Confidence intervals should respect bounds

[nhejazi]

Construction of Wald-style confidence intervals (as done in confint.survtmle) may require some adjustment, as it is possible for the routine to produce intervals that cross zero. This appears to be in conflict with the concept/definition of cumulative incidence, which is lower bounded by zero (right? @benkeser). In the README example, this does not appear to be a problem for confint.survtmle as this generates an interval around only the cumulative incidence estimate at the last time point; however, when the same approach is applied to earlier time points (as in the new routine confint.tp.survtmle), negative values may arise. Of course, a quick fix is to simply replace such values with zero, but this then leads to uneven intervals, which are possibly theoretically problematic. There likely are some relevant theoretical insights that I am neglecting here as well as options for correcting this behavior if it is indeed undesirable (e.g., confidence intervals for non-negative random quantities).

[benkeser]

The easiest solution is to construct confidence intervals on the logit scale and back-transform, i.e.,
$ expit(logit(\hat{F}) \pm 1.96 * \hat{se}(logit(\hat{F}))) $ ,
where $\hat{se}(logit(\hat{F}))$ is the estimated standard error of $logit(\hat{F})$, computed using the delta method. There may be an example of this in the drtmle vignette -- I can't remember.

[nhejazi]

Looks like there's some explanation and an implementation here in the drtmle vignette: https://benkeser.github.io/drtmle/articles/using_drtmle.html#confidence-intervals. Would be best to complete the initial confidence interval estimation implementation as well as extensions of this implementation for arbitrary contrasts ASAP, so as to avoid holding up a CRAN re-release.