# Re: Qestion about the lower boundary in pcVPC calculation

From: Martin Bergstrand <martin.bergstrand>
Date: Sat, 28 Apr 2018 19:28:56 +0200

Hi Kevin,

I am sorry for the confusion. The lower boundary (lb_ij) refers to the lower=
theoretical boundary for PRED (the population typical prediction). For most=
PK models this is 0 (concentrations can’t be negative). In this cas=
es the equation can be simplified. Note that the lower boundary is for the p=
redictions and lower boundary’s for observations (i.e. lloq and llod=
) is not relevant for this parameter.

More often for PD models the theoretical lower boundary is different from 0 (=
e.g. -1 for relative change from baseline or positive values for some scores=
). In these cases the lb_ij parameter becomes important to take into account=
.

I hope this answers you question.

Kind regards,
Martin Bergstrand, Ph.D.
Partner and Senior Consultant
Pharmetheus AB

+46(0)709 994 396
martin.bergstrand
www.pharmetheus.com

> 28 apr. 2018 kl. 15:19 skrev Wang Kevin <fengdubianbian
>
> Hi All,
>
> I’m trying to understand what pcVPC did in PsN.
> When I reading below paper,
> “Martin Bergstrand, Andrew C. Hooker, Johan E. Wallin, and Mats O.=
Karlsson
> Prediction-Corrected Visual Predictive Checks for Diagnosing Nonlinear
> Mixed-Effects Models”
> I got confused about the meaning of lb_ij(lower boundary) on equation (1).=

>
> pcY_ij=lb_ij+(Y_ij-lb_ij)*(pred_bin-lb_ij)/(pred_ij-lb_ij)
> Yij = observation or prediction for the ith individual and jth time poin=
t,
> pcYij = prediction-corrected observation or prediction,
> PREDij = typical population prediction for the ith individual and jth ti=
me point,
> and PReEDbin = median of typical population predictions for the specific=
bin of independent
> variables.
>
> For example, if a pk model was simulated with 3 different dose and the tim=
e is real time not nominal time.
> How to calculate lb_ij?
>
> Below is a pcVPC simulated data example (not real)
> ID
> DV
> TIME
> strata_no
> DOSE
> 1
> 2.0
> 0.90
> 1
> 1
> 1
> 12.6
> 3.10
> 1
> 1
> 1
> 2.8
> 5.00
> 1
> 1
> 1
> 1.5
> 8.00
> 1
> 1
> 1
> 1.0
> 12.00
> 1
> 1
> 2
> 1.0
> 0.90
> 2
> 2
> 2
> 22.3
> 6.10
> 2
> 2
> 2
> 12.0
> 5.10
> 2
> 2
> 2
> 3.0
> 8.30
> 2
> 2
> 2
> 1.0
> 12.00
> 2
> 2
> 3
> 1.0
> 1.00
> 3
> 3
> 3
> 40.1
> 3.10
> 3
> 3
> 3
> 11.7
> 5.40
> 3
> 3
> 3
> 6.6
> 8.00
> 3
> 3
> 3
> 2.0
> 12.00
> 3
> 3
>
> Any help or suggestion is appreciated.