Programming the statistical procedures from SAS

proc phreg - bayesian piecewise exponential model

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proc phreg - bayesian piecewise exponential model

I am fitting a bayesian piecewise exponential model to survival data. I am using the  in-built gamma prior. I specify the (piecewise) intervals on which to get the lambdas . In the example below, the intervals are [0,10),[10,Infty). I run the same type of model for many segments in my data, using differnet intervals. For all my datsets, the number of "events" overall is very low. I am facing some issues...

 

1.)

For all my models, I find that the initial values for the lambdas are exactly the same as the final MLE estimates. Is it because of the low-event nature or is there something else wrong - should I experiment with more seed values- say 5 different ones- and then take the average of the MLEs for my lambdas? How does SAS choose the initial values for the lambdas ?

 

Initial Values of the Chain
Chain Seed Lambda1 Lambda2
1 1 0.000945 0.000155

 

Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error
95% Confidence Limits
Lambda1 1 0.000945 0.000668 0 0.00225
Lambda2 1 0.000155 0.000090 0 0.000331

 

Here is the ESS diagnostic: I read somewhere that ESS should be around 1000.

 

Effective Sample Sizes
Parameter ESS Autocorrelation
Time
Efficiency
Lambda1 10000.0 1.0000 1.0000
Lambda2 9818.3 1.0185 0.9818

proc phreg data=seg1;
model exposure*censored(1)=;
bayes seed=1 piecewise=hazard (INTERVAL=( 10) prior=gamma );
run;

 

Note: I don't use any explanatory variables in my model. 

 

2) I am not sure how to specify a Gamma(a=0.001,0.001) prior --- the syntax I used below resulted in error messages: piecewise=hazard  (INTERVAL=( 10,20) prior=gamma(a=0.001 b=0.001 ))

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