proportional hazards model with fixed interval censoring = cloglog GLM with fixed effect of time?

Consider a survival analysis with time-constant coefficients, interval-censored, where the observation intervals are consistent across all individuals (e.g. each individual is observed at the end of every time period). I think I remember seeing it asserted somewhere that in this case a Cox proportional hazards model is equivalent to a binomial (Bernoulli) GLM with a complementary log-log link and a fixed effect of time for every observation period (this corresponds to the baseline hazard that is factored out of the Cox PH likelihood). Is this known to be true/false, and can someone provide a supporting argument or pointers to supporting references?

If true, this provides a very convenient way to avoid the computational/technical difficulties of fitting interval-censored Cox models (e.g. see this question and more generally these questions ...)

• it looks like this might be covered here ... also, I realized my question looks a lot like this one ... (I don't think it can be closed as duplicate until there's an answer to one or the other) (The link from that Q is broken, on wayback machine here: web.archive.org/web/20141121080306/http://www.ics.uci.edu/… looks to be substantially similar ... – Ben Bolker Sep 30 '19 at 21:12