Formula for Andersen Gill extension to Cox model

1

Ok I am writing a paper draft where I want to include a table of equations used in different models. Some models use standard Cox models, others use the Andersen Gill counting process formulation with delayed entry.

I can represent the Cox models as follows:
Screenshot 2020-03-20 at 18.31.11

My question is how can I denote and Andersen Gill delayed entry model? I can’t find examples in the literature analgous to the picture.

By the way I have no clue how to render latex here but for completeness here is the latex code for that:
h\left(t\right)\ ~\ e^{\gamma_0\cdot\left(\gamma_1.group\right)}

Many thanks.

Edit: there is an error it should be gamma0 + (gamma1 * group)

2

i guess the appearance is the same but instead of h it’s lambda for the intensity function?

1 Like
3

I thought maybe so but I wasn’t 100% sure!

4

But then how do I depict delayed entry in the model ?

Something like this ?

Screenshot 2020-03-21 at 08.45.37

5

not sure what you mean by “delayed entry”? left censored? the distinguishing feature of AG is the extension to recurrent events.

6

Left truncation rather than censoring.

Basically I’m trying to write equations for this R code:

# Model 1 standard Cox
coxph(Surv(time = censor_time, event) ~ group), data=data)

# Model 2 A-G
coxph(Surv(time = entry_time, time2 = censor_time, status) ~ group), data=data)

So I thought it would be clearer for readers not so familiar with all this that the right hand side of my equations should reflect the fact that the R code has 2 time variables on its right hand side.

Edit: how about this (I realised also that gamma_0 should be there as not estimated by Cox)

Screenshot 2020-03-21 at 12.49.18