[R] Joint confidence interval for fractional polynomial terms

[Frank Harrell]

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
> 
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-----
Frank Harrell
Department of Biostatistics, Vanderbilt University
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