# Basic question regarding model specification for interaction testing using a Cox PH Model

I have a very basic question regarding modelling when testing for interaction for finding heterogeneity in treatment effects in subgroups.

As far as I understand the general specification of the model where a single single subgroup is considered will be

Treat+Subgroup+Subgroup x Treat

However when analysing multiple subgroups what would be the correct way to specify the model

Treat+Subgroup1+Subgroup2+Subgroup1 x Treat
or
Treat+Subgroup1+Subgroup2+Subgroup1 x Treat+Subgroup2 x Treat

Thinking about HTE in terms of subgroups is a recipe for disaster as it invites dichotomization of continuous predictor variables.

For analyzing multiple interacting variables get composite (“chunk”) tests pooling all interaction terms that involve treatment. Best done with a likelihood ratio \chi^2 if using frequentist methods. This chunk test has a perfect multiplicity adjustment and is not harmed by collinearities among interacting factors. You can also do this with a Wald test (automatic if using the R rms packge).

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Thank you. So, in this case, the model specification for cph will be like this

Treat+Subgroup1+Subgroup2+Treat x Subgroup1 + Treat x Subgroup 2 ?

Don’t use ‘subgroup’.

General example:

f <- cph(Surv(dtime,event) ~ treat * (sex + rcs(age,4) + ethnicity) + rcs(blood.pressure,3))
anova(f)

2 Likes

Thank you once again. But another question.
Why is treat not also added as a term in the model ? I mean why is the model not specified as
Is
treat+sex+rcs(age,4)+ethinicity+treat x sex+treat x rcs(age,4)+treat x ethnicity
the same as
treat x (sex + rcs(age,4) + ethnicity) ?

In R, * means to include main effects automatically. To only include cross-product terms you must use : but rms doesn’t like that.

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Thank you. This cleared the matter a lot.