Theory question: Need references for DiD-Cox regression

Hello statalisters,

I hope I'm not posting at the wrong place here. If I do, please let me know.
I found a very informative old Statalist-Post about how to run DiD Cox-regressions (see http://www.statalist.org/forums/foru...cox-regression).
One of the issues discussed there is whether one should run a combined DiD-regression (Model 1) or two seperate Cox-regressions, one for each group (Model 2):

Model 1 (combined Model):
y = log h(t| G, P) = a(t) + b1 G + b2 P + b3 G P where G=1 for treatment group and P=1 for after-treatment-period and b3=DiD

Model 2 (Separate models):
Group = 0: y = a0(t) + c1 P
Group = 1: y = a1(t) + c2 P where c1-c2 = DiD

So, my question is whether someone could suggest related literature/references about running DiD Survival analyses and interpretation of coefficients for me to read and to cite.
Also, in fact I'm not running Cox regression but the proportional hazard equivalent for discrete-time, that is cloglog regressions.
Does that make a fundamental difference for DiD survival analyses?

Kind regards,
Boris