The figure below is a line graph showing the time course of drug concentration when a certain drug was administered to 12 patients. After administration, the drug is absorbed into the body, and the concentration rises rapidly, and then the concentration slowly decreases due to distribution and metabolism. This graph shows the basic pattern of pharmacokinetics.
Observing the individual patient curves reveals individual differences in concentration changes, which are usually due to the type of drug, the route of administration, and individual patient characteristics (e.g., body weight and metabolic capacity).
For example, in patients with a large body weight, the distribution volume increases, which may result in a lower maximum concentration (Cmax). In addition, the concentration profile may change depending on the dosage and type of drug.
These factors that can potentially affect pharmacokinetics are called "covariates," and analysis may be performed to determine how differences in covariates affect drug concentrations.
In this blog, we will show how to use the curve fitting platform in JMP (JMP Pro) to set patient weight, dosage and administered drug as covariates* and analyze their effect on pharmacokinetics.
*In some cases, "drug" is not considered a covariate, but here we consider it a covariate because we believe that the type of drug may affect pharmacokinetics.
Summary of data and covariates used
The data used in this analysis were from 12 patients whose drug concentrations were measured at multiple time points after administration. In addition, information on the administered drug, body weight, and dose was recorded for each patient as covariates.
The bar graph below shows the dosage and weight of each patient. Patient IDs 1 to 6 were given drug A, and 7 to 12 were given drug B, indicating that there were differences in dosage and weight between patients.
Analytical procedures
JMP's "Curve Fitting" is a platform that allows you to fit nonlinear models to parameters. The pharmacokinetic model is analyzed using the following steps:
① Estimation of pharmacokinetic parameters : A "one-compartment oral administration" model was applied to each patient to estimate three parameters: "AUC (area under the curve)," "elimination rate," and "absorption rate."
② Modeling the relationship between parameters and covariates : Perform regression analysis with the estimated parameters as the objective variable and weight, dosage, and drug as explanatory variables (with variable selection).
➂ Explore the relationship between covariates and the model : Visualize the effect of covariates (weight, dose, drug) on the relationship between time and drug concentration.
From fitting nonlinear models to exploring relationships between covariates and pharmacokinetics
①Estimation of pharmacokinetic parameters
The steps in JMP are as follows:
Select Analyze > Advanced Modeling > Fit Curve and specify the roles of the columns: weight, dose, and drug are set as "additional variables".
Then, specify the report option Pharmacokinetic Model > One Compartment Oral Dosing, which will display the fit of the model to each patient, estimating the pharmacokinetic parameters (AUC, elimination rate, absorption rate) and displaying the fitted "plots."
The report shows the prediction model equation and the estimated parameters (AUC, elimination rate, absorption rate) for each patient. JMP formulates a one-compartment model using the equation shown in "Prediction Model" below, where a is the AUC (area under the curve), b is the elimination rate, and c is the absorption rate.
What we did here can be said to be that we fitted a one-compartment model to the pharmacokinetics of each patient and extracted three parameters (AUC, elimination rate, and absorption rate) that characterize the patient's pharmacokinetics.
② Model the relationship between parameters and covariates
If you select the option "Create parameter table" for the fitted model, a table like the one shown below will be output.
A regression model is constructed with the estimated parameters as the objective variables and the covariates (weight, dosage, drug) as explanatory variables. In this process, variables are selected using JMP Pro's "curvilinear experimental design analysis" to select an appropriate model.
*The analysis that follows can only be performed in JMP Pro.
Run the fitted model option [Curvilinear experimental design analysis] . Then, for each of the parameters AUC, elimination rate, and absorption rate, a model is fitted that explains the weight, dosage, and drug specified in the "Additional variables". At this time, a "brute force" variable selection is performed from the second-order model to select terms that are useful for prediction.
Details of the regression analysis are provided in the report "Generalized Regression on Model Parameters" .
3. Explore the relationship between covariates and the model
The models obtained in step 2 are combined and the pharmacokinetic profile over time is formulated as a function of the additional variables.
The report "Curvilinear Experimental Design Profiler" allows you to explore how the relationship between time and drug concentration changes by changing the values of additional variables. For example, for a patient with weight 70, dose 4.5, and taking drug A, the relationship between time and drug concentration is shown as a yellow filled profile.
In the profile below, when the covariate values are changed, the peak time becomes later and the peak drug concentration decreases.
Additionally, we recorded a video of the profile as we varied the covariate values, allowing us to visually see how the shape of the yellow profile changes as the covariates are changed.
summary
This analysis used data from 12 patients to observe changes in drug concentrations over time.
In addition, by utilizing the curve fitting function of JMP Pro, we were able to examine the relationship between the pharmacokinetics and the covariates "body weight," "dosage," and "type of drug."
by Naohiro Masukawa (JMP Japan)
Naohiro Masukawa - JMP User Community
