R help - Jan 2012 - Joint confidence interval for fractional polynomial terms

Dear R users,

The package 'mfp' that fits fractional polynomial terms to predictors.
Example:
data(GBSG)
f <- mfp(Surv(rfst, cens) ~ fp(age, df = 4, select = 0.05)
                 + fp(prm, df = 4, select = 0.05), family = cox, data = GBSG)
print(f)

To describe the association between the original predictor, eg. age and
risk for different values of age I can plot it the polynomials and fitted
coefficients as:

plot(0.407*I((age/100)^-2) + -4.96*I((age/100)^-0.5) ~ age, GBSG)

But I can't work out how to get a 95% confidence interval for this
curve... Any suggestions? I could bootstrap it, but is there a
mathematical solution?

Many thanks
Eleni Rapsomaniki
Medical Statistician
UCL, London

This does not exactly answer your question but if you were to use restricted
cubic splines instead of FPs, an upcoming new release of the rms package
allows one to easily obtain simultaneous confidence bands for any series of
predictions.  So for your case you would hold all covariates constant except
for the one varying on the x-axis, and tell the Predict function to use
conf.type='simultaneous'.  I've also added pointwise bootstrap
nonparametric
confidence bands for this context.

Simultaneous confidence bands handle the simultaneous uncertainty of all the
terms making up the spline function that are "in play" for the range
of
predictions being requested, i.e., terms that are involved because of the
knot locations and the Xs being requested.

Note that with fractional polynomials, if you use any term selection, the
pointwise confidence intervals are not even correct.
Frank

Eleni Rapsomaniki-3 wrote
> 
> Dear R users,
> 
> The package 'mfp' that fits fractional polynomial terms to
predictors.
> Example:
> data(GBSG)
> f <- mfp(Surv(rfst, cens) ~ fp(age, df = 4, select = 0.05)
>                  + fp(prm, df = 4, select = 0.05), family = cox, data >
GBSG)
> print(f)
> 
> To describe the association between the original predictor, eg. age and
> risk for different values of age I can plot it the polynomials and fitted
> coefficients as:
> 
> plot(0.407*I((age/100)^-2) + -4.96*I((age/100)^-0.5) ~ age, GBSG)
> 
> But I can't work out how to get a 95% confidence interval for this
> curve... Any suggestions? I could bootstrap it, but is there a
> mathematical solution?
> 
> Many thanks
> Eleni Rapsomaniki
> Medical Statistician
> UCL, London
> 
> ______________________________________________
> R-help@ mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 

-----
Frank Harrell
Department of Biostatistics, Vanderbilt University
--
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Dear Professor Harrell,

Once again thank you for your helpful reply. I could use rcs instead, so I
look forward to your latest rms release (soon I hope?)
Initially I favoured fractional polynomials thinking that the model would
be easier to present, but now I see that with either method unless one
plots the fitted function results are just as hard to interpret. That's
why the simultaneous CI plot will be very useful.

Eleni
> On Jan 9, 2012, at 8:45 AM, "Eleni Rapsomaniki" <e.rapsomaniki
at ucl.ac.uk>
> wrote:
>
>> Dear R users,
>>
>> The package 'mfp' that fits fractional polynomial terms to
predictors.
>> Example:
>> data(GBSG)
>> f <- mfp(Surv(rfst, cens) ~ fp(age, df = 4, select = 0.05)
>>                 + fp(prm, df = 4, select = 0.05), family = cox, data
>> GBSG)
>> print(f)
>>
>> To describe the association between the original predictor, eg. age and
>> risk for different values of age I can plot it the polynomials and
>> fitted
>> coefficients as:
>>
>> plot(0.407*I((age/100)^-2) + -4.96*I((age/100)^-0.5) ~ age, GBSG)
>>
>> But I can't work out how to get a 95% confidence interval for this
>> curve... Any suggestions? I could bootstrap it, but is there a
>> mathematical solution?
>>
>> Many thanks
>> Eleni Rapsomaniki
>> Medical Statistician
>> UCL, London
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>