[R] Plotting confidence bands around regression line

[Frank Harrell]

Thanks Michael,

That's the method that Dana Quade taught me in his intro 
nonparametrics course at UNC in the mid 1970s, at least for a single 
predictor.  His method did not incorporate the shift you mentioned 
though.  The method looks robust.  Not sure about efficiency.

Frank

Frank E Harrell Jr   Professor and Chairman        School of Medicine
                      Department of Biostatistics   Vanderbilt University

On Tue, 10 Aug 2010, Michal Figurski wrote:

> Frank,
>
> I had to order this article through Inter-Library Loan and wait for it
> for a week!
>
> I'll try to make it short. In Passing-Bablok the principle is to
> calculate slopes between all possible pairs of points in the dataset,
> and then to take a "shifted" median of those slopes, where the offset is
> the number of slopes of value <(-1). Because of this, bootstrap is out
> of question - it would take too much time.
>
> Let "n" be the number of data points, N - the number of slopes and K -
> the offset. The locations of CI boundaries in the set of N slopes are
> then calculated with formulas:
> M1 <- N - qnorm(1 - conf.level/2) * sqrt((n*(n-1)*(2*n+5))/18))/2
> M2 <- N - M1 + 1
>
> CIs for intercept are calculated as medians of y(i) - slopes[M1,M2]*x(i)
>
> I hope I don't confuse anyone.
>
> The article has a "mathematical derivations" section and "justification"
> for these formulas. It looks solid to me, although after 25 years the
> flaws may be apparent to some of you.
>
> --
> 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 12:29, Frank Harrell wrote:
>>
>> Please give the prescription. The article is not available on our
>> extensive online library. I wonder if the method can compete with the
>> bootstrap.
>>
>> Frank
>>
>> Frank E Harrell Jr Professor and Chairman School of Medicine
>> Department of Biostatistics Vanderbilt University
>>
>> On Tue, 10 Aug 2010, Michal Figurski wrote:
>>
>>> David,
>>>
>>> I would consider myself intermediate in R, but a beginner in statistics.
>>> I need a formula that would allow me to calculate confidence boundaries
>>> of the regression line given the slope, intercept and their CIs (and
>>> *any* range).
>>>
>>> Passing-Bablok regression doesn't yet exist in R - I am developing it.
>>> Therefore I am sure there is no predict method for it ;)
>>>
>>> I believe I have provided sufficient data to address this problem, but
>>> if that would help anyone, here is more:
>>>
>>> # data frame
>>>> a <- structure(list(x = c(0.1, 1.43, 4.21, 3.67, 3.23, 7.72, 5.99,
>>> 9.16, 10.6, 9.84, 11.94, 12.03, 12.89, 11.26, 15.54, 15.58, 17.32,
>>> 17.65, 19.52, 20.48, 20.44, 20.51, 22.27, 23.58, 25.83, 26.04, 26.92,
>>> 28.44, 30.73, 28.78), y = c(1.08, 1.39, 1.84, 0.56, 7.23, 4.91, 3.35,
>>> 7.09, 3.16, 8.98, 16.37, 7.46, 15.46, 23.2, 4.63, 11.13, 15.68, 13.92,
>>> 26.44, 21.65, 21.01, 20.22, 22.69, 22.21, 23.6, 17.24, 45.24, 30.09, 40,
>>> 49.6)), .Names = c("x", "y"), row.names = c(NA, -30L), class =
>>> "data.frame")
>>>
>>> Then I run the regression procedure (in development - now part of the
>>> 'MethComp' package):
>>>> print(PBreg(a))
>>>
>>> # 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). I
>>> would appreciate if anyone could point me to a handbook or website where
>>> it is described.
>>>
>>> Regarding 2 - the predict method for 'nls' class currently *ignores* the
>>> interval parameter - as it is stated in documentation.
>>>
>>> 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 11:38, David Winsemius wrote:
>>>>
>>>> On Aug 10, 2010, at 11:23 AM, Michal Figurski wrote:
>>>>
>>>>> David,
>>>>>
>>>>> I may have stated my problem incorrectly - my problem is to *obtain
>>>>> the coordinates* for confidence boundary lines. As input data I have
>>>>> only CIs for slope and intercept.
>>>>
>>>> Wouldn't you also need to specify the range over which these estimates
>>>> might be valid and to offer the means for the X values? What level of R
>>>> knowledge are you at? You have provided no data or code. Many R methods
>>>> offer predict methods that return CI's.
>>>>
>>>
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>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>