The conclusion you'd draw is the same using a P value and a confidence interval. Having a statistically significant P value, meaning a P value less than a given

The conclusion you'd draw is the same using a P value and a confidence interval. Having a statistically significant P value, meaning a P value less than a given significance level, then implies that the confidence interval at that significance level does not include the null hypothesis value. If your significance level is .05 (meaning you are willing to accept a 5% chance of a type 1 error in which you reject the null hypothesis incorrectly), you can use either a confidence interval or a p value. You could look at a 95% condfidence interval and see if the % faster time to recovery range includes the null hypothesis of zero, or you could calculate a P value to see if it is less than .05. Both of them will give you the same conclusion. Based on the P values given, you know that the 95% confidence interval for % faster time to recovery will not contain 0% (nor will the 99% interval or the 99.9% interval). But, the % difference in mortality at a 95% confidence interval will contain zero, since p>.05.