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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
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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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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
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Symbol Unit /Dimension
Definition Calculation
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
directly taken from analytical data
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
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Symbol Unit /Dimension
Definition Calculation
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)
directly taken from analytical data
tz Time Time p.a. of last analyticallyquantifiable concentration
directly taken from analytical data
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 !
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1.1.2 Parameters after mult iple dosing (at steady state)
Symbol Unit /Dimension
Definition Calculation
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
directly taken from analytical data
Cmin,ss Amount/volume
Minimum observed plasma or serumconcentration during a dosing intervalat steady state
directly taken from analytical data
Ctrough Amount/volume
Measured concentration at the end ofa dosing interval at steady state (takendirectly before next administration)
directly taken from analytical data
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
directly taken from analytical data
Time Dosing interval directly taken from study design
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1.2 Parameters obtained from urine
Symbol Unit /Dimension
Definition Calculation
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
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2 PHARMACOKINETIC PARAMETERS OBTAINED FROM COMPARTMENTALMODELING
Symbol Unit /Dimensions
Definition Calculation
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)
by multiexponential fitting
I (Time)-1 Exponent of the ith (descending)exponential term of a polyexponentialequation
by multiexponential fitting
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
Note: Ci is the linear coefficient of thepolyexponential equation
C(0) Amount/ volume Initial or back-extrapolated drug
concentration following rapidintravenous injection =
n
1=i
iC)0(C
Note: Ci is the linear coefficient of thepolyexponential equation
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
by multiexponential fitting
Km Amount/ volume Michaelis Menten constant by nonlinear fitting
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Symbol Unit /Dimensions
Definition Calculation
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
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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
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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
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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
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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
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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
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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
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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
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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%
=