stab for R -
A Data Analysis Tool for Drug Stability
with R (play the flash demo)
Created by Hsin-ya Lee , and Yung-jin Lee (mobilePK@gmail.com)
College of Pharmacy,
Kaohsiung Medical University
Kaohsiung, Taiwan 807
Introduction:
This package is used to analyze stability data. We follow the ICH
guideline 'Q1E Evaluation for Stability Data' (linked to USA FDA site) to design this tool (Here's its .pdf.). This guideline describes when extrapolation
should be
considered as proposing a retest period for a drug substance or a shelf life
of a drug product that extends beyond the period covered by available data from
the stability study under the long-term storage condition.
Installation & Upgrade: stab for R is one of
R
packages. Thus, users have to
download and install
R first, and then run it.
Under R Console, users can click
"Packages"
from the menu then ->"Install package(s)..." --> select a CRAN mirror site near
you and you will see the list of currently available
R packages.
Just select "stab" from the list and click "OK" to start
installation. Then it's done! If you want to
upgrade from
previous version of stab for R when a new version is released, please go the menu and
click
"Packages", and then select "Update packages...". then
select a CRAN mirror site near you and click "OK". Done! Pretty easy to upgrade.
If you're running Linux PC or Mac OS X, you may not see the menu
but
the R Console. You can read this
R
Installation and Administration (pdf ) for detailed information. You
can also type help("INSTALL") or help("install.packages") in R Console for
information on how to install packages from this directory. Don't worry
about this. You only need
to do this once. After these installation, you now can run stab by simply typing
"library(stab) (enter)"
under R Console.
Remove stab for R: Simply go to the directory of R where you
installed and then go to the sub-directory of /library, delete stab.
Methods::
This package includes
two steps. In the first step, Decision Tree for Data Evaluation
follows "Appendix A" of ICH guideline "Q1E
Evaluation for Stability Data" that assists users evaluating stability data and
guide users to consider doing an extrapolation for a
proposed retest period or shelf life.
In the second
step, Statistical Approaches to Stability Data Analysis is
conducted for two different situations. First one is for a single batch.
This approach estimates the retest period or shelf life for a
single batch of drug product. The relationship between residuals and time is assumed to be
linear. Two-sided 95 % confidence intervals of the regression line for
residuals (% relative to the original amount) of a drug product intersect with upper and lower acceptance
criteria of label claimed. Then, the shortest one is the shelf life.
When there are multiple batches (e.g. 3 batched) available, analysis of
covariance (ANCOVA) is first employed to test the difference in slopes and
intercepts of the regression lines with different factors
(packages, dosage forms, etc.). Then, based on the
statistical results, there can be three possibilities.
(1). slope
(P>=0.25) and intercept (P>=0.25): the tests for
equality of slopes and equality of intercepts are all no differences. The data from all batches then
should be
combined. Then, a single retest period or shelf life is estimated
from the combined data. (2). slope
(P>=0.25) and intercept (P<0.25): the test rejects
the hypothesis of equality of intercepts but fails to reject the
hypothesis with that all
slopes are equal. The data should be
combined to estimate the common slope. The retest
periods or shelf lives for individual batches can be estimated. Then,
the shortest estimate among batches should be chosen as the shelf life
for all batches. (3). [slope
(P<0.25) and intercept (P>=0.25)] or [slope (P<0.25) and intercept
(P<0.25)]: the result in this scenario shows that the test rejects the hypothesis of
equality of all slopes. It is not appropriate to combine the data from all
batches in this situation. The retest periods or shelf lives for individual batches
is estimated. Then, the shortest estimate among batches should be
chosen as the shelf life for all batches.
Please note the "batch" should be numerical ONLY (e.g., 1, 2, 3...)
as the following example; otherwise, it may cause error.
Cross Validation with FDA provided SAS Stability
programs: Please check with
this .pdf file and use bookmarks to browse
this pdf file. Please note that in SAS output, the lines for
the upper and lower ranges were drawn between 90% and 110% (set as default). We did not change that (should be in the file - stab.dat marked with '/* line B */'), though we used different ranges; however, they would not affect the final results. They were just like marks over there.
Note: Please use "PageUP"/"PageDown" keys to switch plots back and forth on the graphic window of R.
Sample output file
------------------ stab for R v0.1.2 -------------------
developed by Hsin-ya Lee and Yung-jin Lee, 2007-2010.
generated on Thu Nov 18 08:27:04 2010
-- --- List of input data --- --
batch time assay (%)
1 1 0 99.2
2 1 3 97.1
3 1 6 96.1
4 1 9 95.2
5 1 12 93.8
6 1 18 93.1
7 1 24 92.4
8 2 0 98.7
9 2 3 97.0
10 2 6 96.2
11 2 9 95.1
12 2 12 94.2
13 2 18 93.3
14 3 0 102.5
15 3 3 98.9
16 3 6 97.1
17 3 9 95.6
18 3 12 94.1
19 3 18 93.1
Analysis settings for multiple batches:
---------------------------------------------
The lower acceptance limit is set to 90 %.
--Output: ANCOVA model: batch vs. time vs. assay (%)--
Analysis of Variance Table
Response: assay
Df Sum Sq Mean Sq F value Pr(>F)
batch 2 8.683 4.342 5.4055 0.01957 *
time 1 94.715 94.715 117.9215 6.859e-08 ***
batch:time 2 8.101 4.051 5.0432 0.02392 *
Residuals 13 10.442 0.803
---
Signif. codes: 0 ．***・ 0.001 ．**・ 0.01 ．*・ 0.05 ．.・ 0.1 ． ・ 1
Type P values
1 Intercept 0.01956915
2 Slope 0.02392274
--------------------------
at a sig. level of 0.25.
--------------------------------------------------------------------------
-- ANCOVA Output: Testing for poolability of batches --
--------------------------------------------------------------------------
The test rejects the hypothesis of equality of slopes (there is a
significant difference in slopes and intercepts among batches).
--Model #3: one-sided lower LC analysis--
separate intercepts and separate slopes between batches.
------------------------------------------------------------------------
--linear regression model: Assay (%) vs. time--
Call:
lm(formula = assay ~ batch * time, data = ANCOVAdata)
Coefficients:
(Intercept) batch2 batch3 time batch2:time
98.04611 0.06961 2.86389 -0.26976 -0.02595
batch3:time
-0.23357
Analysis of Variance Table
Response: assay
Df Sum Sq Mean Sq F value Pr(>F)
batch 2 8.683 4.342 5.4055 0.01957 *
time 1 94.715 94.715 117.9215 6.859e-08 ***
batch:time 2 8.101 4.051 5.0432 0.02392 *
Residuals 13 10.442 0.803
---
Signif. codes: 0 ．***・ 0.001 ．**・ 0.01 ．*・ 0.05 ．.・ 0.1 ． ・ 1
**************************************************************************
-- Output --
--------------------------------------------------------------------------
--Summary: linear regression model--
--- Batch#: 1 ---
Y = 98.0461 +( -0.2697605 ) X
Time Observed assay(%) Calculated assay(%) Residuals
1 0 99.2 98.04611 -1.15389222
2 3 97.1 97.23683 0.13682635
3 6 96.1 96.42754 0.32754491
4 9 95.2 95.61826 0.41826347
5 12 93.8 94.80898 1.00898204
6 18 93.1 93.19042 0.09041916
7 24 92.4 91.57186 -0.82814371
--- Batch#: 2 ---
Y = 98.11571 +( -0.2957143 ) X
Time Observed assay(%) Calculated assay(%) Residuals
1 0 98.7 98.11571 -0.5842857
2 3 97.0 97.22857 0.2285714
3 6 96.2 96.34143 0.1414286
4 9 95.1 95.45429 0.3542857
5 12 94.2 94.56714 0.3671429
6 18 93.3 92.79286 -0.5071429
--- Batch#: 3 ---
Y = 100.91 +( -0.5033333 ) X
Time Observed assay(%) Calculated assay(%) Residuals
1 0 102.5 100.91 -1.59
2 3 98.9 99.40 0.50
3 6 97.1 97.89 0.79
4 9 95.6 96.38 0.78
5 12 94.1 94.87 0.77
6 18 93.1 91.85 -1.25
**************************************************************************
-- Summary and plots --
--------------------------------------------------------------------------
One-sided lower LC analysis
batch# shelf life*
1 1 24.93071
2 2 23.46921
3 3 17.58738
-------------------------
*: estimated shelf life
time fit Lower
1 0 98.04611 97.01794
2 1 97.77635 96.81025
3 2 97.50659 96.59983
4 3 97.23683 96.38611
5 4 96.96707 96.16839
6 5 96.69731 95.94584
7 6 96.42754 95.71750
8 7 96.15778 95.48230
9 8 95.88802 95.23915
10 9 95.61826 94.98703
11 10 95.34850 94.72519
12 11 95.07874 94.45326
13 12 94.80898 94.17134
14 13 94.53922 93.87998
15 14 94.26946 93.58008
16 15 93.99970 93.27268
17 16 93.72994 92.95889
18 17 93.46018 92.63974
19 18 93.19042 92.31613
20 19 92.92066 91.98884
21 20 92.65090 91.65851
22 21 92.38114 91.32566
23 22 92.11138 90.99071
24 23 91.84162 90.65402
25 24 91.57186 90.31585
26 25 91.30210 89.97645
27 26 91.03234 89.63598
28 27 90.76257 89.29462
29 28 90.49281 88.95247
30 29 90.22305 88.60966
31 30 89.95329 88.26626
32 31 89.68353 87.92234
33 32 89.41377 87.57798
34 33 89.14401 87.23322
35 34 88.87425 86.88811
36 35 88.60449 86.54268
37 36 88.33473 86.19697
38 37 88.06497 85.85101
39 38 87.79521 85.50483
40 39 87.52545 85.15844
41 40 87.25569 84.81187
42 41 86.98593 84.46512
43 42 86.71617 84.11823
44 43 86.44641 83.77119
45 44 86.17665 83.42403
46 45 85.90689 83.07674
47 46 85.63713 82.72935
48 47 85.36737 82.38186
49 48 85.09760 82.03428
time fit Lower
1 0 98.11571 97.40949
2 1 97.82000 97.16947
3 2 97.52429 96.92621
4 3 97.22857 96.67878
5 4 96.93286 96.42597
6 5 96.63714 96.16633
7 6 96.34143 95.89817
8 7 96.04571 95.61985
9 8 95.75000 95.33009
10 9 95.45429 95.02842
11 10 95.15857 94.71531
12 11 94.86286 94.39204
13 12 94.56714 94.06026
14 13 94.27143 93.72163
15 14 93.97571 93.37764
16 15 93.68000 93.02947
17 16 93.38429 92.67806
18 17 93.08857 92.32411
19 18 92.79286 91.96817
20 19 92.49714 91.61063
21 20 92.20143 91.25181
22 21 91.90571 90.89194
23 22 91.61000 90.53123
24 23 91.31429 90.16980
25 24 91.01857 89.80778
26 25 90.72286 89.44525
27 26 90.42714 89.08230
28 27 90.13143 88.71898
29 28 89.83571 88.35535
30 29 89.54000 87.99144
31 30 89.24429 87.62729
32 31 88.94857 87.26293
33 32 88.65286 86.89839
34 33 88.35714 86.53368
35 34 88.06143 86.16883
36 35 87.76571 85.80384
37 36 87.47000 85.43874
38 37 87.17429 85.07353
39 38 86.87857 84.70822
40 39 86.58286 84.34283
41 40 86.28714 83.97735
42 41 85.99143 83.61181
43 42 85.69571 83.24620
44 43 85.40000 82.88053
45 44 85.10429 82.51480
46 45 84.80857 82.14902
47 46 84.51286 81.78320
48 47 84.21714 81.41733
49 48 83.92143 81.05142
time fit Lower
1 0 100.91000 99.09266
2 1 100.40667 98.73266
3 2 99.90333 98.36430
4 3 99.40000 97.98520
5 4 98.89667 97.59229
6 5 98.39333 97.18177
7 6 97.89000 96.74936
8 7 97.38667 96.29077
9 8 96.88333 95.80277
10 9 96.38000 95.28410
11 10 95.87667 94.73602
12 11 95.37333 94.16177
13 12 94.87000 93.56562
14 13 94.36667 92.95187
15 14 93.86333 92.32430
16 15 93.36000 91.68599
17 16 92.85667 91.03933
18 17 92.35333 90.38614
19 18 91.85000 89.72781
20 19 91.34667 89.06538
21 20 90.84333 88.39965
22 21 90.34000 87.73125
23 22 89.83667 87.06064
24 23 89.33333 86.38820
25 24 88.83000 85.71424
26 25 88.32667 85.03898
27 26 87.82333 84.36262
28 27 87.32000 83.68532
29 28 86.81667 83.00721
30 29 86.31333 82.32840
31 30 85.81000 81.64896
32 31 85.30667 80.96899
33 32 84.80333 80.28853
34 33 84.30000 79.60765
35 34 83.79667 78.92640
36 35 83.29333 78.24481
37 36 82.79000 77.56291
38 37 82.28667 76.88074
39 38 81.78333 76.19832
40 39 81.28000 75.51568
41 40 80.77667 74.83284
42 41 80.27333 74.14981
43 42 79.77000 73.46661
44 43 79.26667 72.78326
45 44 78.76333 72.09976
46 45 78.26000 71.41613
47 46 77.75667 70.73238
48 47 77.25333 70.04852
49 48 76.75000 69.36455
------------------------------------------------------------------
Drug product with lower acceptance limit of 90 % of label claim
Shelf life = 17 (months/weeks)
******************************************************************
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