Model patient covariate

Using the NLME, the population model contains three components the structural model, the statistical model and - if necessary - the (integrated) patient covariate model (Fig. 17.2). 

The covariate distribution model defines the distribution and correlation of covariates in the population to be studied. The aim of a covariate distribution model is to create a virtual patient population that reflects the target population for simulations including patients covariates. This model is of great importance for the realistic simulation of clinical trials. 

Recording details of the studies, including the models used and associated parameter values reported, is an obvious starting place. Additional details include the chemical analysis method, the pharmacokinetic analysis method, the studied population (specifically subpopulations), number of healthy volunteers or patients, number of pharmacokinetic samples per patient, the dose, the formulation, and the route of administration. If one publication includes several groups of patients (or the same patient received two different formulations/concomitant medications), then each cohort may need to be treated as a repeated measure of the same study or within the same study, which may be indexed according to a study or patient covariate. 

The first simulation is to show how half-life, a pharmacokinetic parameter physicians are particularly interested in, varies as function of patient covariates. Many times when a modeler shows nonscientists an equation, some of them cannot understand how the variables interact or how the dependent variable might change when the one of the predictor variables is... 

This example in population pharmacokinetics illustrates the process of starting with a data set and then moving through model development, ultimately leading to a model that can explain the data in terms of a few pharmacokinetic parameters and patient covariates. Once a model is developed, it can be used for many purposes, including answering questions to which no answer might be readily available or to just explain data. 

Population PK/PD models, which in addition to the characterization of PK and PD, involve relationships between covariates (for instance, patient characteristics such as age, body weight) and PK/PD parameters, allow us to assess and to quantify potential sources of variability in exposure and response in specific target population, even under erratic and limited sampling conditions. Often implications of significant covariate effects can be evaluated by computer simulations using the population PK/PD model. 

These models can be written in a more precise form by defining a binary indicator to denote treatment. Let z = 0 for patients randomised to the placebo group and let z = 1 for patients randomised to the test treatment. The model with a single covariate and assuming a common slope can then be written ... 

Again let z = 0 for patients in the control group and z = 1 for patients in the test treatment group and assume that we have several covariates, say Xj, and X3. The main effects model looks at the dependence of pr(y= 1) on treatment and the covariates ... 

The method provides a model for the hazard function. As in Section 6.6, let z be an indicator variable for treatment taking the value one for patients in the active group and zero for patients in the control group and let Xj, X2, etc. denote the covariates. If we let t) denote the hazard rate as a function of t (time), the main effects model takes the form ... 

Both candidate models were then re-evaluated using the final dataset of 8388 observations from 906 patients of the 19 studies. With the final dataset, the addition of the linear elimination pathway resulted in only a single point reduction in OFV compared to the model with saturable elimination only. Therefore, a two-compart-ment model with saturable elimination was considered the final structural model and was used for the development of the covariate model (see Table 14.4). 

Some factors or covariates may cause deviations from the population typical value generated from system models so that each individual patient may have different PK/PD/disease progression profiles. The relevant covariate effects on drug/disease model parameters are identified in the model development process. Clinical trial simulations should make use of input/output models incorporating... 

Objective The objective of this analysis was to develop a population pharmacokinetic model for NS2330 and its major metabolite Ml, based on data from a 14-week proof of concept study in Alzheimer s disease patients, including a screening for covariates that might influence the pharmacokinetic characteristics of the drug and/or its metabolite. Subsequently, several simulations should be performed to assess the influence of the covariates on the plasma concentration-time profiles of NS2330 and its metabolite. 

For the appropriate development of covariate distribution models, the pharmaceutical industry has huge amount of data in their clinical databases. In addition, there are also public databases available which can be used, like the Congestive Heart Failure Database (http //www.physionet.org/) derived from patients undergoing cardiac catheterization at Duke Medical Centre during 1990-1996 (about 4000 patients, data on demographics, risk factors histories, cardiac catheterization, EKG, cardiac scores, follow-up data). 

A population PK evaluation of patients from the safety and efficacy trials can be used to assess the impact of renal function on the disposition of a drug. Special care must be taken that patients with severe renal impairment are adequately represented in the population. The population PK approach assess the impact of various covariates on the disposition of a drug. Non linear mixed effects modeling may be used to model the relationship between various covariates and pharmacokinetic parameters. CLcr as a measure of renal function may be one of the covariates. This type of approach has it advantageous as it involves assessment of the effect of renal impairment on the PK in the target population. 

Population pharmacokinetics can be extended to pharmacodynamics and PK/PD modeling using a link model like an effect compartment (Sheiner et al. 1979). In huge clinical trials only a limited number of patients can be included in a pharmacokinetic satellite study. The model is developed in this satellite. Knowing the demographic covariates of the patients in the whole study, concentration time curves and even effect time curves can be predicted. 

Tadalafil pharmacokinetics in patients with ED showed linear relation with respect to dose and duration of treatment, and a one-compartment model adequately described the data. The absorption rate was rapid (1.86 h ), and the t)q)ical population estimates of the apparent oral clearance (CL/F) and apparent volume of distribution were 1.6 L/h and 63.8 L, respectively. Disposition parameters showed a moderate degree of interindividual variability (39-45%). The value of CL/F decreased slightly with increasing serum y-glutamyl transferase (GGT) concentration, the only statistically significant covariate detected. Systemic exposure to tadalafil was not influenced by age, weight, smoking status, alcohol consumption, liver enz nne status, ED severity, cardiovascular condition, or diabetes mellitus. 

Last, population pharmacokinetics of sibrotuzumab, a humanized monoclonal antibody directed against fibroblast activation protein (FAP), which is expressed in the stromal fibroblasts in >90% of malignant epithelial tumors, were analzyed in patients with advanced or metastatic carcinoma after multiple IV infusions of doses ranging from 5 mg/m to a maximum of 100 mg (78). The PK model consisted of two distribution compartments with parallel first-order and Michaelis-Menten elimination pathways from the central compartment. Body weight was significantly correlated with both central and peripheral distribution volumes, the first-order elimination clearance, and ymax of the Michaelis-Menten pathway. Of interest was the observation that body surface area was inferior to body weight as a covariate in explaining interpatient variability. 

The first attempt at estimating interindividual pharmacokinetic variability without neglecting the difficulties (data imbalance, sparse data, subject-specific dosing history, etc.) associated with data from patients undergoing drug therapy was made by Sheiner et al. " using the Non-linear Mixed-effects Model Approach. The vector 9 of population characteristics is composed of all quantities of the first two moments of the distribution of the parameters the mean values (fixed effects), and the elements of the variance-covariance matrix that characterize random effects.f " " ... 

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