survival analysis: generalised linear regression with complementary log-log (cloglog) link function in R I've been looking for layman-accessible information about implementing the generalised linear regression with a complementary log-log (cloglog) function as survival analysis in R, but couldn't find anything satisfactory.
A similar question has been asked here:  link
however, I'm still unsure how to use that function on data.
Another question was answered here: link
but I don't understand 1) what the offset actually does and why we include it? 2) if this is what I'm looking for: they refer to it as logistic regression, which is not what I'm after. (I don't have enough reputation to comment on those posts).
The dataset I will be using contains information on the screening time and outcome for a diabetes complication, along with other covariates I would like to include (age, sex, etc.). Although it will contain information on multiple screening events, I assume the model should be supplied only with the last interval, outcome and covariates.
Therefore my dataset should look similar to the icenReg's  miceData.
How do I build a generalised linear regression model with a complementary log-log function to model survival (time to event) in R? And if possible, how do I extract and interpret the results?
Thanks in advance for your help!

The discrete-time survival analysis you want to do is just a form of binomial regression. This page nicely outlines how to proceed. You put your data into a person-period format, with one row for each at-risk individual in each time period, as shown in this answer, with the time period specified in the row along with covariate values in place and the event indicator for the individual in that time period. This answer has helpful links to more reading.
The advantage of using the cloglog link instead of the default logit is that it's suitable for evaluating a proportional hazards model in discrete time ("interval-censored" data). See this page for details. Coefficients for covariates then have the usual interpretation as for log-hazards in Cox continuous-time models, and the baseline hazard is provided by the time-period-specific coefficients.
Once the data are formatted it's very straightforward. After you set up your regression formula in the generalized linear model, you just specify family=binomial(link="cloglog") instead of accepting the default logit link.
