How to Find the Optimal Level of a Predictor Variable in Proc PHREG

[fikel]

Hello, I have a dataset that contains the levels of a dietary nutrient for different individuals as well as their cancer outcome and length of follow up/censoring time. I have initially divided up up the nutrient data into quintiles to compare each group's cancer outcomes like this:

proc phreg data = nutrient_dataset;

class nutrient_quintile (ref="0") other_categorical_predictor;
model Age_at_EndFollowUp*Cancer_outcome(0) = nutrient_quintile 
other_categorical_predictor other_continuous_predictor
		/ entry=Age_at_Enrollment rl=wald;
run;

Where the predictor/independent variable of interest is nutrient_quintile and other predictors/potential confounders are: other_categorical_predictor and other_continuous_predictor. In reality, there are multiple continuous predictors, but I'm keeping it simple for the post. While analyzing the hazard ratios of the resulting data, it appears that there is a threshold effect for some of the nutrients. What I mean is that instead of seeing each quintile having fewer and fewer cases of cancer, the data shows that once you reach a certain quintile/nutrient level the the risk of cancer stays at about the same lower level. 

Example: Quintile 1 Hazard ratio = 1. Quintile 2 Hazard ratio = 1. Quintile 3 Hazard ratio = 0.8. Quintile 4 Hazard ratio = 0.8. Quintile 5 Hazard ratio = 0.8.

This means that once individuals reach a certain level of the nutrient, their risk stays at about the same lower level. I am still very new to SAS, but I wanted to see if there was a function, proc, or macro that could be used to find the optimal threshold for this nutrient. The continuous variable would be: nutrient_level. It would somehow identify the nutrient level at which individuals above that level have the lower risk. In the example above, the question would be at what nutrient_level does the risk transition from 1 to 0.8?

I know I could guess levels and split the individuals above and below that level until I found the best number, but I know this would take a long time and wanted to see if there were better options.

[SteveDenham · Accepted solution]

Spoiler alert: This method has not been tried on real data, and might not quite be what you are looking for.

I think you can do this using PROC NLMIXED.  Check the example in the documentation here: https://documentation.sas.com/?cdcId=pgmsascdc&cdcVersion=9.4_3.4&docsetId=statug&docsetTarget=statu...  for fitting a failure time/frailty model.  What you would have to do is incorporate a segmented model using nutrient level as a continuous variable.  Code to get started is in the NLIN example here: https://documentation.sas.com/?cdcId=pgmsascdc&cdcVersion=9.4_3.4&docsetId=statug&docsetTarget=statu... 

In any case, Mr. Google is your friend.  I got several results on a search for "failure time" and "nlmixed", so there should be something out there.

SteveDenham

[Rick_SAS]

To build on Steve's suggestion, look at the article "Segmented regression models in SAS," which shows how to use PROC NLIN to build a segmented regression model. You want to estimate the "cutoff point" at which the response variable reaches a plateau. The article provides data and SAS code.  Notice that you need to use the continuous explanatory variable rather than a binned version of it.