Referring to this question: How should be statistics on scientific papers read?, a kind user explained us how to read the following statement from the original research paper:.

Increasing carbohydrate intake was associated with increasing stroke risk (HR = 2.01, 95%CI = 1.04–3.86 highest vs. lowest quintile; p for trend 0.025).

Multivariable Cox modeling estimated adjusted hazard ratios (HRs) of stroke with 95% confidence intervals (95%CI).

In the answer I was told to interpret this as:

The confidence interval suggests that we can conclude, with 95% certainty, that the true hazard rate in the population could fall anywhere between 1.04 and 3.86. In the broader population, the stroke risk associated with increased carbohydrate consumption could be as high as 3.86 times or as low as 1.04 times that of the comparison group.

I don't understand what part of the original text gave this information on the confidence interval.

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    $\begingroup$ Based on the title this question sounds very broad (unanswerable as one cannot explain all possible ways statistics can be used in scientific papers in a single answer). If you mean to ask, for example, 'how this confidence interval was obtained', the question should be edited to reflect that. $\endgroup$ – Juho Kokkala Sep 25 '14 at 9:50
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    $\begingroup$ That sentence is incorrect, though it is a common error. A more correct interpretation of the confidence interval is that if we were to repeatedly sample from the population and compute the hazard ratio in each of these samples, than we would expect 95% of these samples to produce a hazard ratio within that interval. You can read more about confidence intervals here: en.wikipedia.org/wiki/Confidence_interval . $\endgroup$ – Maarten Buis Sep 25 '14 at 11:51
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    $\begingroup$ This interpretation was infered from the text using the part "95%CI = 1.04–3.86", This reads "the 95% confidence interval is [1.04 , 3.86]", which is interpreted as in my previous comment. $\endgroup$ – Maarten Buis Sep 25 '14 at 11:54
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    $\begingroup$ It is not data. Using the word data like this will cause unnecessary confusion on sites like this. $\endgroup$ – Maarten Buis Sep 25 '14 at 12:10
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    $\begingroup$ The data used to estimate a model comes from a random sample. As a consequence your point estimates (in this case, hazard ratios) are uncertain: If you were to repeat the entire research project, you would get a different random sample and thus different point estimates. The confidence interval is a way of quantifying that uncertainty. $\endgroup$ – Maarten Buis Sep 25 '14 at 12:13

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