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I am a Ph.D. student conducting a superiority randomized controlled trial to test the effect of text message reminders on the timeliness of child vaccination. I have considered one-sided alpha (1.64) during sample size calculation. Accordingly, I am planning to conduct one-sided hypothesis testing and wanted to report the CI for the risk ratio based on a one-sided test. In one-sided hypothesis testing, it is recommended to report either Upper CI or Lower CI only and to leave the other side of the CI blank so that it could take minus infinity or plus infinity. The question is am I supposed to report the lower or upper CI for superiority RCT and why? I need your suggestions on how to construct and report the one-sided CI for superiority design RCT.

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    $\begingroup$ There is a related question here, that you may find helpful. $\endgroup$
    – dimitriy
    Jul 22, 2020 at 20:22
  • $\begingroup$ It's in a context of a classifier, but the logic should extend to the logit case. $\endgroup$
    – dimitriy
    Jul 22, 2020 at 20:31

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If your assumption before doing the superiority test is that timely vaccination is more likely to occur with text messages, report the upper limit of the CI on the ratio of the text-messaged group to the non-text-messaged group. This limit is also known as $U$, and will generally be some number above 1, as will your risk ratio. A simple estimate is $$U = \frac{p_1}{p_2} ~ \exp \left( 1.64 \sqrt{\frac{1-p_1}{n p_1} + \frac{1-p_2}{n p_2}} \right)$$ where $p_1$ is the proportion of timely-vaccinated people in the text-messaged group, $p_2$ the corresponding proportion in the non-messaged group, and $n$ is the number of subjects. If you have unbalanced data, see Table I and equation 24 here. And if you need a more sophisticated approach (for example, not relying on the normal approximation), see pages 7-10 here.

A word of warning before you continue with your superiority test: is it really appropriate? See here.

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