estimates can be constrained to be negative, keeping the β-values decreasing with increasing pain score.

Structural models, including linear, E_max and sigmoid E_max models, were fit to the pain relief score vs. time data for both placebo- and CS-706-treated patients. For treated patients, CS-706 plasma concentrations and whole blood COX-2 activity (determined by measurement of prostaglandin E₂ concentration in heparinized plasma following incubation of whole blood with lipopolysaccharide) were evaluated as possible explanatory variables. Plasma concentrations of CS-706 and COX-2 activity were the individual (post hoc) estimates from population PK and PK/PD models developed previously and described briefly below [1, 2].

The PK model was an open two-compartment model with first-order absorption, an absorption lag time (median 14 min) and first-order elimination [1]. Apparent oral clearance (CL/F) was 47.2 l h⁻¹ in the dose range 2–200 mg and was reduced by 43% at higher doses (>200 mg), by 38% in women compared to men, by 64% in subjects expressing poor and intermediate cytochrome P450 (CYP) 2D6 phenotypes, and by 15% in subjects expressing the CYP 2C9 reduced hydroxylator phenotype. The typical apparent volume of the central compartment (V_c/F) in a 73-kg subject was 166 l and was increased approximately 8% per 10% increase in body weight. Oral bioavailability was 42% greater following night-time relative to day-time doses, and decreased with increasing doses according to a saturation model, reaching 50% reduction at a dose of 221 mg.

E_max models described relationships between CS-706 plasma concentrations and pharmacodynamic responses (inhibition of COX-1 and COX-2 activity) [2]. The maximum possible inhibition by CS-706 for COX-1 and COX-2 was 100%. CS-706 potency (EC₅₀) was 397 ng ml⁻¹ for COX-1 and 20 ng ml⁻¹ for COX-2. None of the tested covariates, including age, gender, race, weight, height and body mass index, influenced the pharmacodynamics of CS-706. Predictive PK/PD modelling for COX-1 and COX-2 inhibition indicated a 20-fold potency ratio for COX-2 vs. COX-1 inhibition that is expected to be similar in Japanese and Western populations [2].

Placebo model

The placebo response over time [f_p(t)] in Equation 4 was described by a first-order increase in pain relief, to a stable value:

(6)

where E_p is the maximum placebo effect and k_p is a first-order rate constant describing the stabilization rate of the placebo effect over time, t. E_p and k_p are the estimated parameters.

Drug effect model

The effect of CS-706 plasma concentration [f_D (C_p) in Equation 4] on dental pain relief was described using an E_max model. The models were parameterized in terms of maximum possible response and potency, as follows:

(7)

where C_p is the population PK model-predicted plasma concentration, E_max represents the maximum drug effect achievable and EC₅₀ is the CS-706 plasma concentration at half the maximal effect. E_max and EC₅₀ are the estimated parameters. Utilizing COX-2 data instead of plasma concentration as the explanatory variable for pain relief did not improve the model fit.

Intersubject variability in pharmacodynamic parameters was modelled according to a log-normal distribution:

(8)

where θ_i is the parameter for the i^th participant, θ_T is the typical value of the parameter in the population, and η_i is a random intersubject effect with mean 0 and variance ω².

Baseline pain intensity was examined as a possible covariate to explain variability in response. It was introduced in the model as follows:

(9)

where Cov_i is a derived binary variable with values of 0 or 1 and is the parameter for the i^th participant that describes the effect of the variable on the parameter of interest.

Covariate selection was based on the likelihood ratio test [5]. The maximum likelihood objective function (−2 times the log-likelihood) has asymptotic statistical properties. In this analysis, α= 0.05 was used for model selection.

Maximum likelihood estimates of the parameters were obtained using the Laplacian estimation method in the NONMEM program (version V) [6]. At each stage of the analysis, model development was guided by examination of diagnostic plots to assess the goodness of fit of the model to the data.

Rescue medication model

A model was developed to describe the probability of requiring rescue medication. Model development was guided by graphical evaluation of the data and performed using S-PLUS.

The probability of a patient requiring rescue medication was defined by the following equation:

(10)

where P_ij is the probability at time j that patient i will require rescue medication in the next interval of time (ΔT_ij), given that the person has not already received rescue medication. The likelihood of requiring rescue medication is described by a hazard function, h_ij, and is a exponentially declining function of the last observed pain relief score, PR_ij, as follows:

(11)

where h_ij is the instantaneous risk of requiring rescue medication per unit time that is a function of the last pain relief score PR_ij, h₀ is the probability of requiring rescue medication when there is no pain relief (PR = 0) and λ describes the decline in the rate of rescue medication with increasing pain relief. The estimated parameters are h₀ and λ. For a given hazard, h, the duration over which 50% of patients will require rescue medication can be calculated using the following equation:

(12)

Onset of meaningful pain relief model

Based on graphical exploration, models were developed using S-PLUS to describe the TMPR in all patients, including those who required rescue medication during the study. Almost all (98.2%) of the patients who did not require rescue medication had MPR (Figure 1, upper left panel). This percentage was not dose-dependent, and the distribution of TMPR was log-normal and dependent on dose (Figure 1, lower left panel). However, only 46.5% of patients who required rescue medication had MPR (Figure 1, upper right panel). This percentage was dose-dependent, and the distribution of TMPR was right-censored by time of rescue medication administration and dependent on dose (Figure 1, lower right panel).

Figure 1.

Upper panel: relationship between the probability of meaningful pain relief and dose in patients who do not require rescue medication (left) and those who do (right). Circles and vertical bars are mean and standard error of observations, respectively. Solid line represents model predictions. Lower panel: relationship between the onset time of meaningful pain relief (TMPR) and dose in patients who do not require rescue medication (left) and those who do (right). Circles are observations and solid line represents model predictions (with 95% confidence interval shown in lower right panel)

TMPR model given requirement for rescue medication

Given a patient required rescue medication, the probability of experiencing MPR is modelled with the following equation:

(13)

where P(MPR) is the probability that a person will experience MPR, P₀ is the probability of MPR at a dose of zero, P_max is the maximum possible MPR probability for a very large dose, Dose_i is the patient's dose, and D50_PMPR is the dose at which half of the maximal MPR probability is achieved. The index i references each patient. The model parameters are logit(P₀), logit(P_max), and log(D50_PMPR). The transformations allows more reliable estimates of parameter precision, taking into account the constraints that P₀ and P_max must be in the interval 0–1, and D50_MPR must be positive.

Assuming the patient required rescue medication and experienced MPR, the TMPR is constrained to be less than the observed time of rescue medication administration, T_Rescue,i. The distribution of individual TMPR observations is modelled with the following equation:

(14)

where LTR₀ is the logarithm of the time ratio between TMPR_i and T_Rescue,i for a placebo dose, LTR_max is the maximum possible logarithm of the time ratio, D50_LTR is the dose at which half of the maximum possible time ratio is achieved, and ε_LTR,i is normally distributed variability with mean 0 and standard deviation σ_LTR.

TMPR model given no rescue medication

Given a patient does not require rescue medication during the study, the probability of experiencing MPR is 98.2% and is not dose dependent, as previously mentioned.

Assuming a patient does not require rescue medication and experiences meaningful pain relief, the TMPR is not constrained and is modelled with the following equation:

(15)

where LT₀ is the logarithm of TMPR for a placebo dose, LT_Slope is the slope relating the influence of Dose on the logarithm of TMPR, and ε_LT,i is normally distributed interindividual variability with mean 0 and standard deviation σ_LT.

Pain relief model validation

Comparison of post hoc pain relief scores with observations was used to validate the pain relief model. The parameter of interest was the total pain relief (TOPAR) score, calculated as the area under the pain relief score vs. time curve over predefined intervals of time following oral dose administration. The predictive performance of the model was assessed by comparing model-based estimates of TOPAR scores calculated from the predicted pain relief scores (i.e. the individual post hoc estimates from NONMEM) and TOPAR scores calculated from the observed pain relief scores over periods of 2, 4, 8, 12 and 24 h after a single oral dose. For patients requiring rescue medication, the last observed pain relief score was carried forward. Using this approach, distributions of the predicted values were compared with the observed values.

Dose selection in Westerners and Japanese

The model was used to predict TMPR and TOPAR scores following various dosing regimens in simulated Western and Japanese populations. Five doses were evaluated including placebo and CS-706 doses of 10, 50, 100 and 200 mg. CS-706 plasma concentrations, COX-1 and COX-2 activity, pain relief scores, onset time of meaningful pain relief and the probability of requiring rescue medication were simulated over a 24-h period following a single dose. The final exposure vs. response models included demographic variables, fixed effects parameters, intersubject variability and residual variability. Demographic variable distributions were chosen to reflect a Japanese population and a Western population (Table 1) [1, 2]. For each dosing scenario and each ethnic group (Japanese and Western), 400 simulations were performed. The only differences between ethnic groups were pharmacokinetic in nature, e.g. body weight or frequency of metabolizing phenotypes. Pharmacodynamic parameters were assumed to be the same [2]. TOPAR scores were calculated and values were summarized using descriptive statistics.

Table 1.

Demographic variables in Japanese and Western populations used in simulations

Characteristic	Proportion of population
	Japanese	Western
Gender (male)	1	0.50
Race (non-White)	1*	0.54
CYP 2D6 (extensive metabolizer, poor/intermediate metabolizer)	0.98, 0.02	0.91, 0.09
CYP 2C9 (normal/extensive hydroxylator, reduced hydroxylator)	0.96, 0.04	0.85, 0.15
	Mean (SD)
Weight (kg)	60.0 (8.0)	72.6 (11.9)

Race:

^*Japanese.

Results

Exploratory analysis

Table 2 describes the baseline characteristics of all patients in the study population.

Table 2.

Baseline characteristics

	Count or median (range)
Characteristic	All	Placebo	Treatment
Dose (mg)	10, 50, 100, 200 mg CS-706, placebo, 400 mg celecoxib	placebo	10, 50, 100 and 200 mg
Number of patients	304	52	201
Postoperative pain intensity (2/3)	121/183	20/32	80/121
Gender (M/F)	111/193	23/29	72/129
Ethnicity (W/B/A/H/O)	181/14/9/95/5	33/4/1/12/2	120/8/7/63/3
Age (years)	22 (18, 36)	21 (18, 31)	21 (18, 36)
Weight (kg)	68.2 (39.1, 134)	68.6 (41.8, 103.6)	67.3 (39.1, 134)
Height (cm)	166 (125, 193)	168 (147, 188)	168 (125, 193)

Pain Intensity: 2, moderate pain; 3, severe pain. Ethnicity: White, Black, Asian, Hispanic, Other.

Figure 2 shows the percentage of patients in each treatment group who did not require rescue medication over time. Subjects in the Phase 2a study population who requested rescue medication during the first 90 min after dosing were encouraged to wait to allow adequate time for study medication to take effect. The plots reveal a greater frequency of patients who did not require rescue medication at 2 h and at 24 h after dose administration with increasing doses.

Figure 2.

Kaplan–Meier plot showing percentage of patients who continued to experience pain relief (i.e. did not require rescue medication) vs. time by dose over 24 h and (inset) over 4 h. Placebo, (); 10 mg, (); 50 mg, (); 100 mg, (); 200 mg, ()

Figure 3 shows bar plots of pain relief scores over time. Inspection of these plots showed a clear dose–response relationship. The placebo group showed a gradually increasing effect that stabilized after about 4 h. In comparison, CS-706 treatment groups showed a greater and more sustained response, with the greatest degree of improvement in pain relief occurring between the 10–50-mg doses. Pain relief vs. time profiles at doses of 100 and 200 mg were similar to that at 50 mg.

Figure 3.

Bar plots showing frequencies of pain relief scores vs. time by dose. pain relief score 0, (); pain relief score 1, (); pain relief score 2, (); pain relief score 3, (); pain relief score 4, ()

Pain relief model

A standard categorical response model incorporating placebo and drug effects was used to describe pain relief. Final model parameter estimates describing the effect of CS-706 treatment on the alleviation of acute postoperative dental pain are presented in Table 3. Figure 4 shows that the predicted pain relief score probabilities (lines) match the observed values (symbols) satisfactorily. In addition, the distribution of the random individual effect on the response was reasonably symmetrical and centred at zero, and suggests that the post hoc individual estimates of pain relief are normally distributed, in accordance with the model assumptions (not shown).

Table 3.

Parameter estimates, standard error of estimates and variability estimates describing the effect of CS-706 on postoperative dental pain relief

Description (units)	Parameter	Estimate	SE	Odds ratio *
Parameters describing pain relief model
Logit of the probability that PR ≥1 extrapolated to time = 0 h	θ1	−3.30†	0.29
Incremental change in logit for PR ≥2	θ2	−2.39	0.11	0.09
Incremental change in logit for PR ≥3	θ3	−1.86	0.09	0.16
Incremental change in logit for PR ≥4	θ4	−3.45	0.11	0.03
Parameters describing placebo response
Maximum extent of placebo response	Ep	12.0	1.2
Rate of stabilization of placebo response over time (h−1)	Kp	0.055	0.009
Intersubject variability	ω2	9.90	1.21
Parameters describing CS-706 response
Maximum extent of CS-706 response	Emax	12.6	0.6
Plasma concentration producing 50% of maximum response (ng ml−1)	EC50	87.0	8.9

^*Odds ratio relative to the next lower PR level is calculated as exp(θ).

^†Corresponds to probability of PR ≥ 1 extrapolated to 0 h = 0.04 or 4%.

Figure 4.

Observed and predicted pain relief score probabilities (PR ≥ i) where i = 0,1, 2, 3, 4 vs. time by dose. P(PR ≥ 1), (□-□-□); P(PR ≥ 2), (▵-▵-▵); P(PR ≥ 3), (▪-▪-▪); P(PR ≥ 4), (▴-▴-▴)

Rescue medication model

The probability of a patient requiring rescue medication was described using a hazard model. Figure 5 shows the shape of the hazard function or the rate of requiring rescue medication at the last pain relief score for the observed data.

Figure 5.

Upper panel: the rate of rescue medication per day vs. pain relief score showing the shape of the hazard function. N is the number of observations, rescue is the number of rescue medication events. Lower panel: mean (SE) observed (circles and vertical lines) and model predicted probabilities (solid line) of requiring rescue medication vs. pain relief score. Observed probability calculated as number of rescue events divided by N. The probability of requiring rescue medication in the next study interval given no prior rescue medication is a function of the rate of rescue medication per day

The model adequately described the data (Figure 5; lower panel) and parameter estimates are presented in Table 4. The model suggests that patients with a pain relief score of 0 have a hazard of 2.08, and therefore a 50% chance of requiring rescue medication within 20 min, and that because λ is 0.2, this rescue time increases fivefold for every unit increase in PR score. The mean predicted probabilities for requiring rescue medication matched the mean observed values satisfactorily (Figure 5, lower panel).

Table 4.

Parameter estimates and standard errors of estimates for the rescue medication model

Description (units)	Parameter	Estimate	SE *
Discontinuation hazard at PR = 0 (h−1)	h0	2.08	0.21
Fractional decrease in discontinuation hazard per unit increment in PR	7	0.201	0.011

^*Standard error of parameter estimate.

Onset of meaningful pain relief model

Parameter estimates for the TMPR model are presented in Table 5. In patients who did not require rescue medication, median TMPR was 1.6 h for a placebo dose (calculated as the antilogarithm of LT₀), and decreased by 3.5% for every 10-mg increase in dose. In patients who required rescue medication within the 24-h period, on average TMPR was 39% of the time of rescue medication administration on placebo (calculated as the antilogarithm of LTR₀), decreasing to a minimum possible fraction of 14%. Figure 1 shows that the model adequately describes the probability of MPR as well as the TMPR.

Table 5.

Parameter estimates for the onset time of meaningful pain relief model

Description (units)	Parameter	Estimate	95% CI *
Patient requires rescue medication
Probability of MPR on placebo (%)	P0	16	(10, 26)
Maximum possible probability of MPR	Pmax	72	(59, 83)
Dose at which half maximal MPR is achieved (mg)	D50PMPR	8.8	(3.0, 26.1)
Logarithm of ratio between TMPR and time of rescue medication on placebo	LTR0	−0.95	(−1.42, −0.48)
Logarithm of ratio between TMPR and time of rescue medication, maximum possible decrease	LTRmax	−1.00	(−1.52, −0.47)
Dose at which half maximal TMPR to time of rescue medication ratio is achieved (mg)	D50LTR	5.8	(0.9, 35.8)
Residual variability in the logarithm of the time ratio	σLTR	0.64	Not estimated
Patient does not require rescue medication
Probability of MPR (%)	PMPR	98.2	(95.0, 99.3)
Logarithm of TMPR on placebo	LT0	0.45	(0.23, 0.67)
Slope relating dose to logarithm of TMPR	LTSlope	−0.0035	[−0.0053,−0.0018]
Residual variability in the logarithm of TMPR	σLT	0.69	Not estimated

^*95% confidence intervals based on the parameter estimate ± 1.96 × SE. Skewed confidence intervals occur when transformed parameters are estimated.

Pain relief model validation

The predictive performance of the pain relief model was assessed by comparing total pain relief (TOPAR) scores, calculated as the time-weighted sum of predicted pain relief scores (i.e. the individual post hoc estimates from NONMEM) and TOPAR scores calculated from the observed pain relief scores over periods of 2, 4, 8, 12 and 24 h after a single oral dose. For the pain relief model, shrinkage toward the mean was calculated to be 10%; it was therefore considered appropriate to the use of post hoc estimates of pain relief for model validation [7]. There was good agreement between the observed and predicted TOPAR scores (Figure 6).

Figure 6.

Scatter plots showing predicted vs. observed total pain relief (TOPAR) scores. Line of identity is shown. TOPAR scores are the areas under the pain relief score vs. time curve over periods of 2, 4, 8, 12 and 24 h after a single oral dose

Dose selection in Westerners and Japanese

Table 6 shows simulated time to onset of meaningful pain relief, by dose, in Japanese and Western patients, indicating that both groups are expected to have similar onset of pain relief. In addition, distributions of TOPAR scores, calculated up to 2, 4, 8 and 24 h in Japanese and Western populations, were similar (not shown). These response characteristics are similar despite lower predicted CS-706 exposure for Japanese subjects [1].

Table 6.

Estimated time to onset of meaningful pain relief, by dose, in Japanese and Western patients

	Mean (SEM) Time (h)
Dose	Japanese	Western
Placebo	2.46 (0.10)	2.56 (0.11)
10 mg	2.37 (0.14)	2.28 (0.13)
50 mg	2.45 (0.14)	2.40 (0.15)
100 mg	2.06 (0.15)	2.21 (0.16)
200 mg	1.90 (0.16)	1.70 (0.14)

Figure 7 shows the influence of dose on the probability of achieving a pain relief score of at least 1, 2, 3 or 4 at 1.5 h postdose, together with the probability of achieving meaningful pain relief and the probability of requiring rescue medication during the study. Overlaying simulations on observed data showed that the models performed reasonably (not shown). The probability of a patient requiring rescue medication was determined to be a function of the last observed pain relief score and it was observed to decrease over time. This probability is <16% for patients with a pain relief score ≥2. The probability of experiencing a PR score of ≥2 at 1.5 h after dose administration increases with increasing dose (see Figure 4). The 1.5 h time point is the earliest point of interest, because this is when CS-706 achieves maximum concentrations, on average, and all patients are still in the study [1]. A plot of predicted probability of PR score ≥2 at 1.5 h after dose administration vs. dose reveals a sigmoidal relationship with the greatest increase in response between the 0 (placebo) and 50-mg dose. The gain in response is substantially reduced as the dose increases above 50 mg (Figure 7).

Figure 7.

Probability of pain relief (PR) score greater than 1, 2, 3 and 4 at 1.5 h postdose, probability of achieving meaningful pain relief (circles) and probability of requiring rescue medication (squares) vs. dose

Discussion

A pain relief model was developed to describe the effect of CS-706 treatment on relief of acute postoperative dental pain. The resulting model was a categorical response model and included placebo and drug effect models. There was a clear dose–response relationship. The placebo group showed a gradually increasing effect that stabilized after about 4 h. Therefore, the placebo response over time was described by a first-order increase in pain relief that achieved a stable response. In comparison, CS-706 treatment groups showed a greater and more sustained response, with the greatest degree of improvement in pain relief occurring between 10 and 50 mg. Little gain in response was obtained between 100- and 200-mg doses.

The effect of CS-706 plasma concentration on dental pain relief was described using an E_max model. The plasma concentration of CS-706 producing 50% of the maximum response was estimated to be 87 ng ml⁻¹, corresponding to the median peak plasma concentration achieved after a single oral dose of 50 mg CS-706.

Based on model parameters (Table 5), the probability of experiencing MPR was 98% in patients who remained in the study for its entire duration (up to 24 h postdose) and did not require rescue medication, and the distribution of TMPR was log-normal and linearly dependent on dose. In patients who required rescue medication within the 24-h period, the overall probability of experiencing MPR was 47%. This probability was dose-dependent, ranging between 16% on placebo up to a maximum achievable probability of 72%. In these patients, log(TMPR) depended on the time that rescue medication was required and increased with dose.

This report models onset time as a function of dose, whether or not the patient requests rescue medication, and the time of rescue medication. Modelling the onset of pain relief is complex because the time of onset is influenced by rapidly changing plasma concentration profiles, potential lag times between plasma concentrations and pain relief, and individual variability in pharmacodynamics. Previous models have quantified onset in terms of pain relief, e.g. the time at which 50% of patients achieve a 75% probability that pain relief is ≥2 [4]. Incorporating parametric hazard models may also be suitable for modelling onset time.

Lee and coworkers have recently reported that variability in expression of the COX genes (PTGS1 and PTGS2) and functional polymorphisms in the promoter region of PTGS2 may be important determinants of an individual's analgesic response to COX-2 inhibitors [8]. Based on the results of Lee and coworkers [8], individuals who are major allele homozygotes for PTGS2 SNP2 are likely to experience meaningful pain relief following CS-706 administration, whereas individuals who are minor allele homozygotes or heterozygotes are expected to show less benefit.

In consideration of models for the clinical end-points of interest, probability of PR, TMPR and rate of requirement for rescue medication, the optimal analgesic dose of 50 mg CS-706 provides rapid and prolonged pain relief for the management of acute dental pain. Based on the results of simulations from the model, Japanese patients are expected to experience a similar pain response and TMPR as Western patients (Table 6), illustrating that the model may be used for dose selection in other patient subpopulations.

In conclusion, a novel modelling approach to capture the multidimensionality of pain relief was applied for a COX-2 inhibitor. The analysis permitted compilation of dose vs. response curves for multiple end-points to facilitate dose selection decisions and to provide a framework to bridge Western data to the Japanese population.

Competing interests

S.R., K.T., J.M. and D.S. are employees of Daiichi Sankyo. At the time of this work, H.K., K.S. and R.W. were employees of Pharsight Corporation and were retained by Sankyo to provide scientific consulting services on CS-706.