Degree of Confidence for an Odd's Ratio 2014 Cochrane Review Bronchiolitis Given the following:
Odds Ratio (M-H, Fixed, 95% CI) 
0.75 [0.46,1.21]
Is there a degree of confidence with which I can say that the true ratio is less than 1?
Here is the background:
The 2014 Cochrane Review "Bronchodilators for bronchiolitis (Review)" is a large study that attempts to answer the question whether or not bronchodilators are helpful in bronchiolitis.
I am very specifically looking at analysis 1.6 which concluded that one cannot say with a 95% degree of confidence that bronchodilators decrease the odds of admission to the hospital.
I had originally thought that I could simply divide the 95% confidence interval by (1.96 x 2)which should give me the standard deviation, and then simply set the odds ratio to 1 or less, which could give me the area under the curve as a percentage. 
As is was using graphing calculators for a bells shaped curve, I rapidly realized that I was well over my head. 
Given that I have a presentation within the next week, I would be extremely grateful if someone could help out on this one. 
This study is almost always interpreted by clinicians as "Bronchodilators have never been shown to make a difference." That seems rather imprecise at best.
What I would like to be able to say is "I can say with a x % certainly that use of bronchodilators decreases the odds of being admitted to the hospital by y %."
Thanks so very much in advance. 
Ben
 A: To my mind, i'm not sure if you're interpreting the 95% CI correctly. It doesn't tell you whether one can say with 95% confidence that the treatment does or does not work. But rather, that if you were to repeat the study 1000 times, and generate confidence intervals in each instance, that 95% of those intervals would contain the true odds ratio.
If you want to find the width of the confidence interval that doesn't span one (i.e. shows the treatment is effective), I feel like you could do so by reversing the process used to generate the odds ratio confidence intervals. I.e. find the standard error in log odds:
SE = (log(1.21) - log(0.75))/1.96 = 0.244
Then you could recalculate a, for instance, 80% confidence interval by using 1.28 instead of 1.96: 
80% CI = log(0.75) +/- 1.28(0.244) = [-0.600, 0.0246] 
Convert back to normal odds ratio scale with antilog: 
exp(-0.600), exp(0.0246) = [0.549, 1.02]
Which still spans one but I think makes the process clear. So by this method you could say that if you were to repeat the experiment 1000 times on the same population, you'd expect that slightly less than 80% of the time you'd expect the confidence intervals to cover the true odds ratio. Although the typical interpretation is just that there is an 80% chance that the true odds ratio is contained within that interval. 
Disclaimer: I'm not sure if this is a particularly unsophisticated way of calculating odds ratios, and if the process changes the interpretation. Happy to be corrected if off the mark
A: This is what the p-value tells you. The $100(1-p)\%$ confidence interval will feature the assumed null value as an endpoint. This is because most$^{\dagger}$ confidence intervals are inversions of hypothesis tests. Casella and Berger work this out. Check out my post here: https://stats.stackexchange.com/a/436821/247274.
$^{\dagger}$There are exotic confidence intervals that are not inversions of hypothesis tests. The comments in the linked post get into that.
