Melinata G. Indrayanto 2006, Unpublished work
Why did USP 3940 still use ‘R” ??
USP Medicines Compendium 2013
Some mathematical equations for evaluation of linearity Funk’s
et al., 1992
i i
Y xo
XO
bx a
y y
y S
S S
X S
V
+ =
− =
= ⋅
=
∑
ˆ ,
ˆ where
100
i i
Y xo
XO
bx a
y y
y S
S S
X S
V
+ =
− =
= ⋅
=
∑
ˆ ,
ˆ where
100
i Y
XO
bx a
y N
S b
S +
= −
= =
ˆ ,
2 where
i Y
XO
bx a
y N
S b
S +
= −
= =
ˆ ,
2 where
0.05 p
and 2
- N
f for
factor student t
t ,
1 1
1 .
. Y
with .
1 1
. .
2
2 2
2 P
2 2
= =
= −
= +
+ +
= −
+ +
=
∑ ∑
i i
XX XX
table Y
XX P
table XO
P
X N
X Q
Q X
N t
S a
Q b
Y Y
N t
S X
The importance of the Xp’s Value for testing the linearity
Xp values must be X1
Lowest Highest
= Working range
The Calibration Curve was not homogeneous
Testing of Homogeneity Homoscedasticity of the Calibration Curve
r close to one is NOT a reliable indicator of linearity
Proving Linearity according to Araujo 2009
i = concentrations level; j = replicat
– The calibration spots should be independent of each other, therefore spots should be applied from different, independently
weighed solutions – not by diluting from one and the same stock solution.
Journal of Planar Chromatography 23 2010 3, 173–179 DOI: 10.1556JPC.23.2010.3.1 173
0933-4173 20.00 © Akadémiai Kiadó, Budapest
stock solution.
– As a consequence, calibration spots should be applied using uniform volume of solutions, but different concentrations, to
avoid the different band-broadening effects of the different amounts of solution per spot or band
Working range WR of a calibration curve
can be defined as:
“the ratio of upper concentration X
u
and lower concentration X
l
”
In QC of Pharmaceutical Industry, WR = 1.5 – 2
Our recommendation: ± 20 from target concentration
with n = 45
If WR 10 , It is recommended to use
“a weighting regression calibration curve”
cited from: S. Kromidas ed. , HPLC Made to Measure, Wiley- VCH, Weinheim, 2006,pp. 105-115
Requirement of assay using Single point Calibration
• Linear response function OK
• Negligible constant systemic error
CL is not significantly different to zero, or •
Negligible constant systemic error CL is not significantly different to zero, or
Intercept 2 from target compound
• Homogeneity of variance