Interaction terms with stcox model and LR tests

[Tara Boyle]

Hello there. I'm learning interaction effects in survival models in semi-parametric tests.

I would like to find the best model to fit my data before then testing PH for COX model (haha if my COX does not satisfy PH I have to do everything again with the parametric tests *facepalm*)
However, I have assessed interaction effects with my data (which is a large dataset consisting of 2 million observations). I am however practising with dummy data for now. Here's a dummy data set below

My question is whether :
1. I can perform a LR comparing all INTERACTIONS in the model (I have 32 interactions) to a Model with 0 interactions - thus trying to understand if the interaction model is better than the non-interaction model

OR

2. Perform a LR comparing one model at a time, adding one interaction term consecutively therefore I will have 33 models (all 32 interactions + the model with no interactions) ?

The reason I ask is all books give examples showing that 1 interaction model is significant therefore comparing an Interaction model to a No interaction model but it would only have 1 interaction term. What happens if you have more than 1?

Perhaps I'm making it too complex but here's an example of what I'm trying to ask

Here is a sample of the data:

* Example generated by -dataex-. For more info, type help dataex
clear
input double(tx ct1 ct2 ct3 ct4 survt perf dd age priortx status)
1 0 0 0 1  72 60  7 69  0 1
1 0 0 0 1 411 70  5 64 10 1
1 0 0 0 1 228 60  3 38  0 1
1 0 0 0 1 126 60  9 63 10 1
1 0 0 0 1 118 70 11 65 10 1
1 0 0 0 1  10 20  5 49  0 1
1 0 0 0 1  82 40 10 69 10 1
1 0 0 0 1 110 80 29 68  0 1
1 0 0 0 1 314 50 18 43  0 1
1 0 0 0 1 100 70  6 70  0 0
end

//Set time 
stset survt, failure(status == 1)

//Univariate analysis on categorical models
sts test ct1, logrank //0.08
sts test ct2, logrank //keep
sts test ct3, logrank //keep
sts test ct4, logrank //keep
sts test tx, logrank  //STILL KEEP 
sts test perf, logrank  //still keep
sts test priortx, logrank //still keep 


//Cumulative variables 
stcox age, nohr  //still keep desp 0.4

//CHECK INTERACTIONS 
stcox c.age i.ct1 i.ct2 i.ct3 i.ct4 i.tx i.perf i.priortx i.priortx#c.age

Let us assume these are the significant Interactions: 
ct1#perf
ct4#priortx

Should I perform LR test with

Model 1: All interactions within the model which would mean
stcox c.age i.ct1 i.ct2 i.ct3 i.ct4 i.tx i.perf i.priortx i.priortx#c.age ct1#perf ct4#priortx 

COMPARED TO 

Model 2: //No interaction model 
stcox c.age i.ct1 i.ct2 i.ct3 i.ct4 i.tx i.perf i.priortx 


OR should I perform a LR with one interaction model at a time 

//1 interaction 
quietly: stcox stcox c.age i.ct1 i.ct2 i.ct3 i.ct4 i.tx i.perf i.priortx i.priortx#c.age
eststo model1

//2 interactions 
quietly: stcox c.age i.ct1 i.ct2 i.ct3 i.ct4 i.tx i.perf i.priortx i.priortx#c.age ct1#perf ct4
eststo model2
//ALL three interactions together
quietly: stcox c.age i.ct1 i.ct2 i.ct3 i.ct4 i.tx i.perf i.priortx i.priortx#c.age ct1#perf ct4#priortx 
eststo model3

estout model1 model2 model3 , eform stats(n chi2 bic, star(chi2)) prehead("Hazard Ratios")
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[Tara Boyle]

Or perhaps I could create a loop ? To make backward selection easier ?