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Dear all，
I have a problem about the statistical method used in PK data analysis.
Total 4 subjects. Each of them did two PK studies(PK1 and PK2). PK1 served as self-control.
Responses of PK1 are 204.9, 199.3, 225.6 and 256.10. Responses of PK2 are 341.5, 390.0, 330.6,
368.9.
Two statistical analysis methods were used on the SPSS. Statistical power was calculated from
G*Power3.
First, wilcoxon signed-rank test was used. The p value is 0.068, and statistical power is 0.966.
Second, we use the paired-t test after log transformation. The p value is 0.016, and statistical
power is 0.982.
For these two methods, the p values show differences. Consequently, the conclusions are opposite.
My questions are:
1) Is there something wrong in the above statistical analysis?
2) Why the results of these two methods do not match? (Usually if there is adequate statistical
power, these two methods should draw same conclusion)
3) Which method should be used in this case?
4) In this study, 4 subjects get great statistical power. Is it necessary to increase the number of
subject?
Thanks in advance, :-)
Xiaoming
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Given the number of subjects you have you should use a nonparametric test. The results of your test
are difference because they are different tests and are based on different assumptions about the
distribution of your data. Given only 4 observations per group, the normality assumption for the
T-test is hard to verify.
I'm not sure I understand why you are looking at post-hoc power. The power of a test is something
to be considered before you do the experiment.
Pete Bonate
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Hi, Xiaoming
Firstly, I'd like to confirm if the following my understanding is correct:
1. You are comparing a PK parameter obtained in two conditions, 1 & 2, in the same subjects by
one-way crossover design.
2. You have a confidence of no sequence effects on the PK.
3. The p-value you mentioned means alpha on the null hypothesis of PK1=PK2.
4. The statistical power you mentioned means 1-beta, where beta stands for PK1PK2.
5. You are thinking some doubts on the statistical analysis you made.
I'm not a statistician and do not use SPSS but have some suggestions for your questions:
1) The two methods calculate statistics in two different ways and usually differ from each other.
2) Because the statistical methods stand different assumptions on the distribution of the values.
3) It depends on what prior information you have on the distribution of the PK and on the study
design.
4) If you do not have a confidence on the distribution of the PK, you need more PK values to confirm
the assumption. This also means, if you need to estimate the degree of the difference in PK more
accurately, you need more samples.
Hope this helps,
Masaki
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The statistical method is according to your data type. I dont understand why you choose wilcoxon?
paired-t test would be better because you just had two group,and one of them used as self-control.
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Dear Xiaoming,
In my opinion the sample size is very less, power is post hoc analysis and depends on variation in
data, lesser the variation less number of subjects required that does not mean you use four
subjects, the moment you are doing this there is good chance on either end to miss the true
variation of population.
If the same subjects are used then paired T test is good choice.
What is your objective/Hypothesis?
Are you comparing PK1 Vs PK2?
What values it represent when you say PK1 and PK2 are these Cmax, AUC, Tmax ....etc
There are statistical methods established for PK statistical analysis.
Regards,
Atish
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Hi Xiaoming,
The purpose of any significance test is to investigate whether there are differences between two
populations with regards to a specific outcome. To do so, we sample a number of subjects from one
population and then compare the outcome of interest to another sample with a number of subjects from
presumably another population. The idea is that the observed differences are so far away from being
caused by mere chance that we can conclude it is unlikely that the two populations (from which we
have sampled) are the same. A major factor in this analysis is that subjects in our sample are
representative of the broader population so any conclusions made based on comparing samples are
valid for the larger population. So I'd like to answer your question by asking you this: Do you
really believe that 4 subjects truly are representative of the larger population? If not, there is
no reason for you to do any significance test.
In more general terms, what is the goal of the project at an early stage of development? People get
too focused on significance testing based on extremely small number of subjects and at very early
stages of the development. In my opinion, instead of looking for differences based on limited data
from small samples one should focus on learning the system under investigation and use that to plan
future studies to learn even more until there are compelling evidence that there is enough knowledge
to move ahead and have a proper head-to-head comparison. I am a little biased so by learning I refer
to developing mathematical models that relates various factors of a study (e.g., dose,
concentration, ...) to an outcome. Once the relationship between those factors and the outcome is
established, one will have more confidence in designing and performing studies that test a
significant difference between various populations. In fact, one can look at the number of subjects
necessary, type of subjects, probability of success with each study design, and more using these
models.
Toufigh
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Dear All:
This is not on the current subject, but if you are interested in doing things optimally, in a
way that leads to maximally precise dosage regimens for patient care, which I would suggest is why
we are all doing this, then I would strongly urge you to use nonparametric (NP) methods for
population PK/PD analysis. They are not bound by the constraints of assuming the shape of the
parameter distributions, and because of this, they get results which have truly maximum likelihoods,
which are not limited by the constraining assumptions of normal, lognormal, bimodal, etc. They also
do better ar perceiving unsuspected subpopulations and outliers. The distributions simply are what
they are.
I am attaching 3 papers for you all to consider [Sorry didn't see the papers and no attachments
anyway - db ]. The real problem is that when you use parametric procedures like so many seem to
want to do (perhaps because the drug industry is not really interested in any form of dosage except
one size fits all), they can never perceive the issue of precise dosage, as there is only one dose
to consider, and one simply assumes it will hit the desired target exactly, and we all know that is
never so, simply because of the diversity among the subjects in the population.
Using NP models, one can also use multiple model (MM) dosage design to develop a dosage regimen
that specifically hits a clinically desired target goal with maximum precision (minimum expected
weighted squared error).
Very best regards to all,
Roger Jelliffe
Roger Jelliffe MD
Professor of Medicine Emeritus, Founder and Director Emeritus,
Laboratory of Applied Pharmacokinetics and Bioinformatics, USC School of Medicine,
Consultant in Infectious Diseases, Children’s Hospital of Los Angeles
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Dear Xiaoming
In the case under discussion, the number of subjects is very small, same population has been used
and distribution of data with this much lesser number of subjects is not verifiable thus,
non-parametric paired test, i.e., Wilcoxon test is appropriate. However, the number of subject is
too small to get a validated outcome and generalizable inference. To avoid biasnss, the statistical
test is considered before experimentation.
Regards.
Truly yours
--
Prof. Dr. Nadeem Irfan Bukhari
University College of Pharmacy,
University of the Punjab,
Allama Iqbal Campus, Lahore-54000
Pakistan
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Dr. Jelliffe,
Can you post the three papers you mention? [Maybe just the citations - db ]
Thank you.
Stan Alekman
Stanley L. Alekman, PhD
Pharmaceutical Consultants
S.L. Alekman Associates Inc.
Stanley110.-at-.aol.com
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Dear Stan:
You bet. They are
Bustad A, Terziivanov D, Leary R, Port R, Schumitzky A, and Jelliffe R: Parametric and Nonparametric
Population Methods: Their Comparative Performance in Analysing a Clinical Data Set and Two Monte
Carlo Simulation Studies. Clin. Pharmacokinet., 45: 365-383, 2006.
Neely M, van Guilder M, Yamada W, Schumitzky A, and Jelliffe R: Accurate Detection of Outliers and
Subpopulations with Pmetrics, a Nonparametric and Parametric Pharmacometric Modeling and Simulation
Package for R. Therap. Drug Monit. 34: 467-476, 2012.
Jelliffe R: Estimation of Creatinine Clearance in Patients with Unstable Renal Function, without a
Urine Specimen. Am. J. Nephrology, 22: 320-324, 2002.
Jelliffe R, Bayard D, Milman M, Van Guilder M, and Schumitzky A: Achieving Target Goals most
Precisely using Nonparametric Compartmental Models and "Multiple Model" Design of Dosage Regimens.
Therap. Drug Monit. 22: 346-353, 2000.
I also threw in the one on creatinine clearance as it is really needed in patients with changing
renal function.
All the best,
Roger
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Let's see. You used a non parametric approach on non normalized data then a parametric approach on
normalized data! What do the individual responses look like? What tests did you do to determine
first the selection of wilcoxon then selection of paired t then the selection of a transform to
normalize the data. Did you run on transformed data in the t test first and did you run transformed
data in the wilcoxon? When buying apples it is best to avoid oranges.
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Dear All,
Thank you so much for the reply and the suggestions.
The aim of our study is to test the changes of PK in two different physiological conditions (PK1 and
PK2). Although the number of animal is limited, I agree that the paired-t test is a good statistical
method for our PK analysis because each animal serviced as self-control in the PK1 and PK2 studies.
I will report the results with statistical analysis and visual analysis to confirm the PK changes.
I read some of PK references, and find that there are a lot of different statistical methods used
for PK data analysis. However, most of author did not explain why selected such statistical method.
I would like to ask for a big favor. Could you please share some of references or guidance, such as
FDA guidance, in which talk about or give some criteria for using statistical method in PK data
analysis?
Thanks J
Xiaoming
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Dear Xiaoming:
The FDA is stuck in parametric methods, as they let themselves be regulated by the industry
they are supposed to regulate. They are mostly oriented about what the industry wants, and in my
opinion, while they do many good things, they are not concerned with optimal individualized dosage
regimens, as they should be. They still go along with the industry's one size fits all for dosing.
So, instead of setting standards as they should do, they behave in a totally passive form and are
content with parametric approaches to modeling. I would forget any FDA guidance in PK/PD analysis.
It simply is not the best.
Again, you might look at:
Bustad A, Terziivanov D, Leary R, Port R, Schumitzky A, and Jelliffe R: Parametric and Nonparametric
Population Methods: Their Comparative Performance in Analysing a Clinical Data Set and Two Monte
Carlo Simulation Studies. Clin. Pharmacokinet., 45: 365-383, 2006.
Neely M, van Guilder M, Yamada W, Schumitzky A, and Jelliffe R: Accurate Detection of Outliers and
Subpopulations with Pmetrics, a Nonparametric and Parametric Pharmacometric Modeling and Simulation
Package for R. Therap. Drug Monit. 34: 467-476, 2012.
Jelliffe R: Estimation of Creatinine Clearance in Patients with Unstable Renal Function, without a
Urine Specimen. Am. J. Nephrology, 22: 320-324, 2002.
Jelliffe R, Bayard D, Milman M, Van Guilder M, and Schumitzky A: Achieving Target Goals most
Precisely using Nonparametric Compartmental Models and "Multiple Model" Design of Dosage Regimens.
Therap. Drug Monit. 22: 346-353, 2000.
See what YOU think after looking at these papers. The Pmetrics software for population modeling,
including modeling of large nonlinear and interacting systems of multiple drugs together, is
available at www.lapk.org. Michael Neely has done a superb job with this software. Relevant clinical
software, BestDose, is also available there. Both are free.
Very best regards,
Roger Jelliffe
Roger Jelliffe MD
Professor of Medicine Emeritus, Founder and Director Emeritus,
Laboratory of Applied Pharmacokinetics and Bioinformatics, USC School of Medicine,
Consultant in Infectious Diseases, Children’s Hospital of Los Angeles
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Dear Xiaoming, with only 4 you cannot use t-test, even after log-transform because normality cannot
be assumed. The non-parametric Wilcoxon is preferred.
Regards,
JaiPhone
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