Model pain relief

Qualifications aside, the inhibition of current observed under voltage-clamp is adequate to account for the suppression of abnormal repetitive impulses and prolonged plateaus that model a neuropathic pain phenotype in a toxin-treated nerve and, most germane, these inhibitions are consonant with the plasma concentrations of drugs that relieve neuropathic pain (Abram Yaksh 1994, Scholz et al 1998, Tanehan Maciver 1991). Na channel blockers may provide pain relief, therefore, through blockade of Na channels. 

The approach involves a semimechanistic or mechanistic model that describes the joint probability of the time of remedication and the pain relief score (which is related to plasma drug concentrations). This joint probability can be written as the product of the conditional probability of the time of remedication, given the level of pain relief and the probability of the pain relief score. First, a population pharmacokinetic (PK) model is developed using the nonlinear mixed effects modeling approach (16-19) (see also Chapters 10 and 14 of this book). With this approach both population (average) and random (inter- and intraindividual) effects parameters are estimated. When the PK model is linked to an effect (pharmacodynamic (PD) model), the effect site concentration (C ) as defined by Sheiner et al. (20) can be obtained. The effect site concentration is useful in linking dose to pain relief and subsequently to the decision to remedicate. 

To model the distribution of pain relief scores and remedication times, subject-specific random effect models are developed. Let the vector of pain relief scores for an individual be Y = (Yi, Y2,..., Y r). At time t the pain relief score is denoted by Y, and the time at which an individual remedicates is denoted by the variable T. The PD model parameter estimates are obtained by maximum likelihood, which estimates the most probable model parameter values for the observed data. P[T, Y] denotes the likelihood of an individual s data, and it is expressed by the following equation ... 

TABLE 25.2 Population Pain Relief Model Parameters... 

Pain Relief Model Baseline placebo effect (m = 1) A -2.5... 

The pain relief model described in Section 25.3.1.1 was implemented with the parameter values presented in Table 25.2. In this example, it is assumed that the placebo effect decreases monotonically with time, by setting the placebo onset rate (a) to zero. The negative values of the baseline placebo effect values (j3 s) indicates that the probability of a high pain relief response is less than that of a lower pain relief score. 

The remedication model described in Section 25.3.1.2 was implemented with the parameter values presented in Table 25.2. The hazard parameter (A) values indicate that the probability of remedication was highest for subjects who had no pain relief (m = 0), but decreased sharply for subjects who had even a small degree of relief. The hazard of remedication for subjects who had complete pain relief (m = 4) is hxed to zero, indicating that there was no probability that these subjects would seek remedication. 

The NONMEM control file provided in Appendix 25.2 (Model Sim) was used to simulate pain relief scores and remedication events according to the population PK/PD models described previously. The NONMEM control file provided in Appendix 25.5 (Model PR-i-RM) was used to estimate the parameters in the pain relief and remedication models, from the simulated pain relief data and PK parameter estimates for each individual. Separate NONMEM control files are provided for simulation and estimation, because the dependent variables are not identical for simulation and estimation. The dependent variables for simulation are pain relief scores and remedication events, whereas the dependent variables for estimation are the probabilities of observing these scores and events. The pain relief scores and remedication events are simulated by utilizing a uniform random variable to assign a pain relief score or remedication event, given the respective simulated probabilities. 

FIGURE 25.2 Proportion and probability of pain relief scores versus time by dose. The numbered symbols represent calculated proportion of subjects with pain relief greater than or equal to the number m > 1, 2, 3, or 4), and the hues represent the corresponding model predicted probabilities (Model PR+RM). 

---