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
	The analyzed pharmacokinetic endpoint (F_a, FD_p, F, C_max, C(t)_plasma(max), AUC_(0-t), AUC_(0-inf).
	The arithmetic mean and geometric mean, respectively, for the given pharmacokinetic endpoint.
	The standard deviation calculated from an untransformed x value.
	The standard deviation calculated from an ln-transformed x value.
	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
	The arithmetic mean.
	The pooled variance calculated from untransformed values.
	The pooled variance calculated from ln-transformed data.
	The number of values in the test population.
	The number of values in the reference population.
	A critical t value.

Equation 6-6: Pooled variances

where:

Variable	Definition
	The standard deviation calculated from either untransformed or ln-transformed data the for the test population and the reference population, respectively.
	The number of values in the test population.
	The number of values in the reference population.

Virtual Bioequivalence Equations

Equation 6-7: Calculation of

where:

Variable	Definition
	The number of sequences m used in the study.
	Partially replicate design: TRR, RTR, and RRT or replicate design: TRTR and RTRT. Note: In GPX™ 10.2, only replicate designs are available.
	The number of subjects within each sequence.
	The total number of subjects used in the study.
	Test product.
	Reference product.
	Where 1 and 2 represent replicate reference treatments.

Equation 6-8: Determine the 95% upper confidence bound

Y_T and Y_R are the means of the ln-transformed PK endpoint (AUC_0-t and AUC_0-inf and/or C_max) obtained from the BE study for the test and reference products respectively.

where:

scaled average BE limits.

= 0.25 Regulatory constant.