pk-glossary pk working group 2004

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Glossary Page 1 of 24

...\PK-glossary_PK_working_group_2004.pdf

Collection of terms, symbols, equations, and

explanations of common pharmacokinetic and

pharmacodynamic parameters and some

statistical functions

Version: 16 Februar 2004

Authors: AGAH working group PHARMACOKINETICS


2/23

Glossary Page 2 of 24


Collection of terms, symbols, equations, and explanations of commonpharmacokinetic and pharmacodynamic parameters and some

statistical functions

TABLE OF CONTENTS

Page

TABLE OF CONTENTS.................................................................................................................2

1 Pharmacokinetic Parameters from noncompartmental analysis (NCA) ...............................3

1.1 Parameters obtained from concentrations in plasma or serum...........................................3

1.1.1 Parameters after single dosing..................................................................................3

1.1.2 Parameters after multiple dosing (at steady state)....................................................6

1.2 Parameters obtained from urine ..........................................................................................7

2 Pharmacokinetic parameters obtained from compartmental modeling................................8

2.1 Calculation of concentration-time curves.............................................................................9

2.2 Pharmacokinetic Equations - Collection of Equations for Compartmental Analysis .........10

3 Pharmacodynamic GLOSSARY ................................................................................................20

3.1 Definitions ..........................................................................................................................20

3.2 Equations: PK/PD Models..................................................................................................21

4 Statist ical parameters ................................................................................................................22

4.1 Definitions ..........................................................................................................................22

4.2 Characterisation of log-normally distributed data ..............................................................23


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AGAH Working group PK/PD modelling Page 3 of 24


1 PHARMACOKINETIC PARAMETERS FROM NONCOMPARTMENTALANALYSIS (NCA)

1.1 Parameters obtained from concentrations in plasma or serum

1.1.1 Parameters after sing le dosing

Symbol Unit /

Dimension /

Dimension

Definition Calculation

AUC

AUC(0-)Amounttime/

volume

Area under the concentration-time

curve from zero up to withextrapolation of the terminal phase

z

z)zt-(0AUC

C=AUC + , Cz may be

measured (Cz,obs) or calculated (Cz,calc)

AUC(0-t),

AUCt

Amounttime/volume

Area under the concentration-timecurve from zero up to a definite time t

+=1

1

1t)-(0 AUCn-

i=

)i-ti(t AUC wit

h t1=0 and tn=t,Concentrations Ci measured at timesti, i=1,,n.

According to the linear trapezoidal rule:

)t(t)C(CAUC ii+i+iiti(t +=+ 1121

)1 or according to the log-linear trapezoidal rule:

)ln(ln

)()(

1

11)1

+

+++

=

ii

iiii

iti(t

CC

ttCCAUC

(the logarithmic trapezoidal rule is used for thedescending part of the concentration-time curve, i.e. ifCi>1.001*Ci+1>0)

AUC(0-tz) Amounttime/volume

Area under the concentration-timecurve from zero up to the last

concentration LOQ (Cz)

See AUC(0-t)

AUCextrap % % Area under the concentration-time

curve extrapolated from tz to in %

of the total AUC 100%AUC extrap = AUCAUC-AUC )z(0-t

AUMC Amount(time)

2/

volume

Area under the first moment of theconcentration-time curve from zero

up to with extrapolation of theterminal phase

2

z

z

z

zz)zt-(0

CCt+AUMC=AUMC

+

,

Cz may be measured (Cz,obs) or calculated (Cz,calc)

AUMC(0-t) Amount(time)

2/

volume

Area under the first moment of theconcentration-time curve from zeroup to a definite time t

+=1

1

1t)-AUMC(0n-

i=

ii )-tAUMC(t

with t1=0 and tn=t. Concentrations Cimeasured at times ti, i=1,,n.

)1i(tAUMC + it

))C(2Ct)2C(C)(tt(t 1iii1ii1ii1+i +++ +++= 61

(linear trapezoidal rule)

2

111

B

CC

B

tCtC iiiiii +++ +

= withii

ii

tt

CCB

=

+

+

1

1lnln

(log-linear trapezoidal rule)

AUMC(0-tz) Amount(time)

2/

volume

Area under the first moment of theconcentration-time curve from zero tothe last quantifiableconcentration

See AUMC(0-t)

AUMCextrap % % Area under the first moment of theconcentration-time curve

extrapolated from tz to in % of thetotal AUMC

100%AUMC extrap =AUMC

AUMC-AUMC )z(0-t


4/23



Symbol Unit /Dimension


Cp orC Amount/ volume Plasma concentration

Cs orC Amount/ volume Serum concentration

Cu Amount/ volume Unbound plasma concentration

CL Volume/ time orvolume/ time/ kg

Total plasma, serum or bloodclearance of drug after intravenousadministration

CL =D

AUC

iv

CL / f Volume/ time orvolume/ time/ kg

Apparent total plasma or serumclearance of drug after oraladministration

CL / f =D

AUC

po

CL int Volume/ time orvolume/ time/ kg

Intrinsic clearance maximumelimination capacity of the liver

CLH,b Volume/ time orvolume/ time/ kg

Hepatic blood clearance, product ofhepatic blood flow and extractionratio

CLH = QHEH

CLCR Volume/ time orvolume/ time/ kg

Creatinine clearance Measured or Cockcroft & Gault formula

CLm Volume/ time Metabolic clearance

Cz, calc Amount/ volume Predicted last plasma or serumconcentration

Calculated from a log-linear regression throughthe terminal part of the curve

CzorCz, obs Amount/ volume Last analytically quantifiable plasmaor serum concentration above LOQ

directly taken from analytical data

Cmax Amount/ volume Observed maximum plasma orserum concentration afteradministration


D Amount Dose administered

f - Fraction of the administered dosesystemically available f =

AUC D

AUC D

po iv

iv po

F % Absolute bioavailability, systemic

availability in %

F = f 100

frel - Fraction of the administered dose incomparison to a standard (not iv)

DAUC

DAUCf

STD

STDrel

= STD = Standard

Frel % Relative bioavailability in % 100f=F relrel

fa - Fraction of the extravascularlyadministered dose actually absorbed

For orally administered drugs: f = fa*(1-EH)

fm - Fraction of the bioavailable dosewhich is metabolized

fu - Fraction of unbound (not protein-bound or free) drug in plasma orserum

fu = Cu /C

HVD Time Half-value duration (time intervalduring which concentrations exceed50% of Cmax)

z (Time)-1 Terminal rate constant (slowest rateconstant of the disposition)

negative of the slope of a ln-linear regressionof the unweighted data considering the last

concentration-time points LOQ

ke orkel (Time)-1

Elimination rate constant from thecentral compartment

calculated from parameters of themultiexponential fit

LOQ Amount/ volume Lower limit of quantification


5/23





MAT Time Mean absorption time MAT = MRT - MRTev iv

(ev = extravasal, e.g. im, sc, po)

MDT Time Mean dissolution time

MRT Time Mean residence time (of theunchanged drug in the systemiccirculation)

MRT =AUMC

AUC

MR - Metabolic ratio of parent drug AUC andmetabolite AUC MR =

AUC

AUC

parent

metabolite

t1/2

Time Terminal half-life1/ 2t =

ln 2

z

t lag Time Lag-time (time delay between drugadministration and first observedconcentration above LOQ in plasma)


tz Time Time p.a. of last analyticallyquantifiable concentration


tmax Time Time to reach Cmax directly taken from analytical data

Vss Volume

or volume/kg

Apparent volume of distribution atequilibrium determined afterintravenous administration

2(AUC)

AUMCD=MRTCL=Vss

Vz Volume

or volume/kg

Volume of distribution during terminalphase after intravenous administration

zAUC = iv

DVz

Vss / f Volume

or volume/kg

Apparent volume of distribution atequilibrium after oral administration

2(AUC)

AUMCD=MRTCL=/fVss

Vz / f Volume

or volume/kg

Apparent volume of distribution duringterminal phase after oral /extravascular administration

zAUCf

= po

D/Vz po instead of iv !


6/23



1.1.2 Parameters after mult iple dosing (at steady state)



Aave Amount Average amount in the body atsteady state

z M

ave

Df=A

AUC,ssAUCss

Amounttime/volume

Area under the concentration-timecurve during a dosing interval atsteady state

by trapezoidal rule

AUCF% % Percent fluctuation of theconcentrations determined from areasunder the curve AUC

AUC+AUC100=AUCF%

)C(below)C(above aveave

Cav,ss Amount/volume

Average plasma or serumconcentration at steady state

ss,AUC=C ssav,

Cmax,ss Amount/volume

Maximum observed plasma or serum

concentration during a dosing intervalat steady state


Cmin,ss Amount/volume

Minimum observed plasma or serumconcentration during a dosing intervalat steady state


Ctrough Amount/volume

Measured concentration at the end ofa dosing interval at steady state (takendirectly before next administration)


DM Amount Maintenance dose design parameter

LF - Linearity factor of pharmacokineticsafter repeated administration

sd

ss,=

AUC

AUCLF

sd = single dose

PTF % % Peak trough fluctuation over onedosing interval at steady state

avss,

minss,maxss,

C

C-C100%PTF =

RA (AUC) Accumulation ratio calculated from

AUC,ss at steady state and AUCafter single dosing

RA (AUC) =sd

AUC

AUC

ss

,

,

RA (Cmax) Accumulation ratio calculated fromCmax,ss at steady state and Cmax aftersingle dosing

RA (Cmax) =C

C

ss

sd

max,

max,

sd = single dose

RA (Cmin) Accumulation ratio calculated fromCmin,ss at steady state and from

concentration at t= after single dose sdss

C

C

,

min,=A (Cmin)R

sd = single dose

Rtheor Theoretical accumulation ratio ze

=1

1

2-1

1=theor -R ,

2/1t

=

TCave Time Time period during which plasma

concentrations are above Cav,ss

derived from analytical data by linear interpolation

tmax,ss Time Time to reach the observedmaximum (peak) concentration atsteady state


Time Dosing interval directly taken from study design


7/23



1.2 Parameters obtained from urine



Ae(t1-t2) Amount Amount of unchanged drug excretedinto urine within time span from t1 to t2.

Cur* Vur

Ae(0- ) Amount Cumulative amount (of unchangeddrug) excreted into urine up to infinityafter single dosing

(can commonly not be determined)

Ae,ssAess

Amount Amount (of unchanged drug) excretedinto the urine during a dosing interval

() at steady state

Cur Amount/

volume

Drug concentration in urine

CLR Volume/ timeor volume/

time/ amount

Renal clearance

)0(

)0()0(

=AUC

Ae

AUC

AeCLR

after multiple dosess

RAUC

AeCL

,

)0(

=

fe - Fraction of intravenous administered

drug that is excreted unchanged inurine iv

ee

D

A=f

fe/f - Fraction of orally administered drugexcreted into urine ef

A

De

po

/ f=

Fe % Total urinary recovery after intravenousadministration = fraction of drugexcreted into urine in %

Fe = fe 100

tmid Time Mid time point of a collection interval

Vur Volume Volume of urine excreted directly taken from measured lab data


8/23



2 PHARMACOKINETIC PARAMETERS OBTAINED FROM COMPARTMENTALMODELING

Symbol Unit /Dimensions


A,B,C or

Ci, i=1,...,n

Amount/ volume Coefficients of the polyexponentialequation

by multiexponential fitting

, , (Time)-1 Exponents of the polyexponentialequation (slope factor)


I (Time)-1 Exponent of the ith (descending)exponential term of a polyexponentialequation


AUC Amounttime/volume

Area under the curve (model)

=

=

=

=

n

1i aiia

ai

n

1i i

i

k

11

k

kCAUC

:larextravascu

CAUC:iv

Note: Ci is the linear coefficient of thepolyexponential equation

AUMC Amount(time)2/

volumeArea under the first moment curve

=

=

=

=

n

1i2

a

2

iia

ai

n

1i2

i

i

k

11

k

kCAUMC

:larextravascu

CAUMC:iv


C(0) Amount/ volume Initial or back-extrapolated drug

concentration following rapidintravenous injection =

n

1=i

iC)0(C


C(t) Amount/ volume Drug concentration at time point t See 2.2

CL Volume/ time Clearance

AUC

DosefCL

=

iv: f=1

fi - Fractional area, area under the various

phases of disposition (i) in the plasmaconcentration-time curve after ivdosing

1fwithAUC

C

fn

1i

ii

i

i =

= =

i Number of compartments in a multi-

compartmental model

k0 (Time)-1

Zero order rate constant Design parameter or determined bymultiexponential fitting

ke orkel (Time)-1

Elimination rate constant from thecentral compartment

calculated from parameters of themultiexponential fit

ka orkabs (Time)-1

Absorption rate constant by multiexponential fitting

k ij (Time)-1

Transfer rate between compartment iand j in a multi-compartmental model


Km Amount/ volume Michaelis Menten constant by nonlinear fitting


9/23



Symbol Unit /Dimensions


MRT Time Mean residence timeiv:

AUC

AUMCMRT=

extravascular: )1

(alag k

tAUC

AUMCMRT +=

Qi Amount/Time Intercompartmental clearance betweencentral compartment and compartmenti

k0 Amount/Time Zero order infusion rate design parameter

t 1/2, i Time Half-life associated with the ith

exponent of a polyexponential equation tln2

1/2, i =

i

Time Infusion duration design parametert Time Time after drug administration

Vc Volume orVolume /amount

Apparent volume of the central orplasma or serum compartment

=

=

n

1ii

c

C

DosefV

iv: f=1

Vmax Amount/Time Maximum metabolic rate


10/23



2.1 Calculation of concentration-time curves

App lication Parameter Calculation

iv bolus concentration after bolus administration [ ]=

=n

1i

t

ipieB)t(C

concentration during infusion

=

=Cterm(t) for t->

BATEMAN-Function

In most cases: ea kk > , this means that

e k ta

approches zero much faster

thane k te

- calc. of ke from slope ofterminal phase

ea kk < - Flip-Flop, but you need anadditional iv administration to distinguishthis case

tk

eac

aterm

aekkV

kDftCtC

=)(

)()(

tkkkV

kDftCtC a

ead

aterm

=

)())()(ln(

ka - feathering-method (can reasonably beused only if there are at least 4 data pointsin the increasing part of the concentration-time curve)

substraction of C from C (semilog. (C-C)versus t - slope -ka)

)()(

)()()( 00 ttkttk

ead

a ae eekkV

kDftC

=

with t0 - lag time

ea

ea

ea

e

a

kk

kk

kk

k

k

t

=

=)ln()ln(

ln

max ,

maxmax

tk

d

a eeV

kDfC

=

tmax does not depend on the bioavailability fand, since ke commonly is substance-dependent and not preparation-dependent,reflects ka

One Compartment Model, Oral Administration With Resorption First Order, multip ledose

)()(

)(tk

atk

e

ead

an

ae ererkkV

kDftC =

=

a

a

e

e

k

tk

k

tk

ead

ass

e

e

e

e

kkV

kDftC

11)()(

Cn(t) = concentration after the nth

consecutivedosing in intervals ; BATEMAN-Functionexpanded by accumulation factor

e

e

k

nk

ee

er

=

1

1;

a

a

k

nk

ae

er

=1

1; n = for steady

state, in most cases ra 1

=

)(

)(lnmax, k

e

k

a

ea

ssa

e

ek

ek

kkt

1

11 tss,max < tmax for ka > ke


16/23



Two Compartment Model, IV Inj (without Resorption), single dose

p

kc

iv

X

kk

EXD

2112

10

pccc XkXkXk

dt

dX+= 211012

Tc

pXkXk

dt

dX= 2112 ; cXk

dt

dE= 10

Xc = amount in central compartmentXp = amount in peripheral comp.

)()()()()0()0( =++=== EtEtXtXXXD pcc E()- Sum of drug eliminated

+

=

tt

tt

C eek

eek

V

ktC

)1(

)(

)1()(

)(*21

*21

0

Concentration in plasma =Conc. in central compartment

civ

V

DkA

=)(

)( 21

;c

ivV

DkB

=)(

)( 21

Vc = volume of the central comp.,

>k21>

( )10212102112102112 42

1kkkkkkkk +++++= )(

( )10212102112102112 42

1kkkkkkkk ++++= )(

, = Macro constants (or Hybridconstants, independent of dose,A+B proportional to dose

disposition rate constants, equal foriv and oral administration

1021 kk = ; 102112 kkk ++=+ k k k12 21 10, , -Micro constants

t

term eBtC

=

)( tBtCterm = ln)(ln t

term eAtCtC= )()( tAtCtC term = ln))()(ln(

>, for elim. phase first term =0A,B, , , can determined byfeathering method

Plot ln(Cterm(t)) vs t with slope ,intercept ln(B)Plot ln((C(t)-Cterm(t))) vs t with slope

, intercept ln(A)

BA

BAk

++

=

21 ;

BA

BA

kk

+

+=

=

2110 ;

))((

)( 2

102112

++

=+=BABA

ABkkk

A,B iv A,B oral

k10=kren+ kmet (+kbil+ kother)

=E

U

k

kren

10

)1()1()0(tt

t eB

eA

AUC

+=

BAAUC +=

AUC - by integration of the generalequation for C


17/23



Two Compartment Model, IV Inj, single dose

p

kc

iv

X

kk

EXD

2112

10

( )ttp eekD

tX

= 12)( Xp = drug amount in the tissues(peripheral compartment)

=lnln

max,pt 0=dt

dXpat tmax,p

== )1()()( max,max, bppfc ftCtC

)()1()( max,,max, pfppbpp tCftC =

Most membranes centralcompartment / tissue are crossed bydiffusion by unbound drug onlyfb = fraction bound (to protein)

BA

D

C

DVc +

==)0(

Vc volume of distribution in thecentral compartment

c

c

pc

pc

c V

Xassumed

VV

XX

V

X)(=

++=

Other volume terms areproportionality factors assuming thatCc = CT, they may take onunphysiological values. Initially Xc andCc high with XT and Cp nearly 0. In theend frequently CT > Cp. Vd = volumeof distribution of the total organism not constant in time!

(c

V

X

ck

k

ss

pc

ssssd Vk

kX

C

XXVV

c

c

+=

+=

+==

12

21, 1

112

21

Vss = volume of distribution at

equilibrium, when flows Xc XTbalance: k12Xc = k21XT

D

BA

BAVss

+

+=

2

22

)(

Vss can also be calculated from macroconstants

ccssp Vk

kVVV

12

21== ;p

p

pV

XC =

In the strictest sense only true atequilibrium

( )pp ttc

p eeV

DkC max,max,

)(

21max,

=

ccdt

dE

VktC

tXk

tCCL =

== 10

10

)(

)(

)(

sse VkCL = ;1221

211010

kk

kk

V

Vkk

ss

ce +

=

=

This is the definition of ke for a two-compartment model

cV

DkBAAUC

=+=

21 ; CLVkV

k

kk

AUC

Dcc ==

= 10

21

1021

AUC

DCLVz

==

Vz volume of distribution duringterminal phase, calculated based onthe rate constant

AUCD

zssec VVkVkCL ==== 10 Vz > Vss > Vc during terminal phaseXT > Xc


18/23



Two compartment Model single dose infusion (or zero order resorption)

p

kc

k

X

kk

EXA

2112

100

T

Dk =0

Infusion of dose D during atconstant rate k0

+

=

tt

tt

C eek

eek

V

ktC

)1()(

)1()(

)(*21

*21

0

General equation for calc. of C(t)during and after infusion, t* =

min(,t)

+

= )1(

)()1(

)()( 21210 tt

C

ek

ek

V

ktC

during infusion, t*=t

(et*-1)e

-t becomes 1- e-t

k0 = k10Ass = k10CssVc;CL

k

Vk

kC

css

0

10

0 =

= For a continuing infusion,

+

=

)(21

)(21

0

)(

)1()(

)(

)1()(

)(

TtT

TtT

Ce

ek

eek

V

ktC

after end of infus ion,

t- = time after end


19/23



Two compartment Model, single dose with Resorption First Order

p

kc

k

X

kk

EXA a

2112

10

+

+

=

tk

aa

a

t

a

t

a

c

a

aekk

kk

ek

ke

k

k

V

DFktC

)()(

)(

)()(

)(

)()(

)(

)(21

2121

)()(

)()()()(

21

2121

aa

a

aa

kk

kk

k

k

k

k

=

+

C-central compartment

with micro constants

tktt aeBAeBeAtC ++= )()( C-central compartment

with macro constants

)(

)( 21

=k

V

DA

cIV ;

)(

)( 21

=k

V

DB

cIV

iva

aoral A

k

fkA

=)(

; iva

aoral B

k

fkB

=)(

iviv

c

BfAf

D

f

V

+=

Without iv data only Vc/f can bedetermined, but based on

knowledge of fAiv and fBiv themicro constants k10, k21, k12 maybe derived

tk

a

ttp

aekk

kBAe

k

kBe

k

kAtC

+

+

=

)(

)(

)()()(

21

21

21

21

21

21

CT-deep compartment

Two compartment Model, multiple dose with Resorption First Order

xa

a

a

x

x

tk

k

nk

tntn

xn

ee

eBA

ee

eBe

e

eAtC

+

+

=

1

1)(

1

1

1

)1()(

Cn concentration attime tx after the n

th

administration at interval

, time after first dosing =n


20/23



3 PHARMACODYNAMIC GLOSSARY

3.1 Definitions

Symbol Unit / Dimension Definition

AUEC Arbitrary unitstime Area under the effect curve

Ce Amount/volume Fictive concentration in the effect compartment

Cp Amount/volume Drug concentration in the central compartment

E (effect unit) Effect

E0 (effect unit) Baseline effect

Emax (effect unit) Maximum effect

EC50 Amount/volume Drug concentration producing 50% of maximum effect

Imax(effect unit) Maximum inhibition

I50 Amount/volume Drug concentration producing 50% of maximal inhibition

keo (Time)-1 Rate constant for degradation of the effect compartment

k in (effect unit) (time)-1

Zero order constant for input or production of response

kout (time)-1

First order rate constant for loss of response

M50 Amount/volume 50% of maximum effect of the regulator

MEC Amount/volume Minimum effective concentration

n - Sigmoidicity factor (Hill exponent)

S (effect unit)/

(amount/volume)

Slope of the line relating the effect to the concentration

tMEC Time Duration of the minimum (or optimum) effective

concentration

Ve Volume Fictive volume of the effect compartment


21/23



3.2 Equations: PK/PD Models

E=Efixed if C Cthreshold fixed effect model

CE

CEE+=

50

max Emax model

nn

n

CE

CEE

+

=

50

max sigmoid Emax model

Rkkdt

dRoutin =

Rate of change of the response over time with nodrug present

RkCIC

Ck outin

+=

50

1dt

dR

RkCIC

CIk outn

n

in

+

=

50

max1dt

dR

Inhibition of build-up of response

RCIC

CIkk outin

+

=

50

max1dt

dR

Inhibition of loss of response

RkCE

CEk

dt

dRoutin

+

+=

50

max1 Stimulation of build-up of response

RCE

CEkkdt

dRoutin

+

+=

50

max1

Stimulation of loss of response


22/23



4 STATISTICAL PARAMETERS

4.1 Definitions

Symbol Definition Calculation

AIC Akaike Information Criterion

(smaller positive values indicate a better fit)

AIC = nln(WSSR) +2p

n = number of observed (measured) concentrations,

p = number of parameters in the model

CI Confidence interval, e.g. 90%-CISEMtxCI n = ,1

CV Coefficient of variation in %

x

SD100=CV , SD = standard deviation

Median = ~x Median, value such that 50% of observedvalues are below and 50% above

(n+1)st

value if there are 2n+1 values or arithmeticmean of n

thand (n+1)

stvalue if there are 2n

values

Mean = x Arithmetic mean

=

=n

i

ixn

x

1

1

MSC Model selection criterion AIC, SC, F-ratio test, Imbimbo criterion etc.

SC Schwarz criterion SC = nln(WSSR) +pln(n)

SD Standard deviation VarSD =

SEM Standard error of mean

n

SDSEM =

SSR Sum of the squared deviations between thecalculated values of the model and themeasured values ( )

n

1=i

C-,,

=SSRcalciobsi

C2

SS Sum of the squared deviations between the

measured values and the mean value C ( )n

1=i

C-,

=SSobsi

C

2

n-=SS

,

,

2

1

1

2

==

n

iobsin

iobsi

C

C

n = number of observed (measured) concentrations

use of the second formula is discouraged althoughmathematically identical

WSS or WSSR Weighted sum of the squared deviationsbetween the calculated values of the modeland the measured values

( )n

1=i

C-,,

=WSSRcalciobsi

Ciw2

Var Variance s = SS/(n-1)

X25% Lower quartile (25%- quantile), value suchthat 25% of observed values are below and75% above

may be calculated as median of values betweenminimum and the overall median

X75% Upper quartile (75%- quantile) may be calculated as median of values betweenthe overall median and the maximum


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4.2 Characterisation of log-normally distributed data

Symbol Definition Calculation

gX Geometric mean of log-normally distributeddata

=

=

n

1iig )ln(x*

n

1expX

sd l Standard deviation to the log-transformeddata

=

= =

n

i

n

i

iil xn

xn

sd

1

2

1

2 )ln(1

)ln(1

1

Scatter Scatter-Factor lsdeScatter =

CIg Confidence interval of log-normallydistributed data

=

=

n

i

nig SEMtxn

CI

1

ln05.0,1)ln(1

exp

CVg Geometric coefficient of variation in %1100 ln = Varg eCV [%]

Per16% 16% percentile of log-normally distributeddata

Scatter

XPer

g

16% =

Per84% 84% percentile of log-normally distributeddata

ScatterXPerg84%

=

pk-glossary pk working group 2004

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