Maybe if we think and wish and hope and pray
It might come true.
Oh, wouldn't it be nice?

The Beach Boys

Months ago, I wrote about how to use the EFFECT statement in SAS to perform regression with restricted cubic splines. This is the modern way to use splines in a regression analysis in SAS, and it replaces the need to use older macros such as Frank Harrell's %RCSPLINE macro. I shared my blog post with a colleague at SAS and mentioned that the process could be simplified. In order to specify the placement of the knots as suggested by Harrell (Regression Modeling Strategies, 2010 and 2015), I had to use PROC UNIVARIATE to get the percentiles of the explanatory variable. "Wouldn't it be nice," I said, "if the EFFECT statement could perform that computation automatically?"

I am happy to report that the 15.1 release of SAS/STAT (SAS 9.4M6) includes a new option that makes it easy to place internal knots at percentiles of the data. You can now use the KNOTMETHOD=PERCENTILELIST option on the EFFECT statement to place knots. For example, the following statement places five internal knots at percentiles that are recommended in Harrell's book:
EFFECT spl = spline(x / knotmethod=percentilelist(5 27.5 50 72.5 95));

### An example of using restricted cubic in regression in SAS

Restricted cubic splines are also called "natural cubic splines." This section shows how to perform a regression fit by using restricted cubic splines in SAS.

For the example, I use the same Sashelp.Cars data that I used in the previous article. For clarity, the following SAS DATA step renames the Weight and MPG_City variables to X and Y, respectively. If you want to graph the regression curve, you can sort the data by the X variable, but this step is not required to perform the regression.

```/* create (X,Y) data from the Sashelp.Cars data. Sort by X for easy graphing. */ data Have; set sashelp.cars; rename mpg_city = Y weight = X model = ID; run;   proc sort data=Have; by X; run;```

The following call to PROC GLMSELECT includes an EFFECT statement that generates a natural cubic spline basis using internal knots placed at specified percentiles of the data. The MODEL statement fits the regression model and the OUTPUT statement writes an output data set that contains the predicted values. The SGPLOT procedure displays a graph of the regression curve overlaid on the data:

```/* fit data by using restricted cubic splines using SAS/STAT 15.1 (SAS 9.4M6) */ ods select ANOVA ParameterEstimates SplineKnots; proc glmselect data=Have; effect spl = spline(X/ details naturalcubic basis=tpf(noint) knotmethod=percentilelist(5 27.5 50 72.5 95) ); /* new in SAS/STAT 15.1 (SAS 9.4M6) */ model Y = spl / selection=none; /* fit model by using spline effects */ output out=SplineOut predicted=Fit; /* output predicted values */ quit;   title "Restricted Cubic Spline Regression"; title2 "Five Knots Placed at Percentiles"; proc sgplot data=SplineOut noautolegend; scatter x=X y=Y; series x=X y=Fit / lineattrs=(thickness=3 color=red); run;``` In summary, the new KNOTMETHOD=PERCENTILELIST option on the EFFECT statement simplifies the process of using percentiles of a variable to place internal knots for a spline basis. The example shows knots placed at the 5th, 27.5th, 50th, 72.5th, and 95th percentiles of an explanatory variable. These heuristic values are recommended in Harrell's book. For more details about the EFFECT statement and how the location of knots affects the regression fit, see my previous article "Regression with restricted cubic splines in SAS."

You can download the complete SAS program that generates this example, which requires SAS/STAT 15.1 (SAS 9.4M6). If you have an earlier release of SAS, the program also shows how to perform the same computations by calling PROC UNIVARIATE to obtain the location of the knots.

Share Distinguished Researcher in Computational Statistics

Rick Wicklin, PhD, is a distinguished researcher in computational statistics at SAS and is a principal developer of SAS/IML software. His areas of expertise include computational statistics, simulation, statistical graphics, and modern methods in statistical data analysis. Rick is author of the books Statistical Programming with SAS/IML Software and Simulating Data with SAS.

1. Thank you for your wonderful work. And I want to konw how to adjusted other confounders in the restricted cubic spline.

2. Hi,

I have 4 knots.
Is there anyway to get the parameters for the curve between the second and third knots, third and fourth knots, etc.

Thank you.

• Yes. When you use knots in a linear regression, you will get estimates for the regression coefficients. The curve of the predicted values is therefore a linear combination of the spline basis, as shown in the article "Visualize a regression with splines." If you want to restrict the interval between the second and third knots, just add together the knots with nonzero support on that interval.

3. can we add spline model in proc MCMC ?

4. Thank you for your wonderful work. And I want to konw how to adjusted other confounders in the restricted cubic spline.

• You can add other effects on the MODEL statement. If you have specific data or syntax that you want to discuss, you can post them to the SAS Support Communities.

5. Hi Rick,
I have 9 data points and I would like to ask you if it's appropriate to apply regression with restricted cubic splines. I have the scatterplot from sgplot, but I can't add it here. The plot shows an upward quadratic then decreases linearly. I will be happy to send the display.

Thanks!

• 6. • 