• Terms and Definitions 1
  • Variable
  • Parameter
  • Model
  • Linear and Nonlinear model
  • Fixed effect parameter
  • Random effect parameter
  • Mixed effects modeling
  • Structural model
  • Random effect model
  • Population PK and PD
• Terms and Definitions 2
  • Maximum likelihood
  • Objective function value
  • Log-likelihood ratio
  • Optimization procedure
  • Point estimate
  • Confidence intervals
  • Maximum a posteriori/post hoc estimates
  • Simulation
  • Clinical trial design
  • Pharmacodynamic terms
• Population analysis methods
  • Naive pooled data approach (NPD)
  • Naive averaged data approach (NAD)
  • Standard two-stage approach (S2S)
  • Three stage analysis (3S)
  • Bayesian estimation
  • One stage analysis
• Estimation methods
  • Ordinary least squares (OLS)
  • Weighted least squares (WLS)
  • Extended least squares (ELS)
• Good Modeling Practices (GMP)
  • Data management
  • Rational modeling process
  • Report

Good Modeling Practices (GMP)

Rational model building

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Covariate model building

An important objective of population pharmacokinetic-pharmacodynamic analyses is to discover relationships between observable covariates and individual kinetic/dynamic parameters which explain part of between subject variability (BSV/BOV).Model building exercise is performed by addition of prognostic factors / covariates such as weight, sex, age, renal function (Creatinine clearance), hepatic function, comedication, genotypes etc., in the initial model and evaluating the goodness of fit of the new model.

Importance of covariate modeling

1. In drug development process, quantitative modeling of covariates will allow one to determine whether subgroups of patients need special dosing recommendations.
2. Simulation of new trials could be performed by including the covariate information.

Identification of influential covariates

1. Primarily, identifying covariates should be based on biological plausibility.
   1. For ex., a possible dependance of drug clearance on individual creatinine clearance could be tested if a compound is known to be excreted unchanged to an appreciable extent.
   2. Another example could be the influence of comedication could be investigated if it the drug is known to induce or inhibit one of the primary metabolizing enzyme.
2. Graphical analyses of covariates
   1. Scatter plots of individual between subject variability of parameters (η_CL's, η_V's) and covariates could be checked for any trend . An example scatter plot between η's and covariates is shown below.
   2. Correlation between observed covariates, like a correlation between age and creatinine clearance is also revealed from scatter plots. In such a case, only one of a pair of correlated covariates is included in the model.

Click for larger image, 235 KB

Covariate model specification

Base model:

CL_i = CL_pop • exp(η_CL)

To add effect of weight on CL, the different types of covariate models that could be used are given below.

1. Linear additive effect

CL_i = (CL_pop + θ•BW) •exp(η_CL)

where
CL_i     = individual clearance
CL_pop   = Population clearance
η_CL     = random between subject variability
θ         = shift parameter describing the systematic dependance of CL on individual body weight.

2. Normalized by median weight

CL_i = (CL_pop + θ•BW/(Median BW)) •exp(η_CL)

3. Centered on median weight

CL_i = (CL_pop + θ•(BW-Median BW)) •exp(η_CL)

4. Power or allometric model

CL_i = (CL_pop•(BW/70)^0.75) •exp(η_CL)

Hypothesis testing

Hypotheses testing on covariates identified based on physiology and graphical analyses are done by including one covariate at a time. Log-likelihood ratio test (Model selection criterion) is used to test the hypothesis and to identify significant covariates. Selction of covariates is based upon both clinical and statistical significance of covariates.