Dear all,
Your constant talking about what bootstrap is and is not suitable for
made me finally verify the findings in the Pawinski et al paper.
Here is the procedure and the findings:
- First of all I took the raw data (that was posted earlier on this
list) and estimated the AUC values using equation coefficients of their
recommended model (#10). Though, I was _unable to reproduce_ the r^2,
nor the predictive performance values. My results are 0.74 and 44%,
respectively, while the reported figures were 0.862 and 82% (41 profiles
out of 50). My scatterplot also looks different than the Fig.2 model 10
scatterplot. Weird...
- Then, I fit the multiple linear model to the whole dataset (no
bootstrap), using the time-points of model #10. I obtained r^2 of 0.74
(agreement), mean prediction error of 7.4% +-28.3% and predictive
performance of 44%. The mean reported prediction error (PE) was 7.6%
+-26.7% and predictive performance: 56% (page 1502, second column,
sentence 2nd from top)! I think the difference in PE may be attributed
to numerical differences between SPSS and R, though I can't explain the
difference in predictive performance.
- Finally, I used Gustaf's bootstrap code to fit linear regression
with model #10 time-points on the resampled dataset. The r^2 of the
model with median coefficients was identical to that of the model fit to
entire data, and the predictive performance was better by only one
profile in the range: 46%. As you see, these figures are very far from
the numbers reported in the paper. I will be in discussion with the
authors on how they obtained these numbers, but I am having doubts if
this paper is valid at all...
- Later I tested it on my own dataset (paper to appear in August), and
found that the MLR model fit on entire data has identical r^2 and
predictive performance as the median coefficient model from bootstrap.
I must admit, guys, *that I was wrong and you were right: this
bootstrap-like procedure does not improve predictions* - at least not to
the extent reported in the Pawinski et al paper.
I was blindly believing in this paper and I am somewhat embarrassed that
I didn't verify these findings, despite that their dataset was available
to me since beginning. Maybe it was too much trust in printed word and
in authority of a PhD biostatistician who devised the procedure...
Nevertheless, I am happy that at least this procedure is harmless, and
that I can reproduce the figures reported in /my/ paper.
Best regards, and apologies for being such a hard student. I am being
converted to orthodox statistics.
--
Michal J. Figurski
HUP, Pathology & Laboratory Medicine
Xenobiotics Toxicokinetics Research Laboratory
3400 Spruce St. 7 Maloney
Philadelphia, PA 19104
tel. (215) 662-3413
Gustaf Rydevik wrote:
On Thu, Jul 31, 2008 at 4:30 PM, Michal Figurski
<[EMAIL PROTECTED]> wrote:
Frank and all,
The point you were looking for was in a page that was linked from the
referenced page - I apologize for confusion. Please take a look at the two
last paragraphs here:
http://people.revoledu.com/kardi/tutorial/Bootstrap/examples.htm
Though, possibly it's my ignorance, maybe it's yours, but you actually
missed the important point again. It is that you just don't estimate mean,
or CI, or variance on PK profile data! It is as if you were trying to
estimate mean, CI and variance of a "Toccata_&_Fugue_in_D_minor.wav" file.
What for? The point is in the music! Would the mean or CI or variance tell
you anything about that? Besides, everybody knows the variance (or
variability?) is there and can estimate it without spending time on
calculations.
What I am trying to do is comparable to compressing a wave into mp3 - to
predict the wave using as few data points as possible. I have a bunch of
similar waves and I'm trying to find a common equation to predict them all.
I am *not* looking for the variance of the mean!
I could be wrong (though it seems less and less likely), but you keep
talking about the same irrelevant parameters (CI, variance) on and on. Well,
yes - we are at a standstill, but not because of Davison & Hinkley's book. I
can try reading it, though as I stated above, it is not even "remotely
related" to what I am trying to do. I'll skip it then - life is too short.
Nevertheless I thank you (all) for relevant criticism on the procedure (in
the points where it was relevant). I plan to use this methodology further,
and it was good to find out that it withstood your criticism. I will look
into the penalized methods, though.
--
Michal J. Figurski
I take it you mean the sentence:
" For example, in here, the statistical estimator is the sample mean.
Using bootstrap sampling, you can do beyond your statistical
estimators. You can now get even the distribution of your estimator
and the statistics (such as confidence interval, variance) of your
estimator."
Again you are misinterpreting text. The phrase about "doing beyond
your statistical estimators", is explained in the next sentence, where
he says that using bootstrap gives you information about the mean
*estimator* (and not more information about the population mean).
And since you're not interested in this information, in your case
bootstrap/resampling is not useful at all.
As another example of misinterpretation: In your email from a week
ago, it sounds like you believe that the authors of the original paper
are trying to improve on a fixed model
Figurski:
"Regarding the "multiple stepwise regression" - according to the cited
SPSS manual, there are 5 options to select from. I don't think they used
'stepwise selection' option, because their models were already
pre-defined. Variables were pre-selected based on knowledge of
pharmacokinetics of this drug and other factors. I think this part I
understand pretty well."
This paragraph is wrong. Sorry, no way around it.
Quoting from the paper Pawinski etal:
" *__Twenty-six____(!)* 1-, 2-, or 3-sample estimation
models were fit (r2 0.341� 0.862) to a randomly
selected subset of the profiles using linear regression
and were used to estimate AUC0�12h for the profiles not
included in the regression fit, comparing those estimates
with the corresponding AUC0�12h values, calculated
with the linear trapezoidal rule, including all 12
timed MPA concentrations. The 3-sample models were
constrained to include no samples past 2 h."
(emph. mine)
They clearly state that they are choosing among 26 different models by
using their bootstrap-like procedure, not improving on a single,
predefined model.
This procedure is statistically sound (more or less at least), and not
controversial.
However, (again) what you are wanting to do is *not* what they did in
their paper!
resampling can not improve on the performance of a pre-specified
model. This is intuitively obvious, but moreover its mathematically
provable! That's why we're so certain of our standpoint. If you really
wish, I (or someone else) could write out a proof, but I'm unsure if
you would be able to follow.
In the end, it doesn't really matter. What you are doing amounts to
doing a regression 50 times, when once would suffice. No big harm
done, just a bit of unnecessary work. And proof to a statistically
competent reviewer that you don't really understand what you're doing.
The better option would be to either study some more statistics
yourself, or find a statistician that can do your analysis for you,
and trust him to do it right.
Anyhow, good luck with your research.
Best regards,
Gustaf
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