Exposure-Response Models

The second example involves the impact of population modeling of exposure-response data on an 

FIGURE 10.5 Expected percentage reduction in seizure frequency with increasing dose in patients who are likely to respond, expressed as percentiles. (Adapted from Miller R, Frame B, Corrigan B, Burger P, Bockbrader H, Garofalo E, Lalonde R. Clin Pharmacol Ther. 2003 73 491-505, with permission from the American Society for Clinical Pharmacology and Therapeutics.) 

FDA approval. Usually evidence of efficacy from two or more adequate and well-controlled clinical trials along with safety information is required for the regulatory approval of a new indication for a drug. The idea is that replication of the results of a single trial is needed to rule out the possibility that a finding of efficacy in a single trial is due to chance. This example describes the application of exposure-response analysis to establish an FDA-approvable claim of drug efficacy based on a dose-reponse relationship that was obtained from two pivotal clinical trials that used different final-treatment doses. 

Response data for two studies were submitted to the FDA for approval for the treatment of postherpetic neuralgia (PHN). Both studies were randomized, double-blind, placebo-controlled, multicenter studies that evaluated the safety and efficacy of gabapentin administered orally three times a day, compared with placebo. In both studies, the patients were titrated to their final-treatment dose by the end of either week 

4 weeks. However, in one study, the final-treatment dose was 3600 mg/day, and in the other study, the patients were randomized to the final-treatment doses of either 1800 or 2400 mg/day. The primary efficacy parameter was the daily pain score, as measured by the patient in a daily diary on an 11-point Likert scale, with zero equaling no pain and 10 equaling the worst possible pain. Each morning the patient self-evaluated pain for the previous day. The dataset consisted of 27,678 observations collected from 554 patients, of 

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Analysis of most (perhaps 65%) pharmacokinetic data from clinical trials starts and stops with noncompartmental analysis (NCA). NCA usually includes calculating the area under the curve (AUC) of concentration versus time, or under the first-moment curve (AUMC, from a graph of concentration multiplied by time versus time). Calculation of AUC and AUMC facilitates simple calculations for some standard pharmacokinetic parameters and collapses measurements made at several sampling times into a single number representing exposure. The approach makes few assumptions, has few parameters, and allows fairly rigorous statistical description of exposure and how it is affected by dose. An exposure response model may be created. With respect to descriptive dimensions these dose-exposure and exposure-response models... 

Second, there are biometrical requirements. Various exposure response models may be used and compared. The models need to be clearly defined, and goodness of fit should be reported, both for the separate exposures as well as for the mixtures. Concentration addition, response addition, and mixed-model results may be compared as possible alternatives, especially when underpinning of mechanistic assumptions is weak. Results at one exposure level (e.g., EC50) do not necessarily predict results at other exposure levels due to different slopes and positions of the curves for separate compounds and the mixtures. Statistical tests should be executed properly to compare predicted and observed responses. If any statements about the significance of results are made, the methods of dose-response analysis need to be reported. 

Therefore, given the estimate of ft (or Pi) in the exposure-response model, AUC is associated with an odds ratio of = 1.001. The 95% confidence interval... 

With completion of the time course and covariate components of the model, focus turned to determining a model to describe the influence of theophylline on apnea frequency. For this analysis the exposure metric was an approximate average steady-state concentration (C vg). The general form of the exposure-response model was... 

This chapter endeavors to show that a population PK/PD approach to the analysis of count data can be a valuable addition to the pharmacometrician s toolkit. Nonlinear mixed effects modeling does not need to be relegated to the analysis of continuously valued variables only. The opportunity to integrate disease progression, subject level covariates, and exposure-response models in the analysis of count data provides an important foundation for understanding and quantifying drug effect. Such parametric models are invaluable as input into clinical trial and development path simulation projects. 

In addition to exposure-response models for clinical efficacy, the simulation also may include models for safety markers. These may include more immediate or direct effects, such as a drug affecting the QT/QTc interval (10). Although less frequent, longer term effects such as changes in liver function likely are not well defined at this point in development. As known, or potentially expected, such effects may be considered with longitudinal mixture models (11). 

Bloomfield DM (2015) Incorporating exposure-response modeling into the assessment of QTc interval a potential alternative to the thorough QT study. Clin Pharmacol Ther 97 444-446... 

Exposure-response modeling, which is already regularly employed in other aspects of drug development (e.g., modeling the impact of drug-drug interactions and other intrinsic and extrinsic factors that can impact exposure, evaluating new... 

One of the questions in ICH E14 Q A R2 addressed the topic of exposure-response modeling. The relevant questions can be paraphrased as follows ... 

Exposure-response modeling can be an important component of a totality of evidence assessment of the risk of QTc prolongation. It can be evaluated in early-phase studies and as part of the conventiontil study of QTc prolongation, and may help inform further evaluation. There are many different types of models for the analysis of concentration-response data, including descriptive pharmacodynamic (PD) models and empirical models that link pharmacokinetic (PK) models (dose-concentration-response) with PD models. 

Prospective Evaluation of Exposure-Response Modeling The IQ/CSRC Study Table 8.1 Results from the Zhang et al. analysis by study type... 

Prospective Evaluation of Exposure-Response Modeling The IQ/CSRC Study... 

Results from the study showed that the upper bound of the 90% confidence interval (Cl) of the mean predicted placebo-adjusted QTc change from baseline at geometric Cmax with aU five QT-positive drugs exceeded 10 msec and that the slope of the exposure-response model was positive for all of these five drugs. In contrast, the upper bound for levocetirizine was less than 10 msec even when a single dose comprising six times the therapeutic dose was administered. 

Exposure-response modeling is not standardized and the results can be operator and model dependent. 

ICH E14 Q A R3 (ICH E14 Implementation Working Group, 2015) contains one new section, numbered 5.1, that addresses exposure-response modeling of QTc data. The following text appears in the Questions column ... 

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