Frank E Harrell Jr Professor and Chairman School of Medicine
Department of Biostatistics Vanderbilt University
On Wed, 11 Aug 2010, Michal Figurski wrote:
Peter, Frank, David and others,
Thank you all for your ideas. I understand your lack of trust in P&B
method. Setting that aside (it's beyond me anyways), please see below
what I have finally came up with to calculate the CI boundaries. Given
the slope and intercept with their 05% & 95% CIs, and a range of x = 1:50 :
ints = c(-1, 0, 1) # c(int05%, int, int95%)
slos = c(0.9, 1, 1.1) # c(slo05%, slo, slo95%)
CIs = data.frame(x=1:50, lo=NA, hi=NA)
for (i in 1:50) {
CIs$lo[i] = min(ints + slos * CIs$x[i])
CIs$hi[i] = max(ints + slos * CIs$x[i])
}
It looks like it works to me. Does it make sense?
Doesn't look like it takes the correlation of slope and intercept into
account but I may not understand.
Now, what about a 4-parameter 'nls' model? Do you guys think I could use
the same approach?
This problem seems to cry out for one of the many available robust
regression methods in R.
Frank
Best regards,
--
Michal J. Figurski, PhD
HUP, Pathology & Laboratory Medicine
Biomarker Research Laboratory
3400 Spruce St. 7 Maloney
Philadelphia, PA 19104
tel. (215) 662-3413
On 2010-08-10 13:12, Peter Dalgaard wrote:
Michal Figurski wrote:
# And the result of the Passing-Bablok regression on this data frame:
Estimate 5%CI 95%CI
Intercept -4.306197 -9.948438 -1.374663
Slope 1.257584 1.052696 1.679290
The original Passing& Bablok article on this method has an easy
prescription for CIs on coefficients, so I implemented that. Now I need
a way to calculate CI boundaries for individual points - this may be a
basic handbook stuff - I just don't know it (I'm not a statistician).
The answer is that you can't. You can't even do it with ordinary linear
regression without knowing the correlation between slope and intercept.
However, if you can get a CI for the intercept then you could subtract
x0 from all the x and get a CI for the value at x0.
(This brings echos from a distant past. My master's thesis was about
some similar median-type estimators. I can't remember whether I looked
at the Passing-Bablok paper at the time (1985!!) but my general
recollection is that this group of methods is littered with unstated
assumptions.)
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