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.
*

*> Thanks in advance.
*

*>
*

*> Regards
*

*>
*

*> Kevin
*

Received on Sat Apr 28 2018 - 13:28:56 EDT

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

Karlsson

t,

me point,

bin of independent

e is real time not nominal time.

Received on Sat Apr 28 2018 - 13:28:56 EDT