A Model-Based Dose–Response Meta-Analysis of Ocular Hypotensive Agents as a Drug Development Tool to Evaluate New Therapies in Glaucoma

Abstract

Purpose:

To characterize dose and response for intraocular pressure (IOP) reduction and incidence of hyperemia using a model-based meta-analysis of IOP-lowering monotherapy studies to evaluate new ocular antihypertensive therapies for glaucoma.

Methods:

Published randomized controlled trials, regulatory documents, and sponsor reports of IOP-lowering monotherapies were used to develop dose–response models to characterize efficacy (IOP change from baseline) and safety (incidence of hyperemia) profiles.

Results:

The meta-analysis for efficacy included 31 trials with 6,516 patients receiving bimatoprost, latanoprost, travoprost, timolol, or placebo. Estimated IOP reduction with placebo was −2.01 mmHg. Maximal IOP reduction was similar among the prostaglandin analogs (estimate, −6.27 mmHg; baseline, 25 mmHg). Estimated median effective IOP-lowering dose (ED₅₀) was 0.002%, 0.00098%, and 0.00063% daily with bimatoprost, latanoprost, and travoprost, respectively. The hyperemia (safety) analysis included 25 trials with 6,244 patients. Typical maximal estimated difference between drug and placebo was 43%, and estimated ED₅₀ of 0.011%, 0.014%, and 0.0015% daily for bimatoprost, latanoprost, and travoprost, respectively. Latanoprost treatment was predicted to incur the lowest rate of hyperemia of the prostaglandins, for equivalent IOP reduction.

Conclusions:

Model-based meta-analyses for IOP reduction and incidence of hyperemia among prostaglandin analogs are well described by maximal efficacy models and can provide a useful methodology for evaluating glaucoma therapies.

Introduction

Over the past 30 years, the development of compounds for the treatment of glaucoma has focused on topical agents that reduce elevated intraocular pressure (IOP), a central factor leading to the loss of retinal ganglion cells and visual field deficits.¹ Currently, the most commonly used drugs for long-term management of glaucoma and ocular hypertension include beta-blockers, such as timolol, and prostaglandin analogs, such as latanoprost, bimatoprost, and travoprost.²

New topical agents continue to be evaluated, with the objective of improving the efficacy and safety over existing therapies. The accepted approach for such evaluations is a randomized, controlled clinical trial, usually comparing a novel agent against the established standard of care. However, data generated from such trials are limited since only a relatively small number of treatment groups can be included and a full dose–response relationship may not be characterized. As a result, key parameters, such as the maximal efficacy (E_max) of the agent, and the dose required for half-maximal response, that is, the amount to produce a specific effect which is 50% of the E_max (ED₅₀), cannot be calculated directly, but instead are estimated from trial data; similar constraints apply to questions of dose-related toxicity and to the comparison of the new agent to existing drugs.

The present study focused on developing a general mathematical model that would allow characterization of these key pharmacodynamic parameters not only for existing glaucoma medications but also allow comparisons to new products under development. A meta-analysis model would permit an evaluation of questions about dose and response, morning versus evening dosing, and comparison with treatments not included in a current clinical trial, as well as assist in studying higher doses. Initially, a pharmacodynamic model to determine the dose–response curves of prostaglandin analogs as a class of agents and the beta-blocker timolol was created. This analysis focused on IOP lowering as the efficacy measure, whereas a separate meta-analysis examined the incidence of hyperemia as the principal indicator of safety, with E_max and ED₅₀ as the key model parameters for both. This model could then be used to characterize these same parameters for a novel compound that is in development. An updated model could be used both to characterize the overall dose–response curve and to compare the model parameters (E_max, ED₅₀) for both efficacy and safety. By comparing the ED₅₀ of the respective medications for efficacy and safety, an estimate for a therapeutic index of existing IOP-lowering agents can be determined and used for comparison with that of a new agent.

Methods

A literature search was conducted using MEDLINE and similar databases for reports from clinical trials on timolol and the prostaglandin analogs bimatoprost, latanoprost, and travoprost published in English from 1990 through 2007 that evaluated medical treatments for open-angle glaucoma or ocular hypertension. Information from 28 published studies was compiled into an initial database. Additional IOP, hyperemia, and covariate data from studies of bimatoprost and travoprost were retrieved from the Summary Basis of Approval documents of the New Drug Applications published on the US Food and Drug Administration Center for Drug Evaluation and Research website (www.fda.gov/cder). Data from unpublished reports of a latanoprost clinical study were identified and added to the database, bringing the total number of trials included to 38. All trials identified reported adherence to the Declaration of Helsinki.

Results on IOP, hyperemia, dosing, and covariates were extracted according to a prespecified protocol. All data were examined carefully for errors, and subgroup or duplicate information for IOP and hyperemia endpoints was removed. To create the final analysis database, the initial search results were filtered and excluded if they included the following criteria: nonrandomized/uncontrolled trials, healthy volunteer trials; open-label trials/extensions; combination treatments; treatments other than timolol, latanoprost, bimatoprost, or travoprost; on-treatment measurements taken within the first 6 days of therapy; washout measurements taken >24 h after daily and >12 h after twice-daily dosing; and percentage change from baseline data. The final analysis database included 31 trials for the efficacy analysis and 25 trials for the safety analysis (listed in the Appendix), and contained detailed information on the efficacy and safety outcomes, data sources, and trial and patient characteristics.

Efficacy endpoint

The primary efficacy endpoint was the absolute change from baseline in the IOP measured at a specific clock time during the day after at least 1 week of treatment. Results of mean IOP over several clock times (mean diurnal) were excluded from the analysis. For trials reporting data from both sitting and supine positions, IOP measurements in the sitting position were used in the analysis.

Efficacy data were analyzed according to the following general dose–response E_max model³: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} { \rm Equation } \ 1 : \ IOP_ { ijkl } = E_0 + \frac { E_ { \max } \cdot Dose_ { ijk } } { Dose_ { ijk } + ED_ { 50 } } + \eta_i + \varepsilon_ { ijkl } \end{align*} \end{document}

where

(1) IOP_ijkl is the observed mean change from baseline of the ith trial for week j in the kth treatment arm at clock-time l.

(2) E₀ is the IOP placebo response.

(3) E_max is the maximal drug effect, reflecting the maximal difference in IOP response between placebo and active treatment.

(4) Dose is the total daily dose of drug.

(5) ED₅₀ is the dose to achieve an IOP response that is 50% of E_max.

(6) \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\eta_i$$ \end{document} is a trial-specific random effect to account for IOP heterogeneity across trials and is assumed to be normally distributed with mean 0 and variance ω².

(7) \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\varepsilon_{ij}$$ \end{document} is the residual IOP variability with variance σ²/N_ik.

(8) N_ik is the sample size of the kth arm in the ith trial.

The correlation (ρ) between repeated observations (with time) for a specific group of patients in a treatment arm was also estimated. Inclusion of this correlation accounts for the adequate weighing of multiple observations in the same group of patients. The impact of trial, patient, drug, drug class, and treatment characteristics on E₀, E_max, and ED₅₀ of the dose–response relationship was evaluated. The base model assumed a different ED₅₀ but a similar E_max for each drug within a class.

Safety endpoint

As hyperemia is the most commonly reported adverse event in patients receiving prostaglandin analogs, the safety analyses were based on the incidence of hyperemia (number of patients) that was reported as an adverse event within a treatment arm in the clinical trial dataset. If a specific trial reported a graded hyperemia score, the number of patients with scores greater or equal to mild hyperemia was used. The following equation, which does not include a time course (applied in IOP measurements), was used to describe these data. \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} { \rm Equation } \ 2 : \ P ( Event ) _ { ij } = f \left\{ E_0 + \frac { E_ { \max } \cdot Dose_ { ij } } { Dose_ { ij } + ED_ { 50 , drug } } + \eta_i \right\} \end{align*} \end{document}

In this equation, P(Event)_ij represents the probability of a patient having hyperemia in the jth treatment arm of the ith trial at a total daily dose, Dose_ij. The number of patients with events is assumed to follow a binomial distribution given the probability of the event and the sample size (N_ij). The hyperemia placebo response (E₀) was dependent on a trial-specific random effect ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\eta_i$$ \end{document} ) assumed to be normally distributed with mean 0 and variance ω², and f¹ represents the inverse logit transformation to constrain probabilities between 0 and 1.

The impact of patient, drug, and treatment characteristics on E₀, E_max, and ED₅₀ of the dose–response relationship was evaluated. The base model assumed a different ED₅₀ but a similar E_max for each drug within a class.

Therapeutic index

The values derived from the efficacy and safety models were combined to create a therapeutic index for an ocular hypotensive agent, defined as the ratio of the dose of a drug that provides an acceptable risk of hyperemia to that which meets the required level of IOP reduction. In the present study, the E_max models for IOP reduction and hyperemia incidence were employed to determine the relative therapeutic indices of the prostaglandin analogs, in which the therapeutic index was defined as the ratio of ED₅₀ for hyperemia and the ED₅₀ for IOP lowering. This procedure was valid, even without considering whether the efficacy (IOP lowering) or safety (hyperemia) actually was acceptable at the ED₅₀, because the objective was to compare relative therapeutic indices among the various drugs. This relative therapeutic index is independent of acceptable hyperemia and IOP lowering if the drugs share a similar E_max.

Statistical analysis

The nonlinear, mixed-effect regression function provided in S-PLUS 6.2 (Insightful Corp., Palo Alto, CA) was used to calculate maximum likelihood estimates of the model parameters of the IOP model. The software package NONMEM, version VI, level 1.0 (Globomax, Hanover, MD), was used to estimate the hyperemia model. Model simulation and graphics were also conducted using S-PLUS 6.2. For both endpoints, a base model structure characterizing the dose and response was developed first. For the IOP model, the time course of placebo was also included in the base model. After the base model was built, the following explanatory covariates were tested for their impact on the model parameters: treatment regimen, baseline IOP (IOP model), race, age, sex, time after first dose, time of day, and time after each dose. Missing baseline or time-independent covariates (race, age, and sex) used the average of all the trials. Missing race information was estimated based on typical racial profiles of the study region.

A stepwise addition and deletion model selection strategy was used, and linear as well as nonlinear relationships between the explanatory variables and model parameters were evaluated. Model selection was performed on the basis of a log likelihood ratio test at an acceptance P value of 0.01. The clinical relevance of any relationship was also considered. Confidence intervals (CIs) were derived from the variance matrix of the parameter estimates. A 90% CI was taken from the 5th to the 95th percentile. Diagnostic plots and procedures were produced to evaluate the validity of the models.

The models were used to predict the mean IOP response and incidence of hyperemia in the patient population and the associated uncertainty as a function of dose and other significant covariates. For model predictions, a total of 2,500 model parameters were sampled from the variance matrix of the parameter estimates.

Results

Dose–response E_max model for prostaglandin analogs and timolol efficacy for modeling IOP response

The data set for modeling IOP responses is summarized in Table 1. The database totaled 766 summary data points from 90 treatment arms in 31 trials involving 30 different treatment regimens in 6,516 patients.

Table 1.

Summary of Analysis Data Set for IOP Reduction

Characteristics	Placebo	Bimatoprost	Latanoprost	Timolol	Travoprost
No. of trials	10	12	20	15	10
No. of arms	10	20	28	15	17
No. of regimens	3	9	9	3	6
No. of data points	70	177	172	147	200
No. of patients	171	1,617	1,502	1,547	1,679
Daily dose, median % (range)	0 (0–0)	0.03 (0.003–0.2)	0.005 (0.0012–0.023)	1 (0.5–1)	0.004 (0.001–0.006)
Treatment days, n (range)	14 (6–29)	28 (6–180)	28 (6–360)	45 (6–360)	30 (7–360)
BID/QAM/QPM, n	72/16/83	579/16/1,082	303/272/1,110	1,313/39/195	0/33/1,646

BID/QAM/QPM, twice daily/once daily in the morning/once daily in the evening; IOP, intraocular pressure.

Final IOP model

Parameter estimates for the final IOP model, including statistically significant covariate effects for placebo and E_max, are shown in Table 2. For placebo response, the final covariate model is as follows: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}{ \rm Equation} \ 3 : \ E_{0} = E_{0, 1} + E_{0, 2} \cdot ( base - 25 ) + E_{0, 3} \cdot ( day - 90 )\end{align*} \end{document}

Table 2.

Maximum Likelihood Model Parameter Estimates for the Final Model of IOP Change from Baseline and 90% CIs

Parameter	Estimate (90% CI)
E_0,1 intercept, placebo (mmHg)	−2.01 (−2.58 to −1.45)
E_0,2 base–25 (mmHg)	−0.394 (−0.502 to −0.287)
E_0,3 day–90 (mmHg/day)	0.000848 (0.000525 to 0.00117)
E_max,1 intercept (mmHg)	−6.27 (−6.82 to −5.72)
E_max,2 base–25 (mmHg)	−0.235 (−0.362 to −0.109)
E_max,3 BID (mmHg)	0.844 (0.584 to 1.1)
E_max,4 QAM (mmHg)	1.18 (0.799 to 1.56)
ED_50,1 bimatoprost (%/day)	0.0020 (0.0009 to 0.0041)
ED_50,2 latanoprost (%/day)	0.00098 (0.00068 to 0.0014)
ED_50,3 travoprost (%/day)	0.00063 (0.00047 to 0.00084)
ED_50,4 timolol (%/day)	0.36 (0.28 to 0.45)
Trial-to-trial variability (mmHg)	1.1 (0.869 to 1.4)
Correlation, ρ	0.383 (0.343 to 0.424)
Residual variability (mmHg)	4.75 (4.51 to 5.00)

BID, twice daily; CI, confidence interval; E₀, IOP placebo response; ED_50, dose required for half-maximal efficacy; E_max, maximal drug effect; ρ, correlation between repeated observations (with time) for patients within a treatment arm; QAM, every morning.

The estimated placebo response for a baseline IOP of 25 mmHg is −2.01 mmHg (90% CI, −2.58 to −1.45). As seen in Equation 3, the placebo response increased with increasing baseline IOP (base) and decreased with time after the first dose (day). It should be noted that the response to an active treatment included the placebo response (Equation 1); however, the difference between active treatment and placebo was not affected by the magnitude of the latter.

With respect to E_max, the final model was as follows: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}&{\rm Equation} \, 4 : \\& \quad E_{\max} = E_{\max , 1} + E_{\max , 2} \cdot ( base - 25 )\\& \quad\quad\quad + E_{\max , 3} \cdot ( freq = BID ) + E_{\max , 4} \cdot ( freq = QAM )\end{align*} \end{document}

The potential maximal IOP change relative to placebo (E_max) was estimated to be −6.27 mmHg (90% CI, −6.82 to −5.72); furthermore, from the E_max,2 term, E_max was found to increase with higher baseline IOP (base). This indicates that higher baseline IOP results in a greater potential for IOP reduction when compared with placebo. There was no significant difference in E_max among the 3 prostaglandin analogs. Time of administration (every morning vs. every evening) and dosing frequency (once every day vs. twice daily) had significant impact on maximal IOP reduction. Across all drugs (prostaglandin analogs and beta-blocker), twice-daily dosing provided a smaller effect than every-evening dosing. These results suggest that tolerance develops to the IOP-lowering effect of prostaglandin analogs. The final model suggests that every-morning dosing and twice-daily dosing result in less IOP reduction than every-evening dosing. The impact of time of administration and dosing frequency was similar among the 3 prostaglandin analogs. There was significant between-trial heterogeneity in the mean effect, with a standard deviation of between-trial variability estimated at 1.1 mmHg. Values of ED₅₀ for timolol, bimatoprost, latanoprost, and travoprost were 0.36%, 0.002%, 0.00098%, and 0.00063%, respectively.

Diagnostics for model evaluation did not exhibit any apparent model misspecification. When the model performance was examined for all trials and treatments as change from baseline in each trial and the model prediction, there was good agreement between the observed IOP and the prediction.

IOP dose–response relationship

The observed dose–response relationships for the 4 drugs, together with the prediction from the E_max model, are shown in Figure 1. There is good agreement between the observed and predicted values, with all 3 prostaglandin analogs producing similar maximum IOP lowering and differing only in the total daily dose required for this effect; timolol did not reduce IOP to the same extent. The similarity of dose–response curves for equipotent doses of the prostaglandin analogs is further emphasized in Figure 2, matching the predictions of the E_max model. In addition, the model showed that for timing of dosing, E_max is obtained by the evening dosing compared with morning or twice-daily administration. This also indicates that the impact of the dose administration time on the dose and response was similar among agents. The analysis of the impact of the time of day on the prostaglandin dose–response relationship for IOP reduction, normalized to bimatoprost for potency, showed that the highest IOP reduction occurred at 8–9 am and the lowest occurred between evening and midnight. When the dose of a prostaglandin analog was normalized to bimatoprost on the basis of relative potency, the dose and response increased with baseline IOP values. There was no clear impact of the final covariate of interest time postdose on IOP for all 4 compounds. This suggests that the drug response was fairly constant throughout the day, and all variation in response during the day was due to the diurnal variation in baseline IOP.

FIG. 1.

Dose and response of every-evening administration of prostaglandin analogs and twice-daily administration of timolol. Solid lines are the model predictions normalized to 8 am and every-evening administration of the prostaglandin analogs and twice-daily administration of timolol. The symbols are the mean observed IOP values for a specific daily dose after adjustment for influential covariates with an ∼95% confidence interval. IOP, intraocular pressure.

FIG. 2.

Dose and response of every-evening administration of the prostaglandin analogs. The solid line is the model-predicted dose–response relationship for bimatoprost normalized to 8 am and every-evening administration. The symbols are the mean observed IOP values with an ∼95% confidence interval for a specific daily dose of each of the prostaglandin analogs after adjustment for influential covariates and relative potency. eq, equivalent.

Diurnal variation in IOP change from baseline

Diurnal variation among several treatment regimens is shown in Figure 3, together with predicted values from the model, when normalized to the typical IOP diurnal variation. The variation in change from baseline over the day was explained essentially by diurnal variation in baseline IOP; E_max (reduction from baseline) was seen in the morning, owing to the maximal baseline IOP occurring in the morning.

FIG. 3.

IOP reduction at different times of the day for the standard treatment regimens. The solid lines are the model prediction normalized to the typical baseline IOP diurnal variation pattern, and the symbols represent the mean observed values after adjustment for the trial-specific random effect with an ∼95% confidence interval. BID, twice daily; QPM, every evening.

Dose–response model for prostaglandin analog and timolol safety trial database for hyperemia incidence modeling

The database for hyperemia totaled 76 summary data points from 76 treatment arms of 25 trials (listed in Appendix), with 29 unique treatment regimens administered to 6,244 patients (Table 3).

Table 3.

Summary of Hyperemia Analysis Data Set

Characteristics	Placebo	Bimatoprost	Latanoprost	Timolol	Travoprost
No. of trials	9	10	15	13	7
No. of arms	10	18	21	13	14
No. of patients	190	1,559	1,379	1,503	1,613
No. of patients with hyperemia	14	683	271	133	568
Daily dose, % (range)	0	0.03 (0.006–0.2)	0.005 (0.0012–0.023)	1.0 (0.5–1)	0.004 (0.001–0.006)
Treatment, no. of days (range)	21 (5–29)	30 (7–180)	28 (5–360)	180 (7–360)	70 (14–360)
Age, years (range)	62 (55–67)	61 (56–69)	64 (56–70)	63 (58–66)	64 (63–66)
BID/QAM/QPM/QPM and QAM	97/16/77/0	579/16/964/0	301/89/806/183	1,264/39/200/0	0/33/1,580/0
Hyperemia/≥mild	114/76	1,559/0	1,219/160	1,503/0	1,613/0

The daily dose and treatment days show the median and range across the trials. The treatment regimen shows the number of patients receiving each regimen. The adverse event (hyperemia)/≥mild row shows the number of patients for each assessment method.

BID/QAM/QPM/QPM and QAM, twice daily/once daily in the morning/once daily in the evening/once daily in the evening and once daily in the morning.

These data were used in the model-building process to estimate parameters for Equation 2; they included E_max and ED₅₀ for the prostaglandin analogs (since they led to an increase in hyperemic events) as well as E₀, the placebo-related incidence of hyperemia. Timolol did not increase the incidence of hyperemia over that seen with placebo; the duration of treatment and dosing frequency also had no effect. The final parameters for the hyperemia model are shown in Table 4. The ED₅₀ values for bimatoprost, latanoprost, and travoprost were estimated as 0.011%, 0.014%, and 0.0015% daily, respectively.

Table 4.

Final Model Parameter for the Incidence of Hyperemia

Parameter	Estimate (90% CI)
E₀ (%)	7.7 (5.7–10.3)
ED₅₀ bimatoprost (%/day)	0.011 (0.0058–0.021)
ED₅₀ latanoprost (%/day)	0.014 (0.0091–0.022)
ED₅₀ travoprost (%/day)	0.0015 (0.00088–0.0027)
E_max (%)	43 (32.0–53.0)
Trial-to-trial variability (ω²)	0.83 (0.31–1.05)

Hyperemia dose and response

Application of the E_max model for the incidence of hyperemia with the prostaglandin analogs is shown in Figure 4. Note that the solid lines indicate the predicted dose–response relationship for a typical trial after adjusting for the trial-specific random effect ( \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} $$\eta_i$$ \end{document} ) in Equation 2. Among patients treated with the 3 prostaglandin analogs, latanoprost 0.005% dosed once daily in the evening was found to be associated with fewer incidences of hyperemia than either bimatoprost 0.03% or travoprost 0.004%.

FIG. 4.

Hyperemia dose–response relationship of prostaglandin analogs and timolol. The symbols reflect the mean observed incidence of hyperemia and an ∼95% confidence interval after adjusting for the trial-specific random effect. The solid line reflects the predicted dose–response relationship for a typical trial.

Therapeutic index of prostaglandin analogs

Because the maximal response for IOP reduction and the incidence of hyperemia were similar between the prostaglandin analogs, the therapeutic index described in the Methods section provides a comparison of the relative efficacy and tolerability among compounds. The therapeutic index—namely, the ratio of ED₅₀ for hyperemia and the ED₅₀ for IOP lowering—is high when there is a greater difference between the dose range that provides an adequate reduction in IOP and the dose range that produces a high incidence of hyperemia. The therapeutic indexes for bimatoprost, latanoprost, and travoprost (Table 5) indicate that latanoprost treatment would lead to the lowest incidence of hyperemia for a given amount of IOP lowering, and travoprost would invoke the highest incidence of hyperemia for a given IOP lowering.

Table 5.

ED₅₀ and 90% CI for IOP Reduction and Incidence of Hyperemia of the Prostaglandin Analogs

Drug	IOP ED₅₀, %/day (90% CI)	Hyperemia ED₅₀, %/day (90%CI)	Ratio (therapeutic index)
Bimatoprost	0.0020 (0.0009–0.0041)	0.011 (0.0058–0.021)	5.5 (2.1–15.0)
Latanoprost	0.00098 (0.00068–0.0014)	0.014 (0.0091–0.022)	14 (8.0–25.0)
Travoprost	0.00063 (0.00047–0.00084)	0.0015 (0.00088–0.0027)	2.4 (1.3–4.6)

Discussion

The principal objective of the model-based meta-analysis was to develop a pharmacodynamic model that accurately characterized dose–response relationships for both IOP lowering and incidence of hyperemia using data from the broad class of prostaglandin analogs and the beta-blocker timolol. The resultant model, based on a meta-analysis of data from a total of 32 trials, fulfilled these requirements. The dose–response relationships for both IOP lowering and incidence of hyperemia were well described by an E_max model.

Individual clinical trials are limited in scope and cannot include all the treatment groups that may be of interest. In contrast, with these models, comparisons with other therapies and regimens not included in the clinical trial can be performed. This approach facilitates the evaluation of new IOP-lowering compounds in a broader context than just a single clinical trial of a compound. The model-based meta-analysis can provide additional comparisons and insight for a project's decision-making process. When the meta-analysis models are updated with the new trial data, simulations can be performed that provide estimates of relevant comparisons and the probability of technical success for the new therapy against response targets related to the product profile.^4–6

Some consistent effects emerged from the meta-analysis with regard to IOP reduction for the included therapies. The large variation observed in reducing IOP over time throughout the day appeared to be explained essentially by diurnal variation in baseline IOP. Also, the prostaglandin analogs appear to share a similar E_max for IOP lowering and hyperemia and only differ in the dose required to produce a certain effect. Having a similar E_max allows the calculation of a therapeutic index that can be used to compare the risk/benefit ratio of prostaglandin analogs. The higher therapeutic index for latanoprost indicates that this therapy has a lower incidence of hyperemia than bimatoprost or travoprost at doses providing equivalent IOP lowering. Another prostaglandin effect was observed as follows: a higher reduction in IOP occurred when the patient was dosed once daily in the evening compared with morning dosing.

In conclusion, the use of model-based meta-analyses for comparing competing therapies is an important and useful tool in drug development. This approach permitted a new IOP-lowering therapy to be compared with multiple agents currently used in clinical practice. This methodology would have utility in evaluating any IOP-lowering agent during the drug development process.

Footnotes

Acknowledgments

Editorial support, including assistance in the manuscript development and styling for the journal, was provided by Lauren Swenarchuk, PhD, of Zola Associates, and Mukund Nori, PhD, MBA, CMPP, of Engage Scientific Solutions and was funded by Pfizer Inc. This research was supported by Pfizer Inc, New York, New York.

Author Disclosure Statement

S.R. is an employee of Pfizer Inc; J.W.M. was contracted by Pfizer Inc, and reports no other disclosures; H.L. was contracted by Pfizer Inc, and reports no other disclosures; D.J.N. is an employee of Pfizer Inc.

Appendix

The final analysis database included 32 trials, with 31 trials for the efficacy analysis (*) and 25 trials for the safety analysis (†).

*^†A 1-month, single-center, double-masked, randomized, parallel, vehicle-controlled, morning dosing, pilot study of the safety and efficacy of AGN 192024 0.03% ophthalmic solution in subjects with open-angle glaucoma or ocular hypertension (192024-003). NDA (New Drug Application) 21-275 medical review. 2000.

*^†A 1-month, investigator-masked, parallel, randomized safety and efficacy study of AGN 192024 0.003%, 0.01% and 0.03% ophthalmic solutions compared to its vehicle and timolol 0.5% in subjects with open-angle glaucoma or ocular hypertension (192024-001). NDA 21-275 medical review. 2000.

*^†A 6-month, multicenter, triple-masked, placebo-controlled adjunctive therapy study of the safety and efficacy of AL-6221 0.0015% and AL-6221 0.004% ophthalmic solution in patients with open-angle glaucoma or ocular hypertension maintained on timoptic 0. (C97-73). NDA 21-257 medical review. 2001.

*^†A 9-month, triple-masked, parallel-group, primary therapy study of the safety and efficacy of AL-6221 0.0015% and AL-6211 0.004% compared to timoptic 0.5% in patients with open-angle glaucoma or ocular hypertension (C97-79). NDA 21-257 medical review. 2001.

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A Model-Based Dose–Response Meta-Analysis of Ocular Hypotensive Agents as a Drug Development Tool to Evaluate New Therapies in Glaucoma

Abstract

Abstract

Purpose:

Methods:

Results:

Conclusions:

Introduction

Methods

Efficacy endpoint

Safety endpoint

Therapeutic index

Statistical analysis

Results

Dose–response Emax model for prostaglandin analogs and timolol efficacy for modeling IOP response

Final IOP model

IOP dose–response relationship

Diurnal variation in IOP change from baseline

Dose–response model for prostaglandin analog and timolol safety trial database for hyperemia incidence modeling

Hyperemia dose and response

Therapeutic index of prostaglandin analogs

Discussion

Footnotes

Acknowledgments

Author Disclosure Statement

Appendix

References

Dose–response E_max model for prostaglandin analogs and timolol efficacy for modeling IOP response