Transcript Test principle

ANALYTICAL METHOD TRANSFER USING
EQUIVALENCE TESTS WITH REASONABLE
ACCEPTANCE CRITERIA AND APPROPRIATE
EFFORT: EXTENSION OF THE ISPE CONCEPT
L. Kaminski§, U. Schepers§, H. Wätzig*
§both authors equally contributed to this article
Supplementary material
Introduction
This file shall provide additional information and hence lead to a better
understanding of some circumstances presented in the original paper
“ANALYTICAL METHOD TRANSFER USING EQUIVALENCE TESTS
WITH REASONABLE ACCEPTANCE CRITERIA AND APPROPRIATE
EFFORT: EXTENSION OF THE ISPE CONCEPT” by Kaminski, L.,
Schepers, U. and Wätzig, H.[1] It does not claim to be an exhaustive
explanation of equivalence tests. Please refer to the above mentioned
work for detailed information about these tests and their use in analytical
method transfer.
[1]
L. Kaminski , U. Schepers and H. Wätzig, J. Pharm. Biomed. Anal (2010), doi:10.1016/j.jpba.2010.04.034
Test principle
• Same test principle for classic t-test and for the
equivalence test!
  xT  x R
  t n , ˆ P Y  C L
Confidence interval
CL
standardized normal
distribution of the θ value
C U    t n , ˆ P Y

CU
θ0 = 0
Reference value
classic two sided t-test
CL  CU
High precision and/or
high number of samples
θ0 = 0
Statistically significant but practically irrelevant difference!  transfer wrongly rejected
The t-test paradoxically rewards imprecise
working and low data numbers
Statistically insignificant but practically relevant difference!  transfer wrongly accepted
Low precision and/or low
number of samples
CL

CU
θ0 = 0
equivalence test
CL  CU
High precision and/or
high number of samples
θ0 = 0
-2%
+2%
Same starting position, but an interval of
relevance (acceptance interval) with e.g. ±2% is
introduced in addition here!
Low precision and/or low
number of samples
CL

CU
-2%
θ0 = 0
+2%
equivalence test
CL  CU
High precision and/or
high number of samples
θ0 = 0
-2%
+2%
The whole confidence interval lies within the interval of relevance  equivalence!
The equivalence test rewards precise
working and high numbers of samples
The confidence interval lies partially outside the interval of relevance  no equivalence!
Low precision and/or low
number of samples
CL

CU
-2%
θ0 = 0
+2%
classic two sided t-test (Figure 3)
When measurement spread
gets higher (e.g. ±2%) the
error probability increases
to almost 40% at the
acceptance limit (approx.
60% acceptance
probability)!
100
acceptance
probability of 95%
90
acceptance probability [%]
80
error probability of
12%
error probability of
5% (ISPE concept)
70
60
50
40
30
20
10
0
0,00
0,50
1,00
1,50
2,00
2,50
true deviation betw een the labs [%]
2,0%
1,0%
0,5%
Acceptance tolerance
of approx. 2,3%
equivalence test (Figure 2)
100
Acceptance limit
90
acceptance probability [%]
80
error probability of
12%
error probability of
5% (ISPE concept)
70
60
50
40
30
20
10
0
0,00
0,50
1,00
1,50
~1,65
2,00
true deviation between the labs (bias) [%]
0.7%
1.0%
1.2%
2,50