# Comparison of two multiple logistic regression curves

I'm reading this paper http://circ.ahajournals.org/content/134/25/2095 , with the aim of applying the same method to my data analysis.

In the paper, the authors compared 30-day survival chances of cardiac-arrest patients with or without bystander cardiopulmonary resuscitation (CPR). (see Fig. 2 attached)

They used a multiple logistic regression model taking many factors into account, and the relationship between 30-day survival chances and ambulance response time was modeled by restricted cubic splines with prespecified knots at 5, 10, 15, 20 min.

After drawing this graph, they abruptly concluded that "The association of between 30-day survival and bystander CPR compared with no-bystander CPR became statistically insignificant when response time was more than 13 minutes (3.7% [95% CI: 2.2-5.4] for bystander CPR vs 1.5% [95% CI: 0.6-2.7] for no-bystander CPR)", with no p value shown. (They write in the Methods section that CI is a 95% bootstrap confidence interval based on 2000 bootstrap samples.)

How did they determine that the difference between the two groups is "statistically insignificant" after 13 min?

• My guess is that after that time confidence intervals for both curves are overlapping, this means there's a probability that the both values are equal (difference could be insignificant). Mar 10, 2017 at 11:04
• I agree with @Maju116. While 95% CI and p-value are not always equivalent, when the CI obviously overlap, the predicted probabilities of survival of the two groups became statistically indistinguishable at the 95% level. One can always run an F-test to see whether they are really different prior to 13 mins and not that different afterwards. Mar 16, 2017 at 14:45