The Population Simulator Mode and Virtual Bioequivalence Equations
This chapter details the equations that define and support the Population Simulator feature in GastroPlus®, which you can use to simulate population in the Virtual Bioequivalence (VBE) run mode to conduct VBE trials. See:
Population Simulation Outputs Equations
Equation 6-1: Geometric mean of x values
Equation 6-2: Lower (L) and upper (U) bounds for 90% confidence intervals calculated from untransformed data
Equation 6-3: Lower (L) and upper (U) bounds for 90% confidence intervals calculated from ln-transformed data
where for all the above equations:
Variable | Definition |
We don't have a way to export this macro. | The analyzed pharmacokinetic endpoint (Fa, FDp, F, Cmax, C(t)plasma(max), AUC(0-t), AUC(0-inf). |
We don't have a way to export this macro. | The arithmetic mean and geometric mean, respectively, for the given pharmacokinetic endpoint. |
We don't have a way to export this macro. | The standard deviation calculated from an untransformed x value. |
We don't have a way to export this macro. | The standard deviation calculated from an ln-transformed x value. |
We don't have a way to export this macro. | A critical t value. |
Equation 6-4: Lower (L) bound and upper (U) bound for 90% confidence interval on the difference between means of test (T, simulated profiles) and reference (R, experimental profiles) as calculated from untransformed data
Equation 6-5: Lower bound expressed as percentage (L%) and upper bound expressed as percentage (U%) for 90% confidence interval on the difference between means of test (T, simulated profiles) and reference (R, experimental profiles) calculated from ln-transformed data
where for Equation 6-4 and Equation 6-5, and the given pharmaceutical endpoint:
Variable | Definition |
We don't have a way to export this macro. | The arithmetic mean. |
We don't have a way to export this macro. | The pooled variance calculated from untransformed values. |
We don't have a way to export this macro. | The pooled variance calculated from ln-transformed data. |
We don't have a way to export this macro. | The number of values in the test population. |
We don't have a way to export this macro. | The number of values in the reference population. |
We don't have a way to export this macro. | A critical t value. |
Equation 6-6: Pooled variances
where:
Variable | Definition |
We don't have a way to export this macro. | The standard deviation calculated from either untransformed or ln-transformed data the for the test population and the reference population, respectively. |
We don't have a way to export this macro. | The number of values in the test population. |
We don't have a way to export this macro. | The number of values in the reference population. |
Virtual Bioequivalence Equations
Equation 6-7: Calculation of
where:
Variable | Definition |
We don't have a way to export this macro. | The number of sequences m used in the study. |
We don't have a way to export this macro. | Partially replicate design: TRR, RTR, and RRT or replicate design: TRTR and RTRT. Note: In GPX.2™, only replicate designs are available. |
We don't have a way to export this macro. | The number of subjects within each sequence. |
We don't have a way to export this macro. | The total number of subjects used in the study. |
We don't have a way to export this macro. | Test product. |
We don't have a way to export this macro. | Reference product. |
We don't have a way to export this macro. | Where 1 and 2 represent replicate reference treatments. |
Equation 6-8: Determine the 95% upper confidence bound
YT and YR are the means of the ln-transformed PK endpoint (AUC0-t and AUC0-inf and/or Cmax) obtained from the BE study for the test and reference products respectively.
where:
scaled average BE limits.