Pharmacodynamics linear models

C(t) modeled according to two-compartment model with zero-order and first-order absorption Pharmacokinetic/pharmacodynamic relationship modeled using Hill model with first-order absorption. Modeled parameters matched experimental parameters when bicompartmental model with zero-order input was used. Linear PKs, anticlockwise hysteresis loop established for all doses studied. Apomorphine and growth hormone concentration predicted with good accuracy... 

Other simpler empirical models have also been used since the early days of pharmacodynamics [412,413] to describe the drug concentration-effect relationship. The linear model relies on a linear relationship between E and c ... 

Pharmacodynamic models mathematically relate a drug s pharmacological effect to its concentration at the effect site. Examples of the types of pharmacodynamic models that have been employed include the fixed-effect model/ maximum-effect models (Emax and sigmoid Emax)/ and linear and log-linear models (11). Unlike pharmacokinetic modelS/ pharmacodynamic models are time independent. However these models can be linked to pharmacokinetic modelS/ as discussed in Chapter 19. 

This approach is called the first order (FO) method in NONMEM. This is the most widely used approach in population pharmacokinetic and pharmacodynamic data analysis, and has been evaluated by simulation. The use of the first-order Taylor series expansion to approximate the non-linear model in r], and, possibly,... 

FIGURE 5-16. The linear model (E = S x C + I) is often used as a pharmacodynamic model when the measured pharmacologic effect is 20% to 80% of fmax- In this situation, the determination of fmax and ECso is not possible. To illustrate this, effect measurements from Fig. 5-14 between 20% and 80% of fmax are graphed using the linear pharmacodynamic model. 

In silico modeling of non-linear drug absorption for the P-gp substrate talinolol and of consequences for the resulting pharmacodynamic effect. Pharmaceutical Research, 23, 1712-1720. 

In the simplest case, drug effects are directly related to plasma concentrations, but this does not necessarily mean that effects simply parallel the time course of concentrations. Because the relationship between drug concentration and effect is not linear (recall the Emax model described in Chapter 2 Drug Receptors Pharmacodynamics), the effect will not usually be linearly proportional to the concentration. 

A mechanism-based PK/PD model for rHu-EPO was used to capture the physiological knowledge of the biological system. An open, two-compartment disposition model with parallel linear and nonlinear clearance, and endogenous EPO at baseline, was used to describe recombinant human erythropoietin (rHu-EPO) disposition after intravenous administration [35]. The pharmacodynamic effect of rHu-... 

Under the assumptions of the direct-link model, neither a counterclockwise (Figure 10.2) nor a clockwise hysteresis loop (Figure 10.4) will be recorded in an effect vs. concentration plot. In principle, the shape of the effect vs. concentration plot for an ideal direct-link model will be a curve identical to the specific pharmacodynamic model, relating effect with concentration, e.g., linear for a linear pharmacodynamic model, sigmoid for the sigmoid Emax model (cf. Table 10.1 and following paragraphs and sections), etc. 

From a modeling point of view, the last equilibrium assumption that can be relaxed, for the processes depicted in Figure 10.1, is H4, between the activated receptors (v variable in the occupancy model) and the response E. Instead of the activated receptors directly producing the response, they interfere with some other process, which in turn produces the response E. This mechanism is usually described mathematically with a transducer function T which is no longer linear (cf. Section 10.4.1). This type of pharmacodynamic model is called indirect response and includes modeling of the response process usually through a linear differential equation of the form... 

Using the approach of Sheiner and Verotta [452], a large number of pharmacodynamic models can be considered as hierarchical models composed of a series of submodels. These submodels are linear or nonlinear, static or dynamic input-output, elementary models. Several possible combinations of such submodels have been considered, but they have systematically associated the linear with dynamic features, and the nonlinear with static ones. Is there hesitation or fear of using nonlinear dynamics in the traditional pharmacokinetic-dynamic modeling context ... 

Population pharmacodynamic data, i.e., observed 24-hour efficacy scores were modeled as a function of individual predicted 24-hour steady state AUCs. Various pharmacodynamic models were explored including linear, Emax, and sigmoidal Emax models. Fixed and random-effect parameters were used to describe the PK/PD relationship. The results of the model development are presented in Table 7. 

Several of the PK/PD models described in Chapter 19 have been employed to explore the relationship between circulating protein concentrations and pharmacodynamic endpoints. For example, a dog model of hemophilia was used to study the activity of recombinant FIX (79). Activity was determined in a bioassay, a modified one-stage partial thromboplastin time assay with pooled human plasma as the internal standard. As shown in Figure 32.14, the relationship between activity and recombinant FIX (BeneFIX) concentration was linear (r = 0.86), suggesting that for every 34.5 ng/mL of FIX, there would be a corresponding 1% increase in FIX activity. In 11 males with hemophilia B, it was necessary to use a sigmoid Emax... 

Biopharmaceutical research often involves the collection of repeated measures on experimental units (such as patients or healthy volunteers) in the form of longitudinal data and/or multilevel hierarchical data. Responses collected on the same experimental unit are typically correlated and, as a result, classical modeling methods that assume independent observations do not lead to valid inferences. Mixed effects models, which allow some or all of the parameters to vary with experimental unit through the inclusion of random effects, can flexibly account for the within-unit correlation often observed with repeated measures and provide proper inference. This chapter discusses the use of mixed effects models to analyze biopharmaceutical data, more specihcally pharmacokinetic (PK) and pharmacodynamic (PD) data. Different types of PK and PD data are considered to illustrate the use of the three most important classes of mixed effects models linear, nonlinear, and generalized linear. 

The focus of this book is primarily on the development of pharmacokinetic and pharmacokinetic-pharmacodynamic models. Models that are reported in the literature are not picked out of thin air. Useful models take time and effort and what is rarely shown is the process that went into developing that model. The purpose of this chapter is to discuss model development, to explain the process, and to introduce concepts that will be used throughout this book. Those criteria used to select a model extend to whether the model is a linear... 

Linear mixed effects models are primarily used in pharmacodynamic analysis or in the statistical analysis of pharmacokinetic parameters. Linear mixed effects models could also be used to analyze concentrationtime data from a 1-compartment model with bolus administration after Ln-transformation. The advantages to using mixed effects in an analysis are that observations within a subject may be correlated and that in addition to estimation of the model parameters, between- and within-subject variability may be estimated. Also, the structural model is based on the population, not on data from any one particular subject, thus allowing for sparse sampling. Most statistical packages now include linear mixed effects models as part of their analysis options, as do some pharmacokinetic software (Win-Nonlin). While linear mixed effects models are not cov-... 

Nonlinear mixed effects models are similar to linear mixed effects models with the difference being that the function under consideration f(x, 0) is nonlinear in the model parameters 0. Population pharmacokinetics (PopPK) is the study of pharmacokinetics in the population of interest and instead of modeling data from each individual separately, data from all individuals are modeled simultaneously. To account for the different levels of variability (between-subject, within-subject, interoccasion, residual, etc.), nonlinear mixed effects models are used. For the remainder of the chapter, the term PopPK will be used synonymously with nonlinear mixed effects models, even though the latter covers a richer class of models and data types. Along with PopPK is population pharmacodynamics (PopPD), which is the study of a drug s effect in the population of interest. Often PopPK and PopPD are combined into a singular PopPK-PD analysis. 

LSA is a modeling approach in pharmacokinetics/pharmacodynamics (PK/PD) that applies general linear principles such as convolution and deconvolution to simplify and generalize linear PK/PD relationships. 

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