I think you guys make it more difficult than it has to be. Estimating
probability of success with a loglog-link is equivalent to estimating
probability of failure with a cloglog-link, so all you have to do is to
change the response variable accordingly (and then you can interpret
parameter estimates (or any contrasts in general) as hazard ratios)...

Though, I wish there was a loglog-link in glm and lmer so you wouldn't have
to do this.
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