Get confidence intervals of restricted cubic splines nadir value (lowest risk of the predictor)

[PabloLamelas]

I'm studying the association between body mass index (BMI) and mortality in different cohorts. I´ve been running multivariable cox model restricted cubic splines using the macro lgtphcurv9 (https://cdn1.sph.harvard.edu/wp-content/uploads/sites/271/2012/09/lgtphcurv9_7-3-2011.pdf) to plot the association between BMI and mortality, which is u-shaped. I'm interested in the lowest risk BMI value and its 95% confidence interval. To get the lowest risk value, I just went to the output table which provides a long table with all the BMI values and the estimate (HR, which then is plotted in a figure), and record the lowest risk value. However, I'm struggling in getting 95% confidence intervals of this value. 

I understand that doing bootstrapping can be an option to create this 95% CI, but I dont know how to run bootstrapping through this macro...

can anybody help me with this?

thanks

Pablo 

[Reeza]

 Bootstrapping involves selecting Subsamples and running it through the macro and collecting the parameter estimates. 

Usually I would recommend David Cassells paper - Don't be loopy, but without knowing your macro in detail (I'm not going to read 50+ pages) I'm not sure it can handle BY group processing. If it can, read Davids paper and follow that method otherwise, you can use the method not recommended in his paper, creating a macro that samples, calls the macro and collects the results. 

[JacobSimonsen]

You dont need bootstrapping. The confidence intervals can be calculated with use of the effect-statement, and the PROC PLM, which should be used after running phreg. Its quite easy, as this example shows.

*first generate some data;
data mydata;
  do i=1 to 10000;
    bmi=rand('uniform',0,10);
	time=rand('exponential',exp(-sin(bmi)));
	output;
  end;
run;

*estimate the spline, and store the result file;
proc phreg data=mydata;
  effect myspline=spline(bmi / knotmethod=list(1,2,3,4,5,6,7,8,9) naturalcubic);
  model time=myspline;
  store result;
run;

*generate the number of bmi-values where the values should be calcuated;
data template;
  do bmi=0 to 10 by 0.01;
  output;
  end;
run;

*then calculate the curve;
proc plm restore=result;
  score data=template out=predicted predicted=predicted lclm=lclm uclm=uclm;
run;

*transform to hazard-ratio scale ;
data predicted;
  set predicted;
  exppredicted=exp(predicted);
  explclm=exp(lclm);
  expuclm=exp(uclm);
  y=exp(sin(bmi));
ruN;

*plot it!;
symbol1 i=join l=1 v=none color=black;
symbol2 i=join l=2 v=none color=black;
symbol3 i=join l=2 v=none color=black;
symbol4 i=join l=1 v=none color=red;
proc gplot data=predicted;
  plot (exppredicted explclm expuclm y)*bmi/overlay;
run;

[PabloLamelas]

Thanks Jacob for your help,
what i really need though is the 95% of the bmi value... i.e: the lowest risk bmi value is 30, what is the 95% of that value? not the 95% CI of the estimate (HR or OR). because the spline analysis provides the lowest value, but is just a single value and no parameters of dispersion are provided...
the following paper states using STATA and they were able to calculate the 95% CI doing bootstrapping.. http://jamanetwork.com/journals/jama/fullarticle/2520627
thanks for your help

[Reeza]

The paper you're referencing was for SAS 9.1 which is at least a decade old. It looks like,the functionality desired regarding cox regression model with spline has been implemented in SAS now. I would review Jacobs answer and assume that he's correct over my answer. 

Re finding the paper, search at Lexjansen.com, in general you can find a paper there on almost any SAS topic. 

[PabloLamelas]

Thanks Reeza,

can you provide more details to find Davis paper?

thanks!

pablo