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Let's take this research published on Plos ONE

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).

How should people read those values? What does it mean confidence interval for example?

Do you know any resource explaining the interpretation of the statistical part of those scientific papers?

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    $\begingroup$ On one hand, I think this is a great question and I'd like to have a good resource handy I could link people to - one that goes beyond "p is the conditional probability of obtaining a test statistic as or more extreme blah blah blah", but actually explains what typical stats mean in a way that's useful to non-geeks. On the other hand, I don't think this is the right board to ask for that. CrossValidated is. $\endgroup$
    – jona
    Sep 24, 2014 at 10:23
  • $\begingroup$ @jona: if you like it can you upvote it? $\endgroup$
    – Revious
    Sep 24, 2014 at 12:18
  • $\begingroup$ which value are you referring to? $\endgroup$
    – Glen_b
    Sep 24, 2014 at 13:31
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    $\begingroup$ Sorry, I meant the referent of the word "that" in your question, which in that context would refer to a single item. Did you mean "those", which would refer to more than one (and imply all the values)? Are you simply after a translation of the abbreviations? (HR=hazard ratio, CI =confidence interval, p="p-value") $\endgroup$
    – Glen_b
    Sep 24, 2014 at 13:39
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    $\begingroup$ Hazard ratio, Confidence interval, p-value $\endgroup$
    – Glen_b
    Sep 24, 2014 at 13:46

1 Answer 1

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I'll take a stab at the portion of the question asking about interpreting these specific results (and I'm going to try to be non-technical about it):

The hazard ratio (HR) of 2.01 suggests that over the course of the study, those in the focal group (in this case, those with increased carbohydrate intake) were about 2 times as likely to experience the outcome of interest (in this case, stroke). Put another way, they had twice the stroke risk of those in the comparison group.

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. One thing to note is that this range does not include 1 (although it comes close), suggesting that there is probably a relationship between carbohydrate intake and stroke in the broader population. If 1 were included, this would mean that we would not be justified in concluding that the hazard ratio was different from equal (1:1).

The p value can be interpreted as the probability of finding a result equal to, or more extreme, than these results in the population by chance alone. Typically, a p value lower than .05 suggests that the results are significant- they are extreme enough to suggest that it is an actual effect, not chance, that is accounting for the results. In this case, the p value is .025, which would allow you to conclude that these results are significant and suggest a relationship between your variables in the population.

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  • $\begingroup$ Thanks a lot. I will open another question for asking how a statistical search may arrive at those probabilistic conclusion. As a profane it's hard for me to understand concept like this one: "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" $\endgroup$
    – Revious
    Sep 25, 2014 at 7:30
  • $\begingroup$ Here it is: stats.stackexchange.com/questions/116711/… $\endgroup$
    – Revious
    Sep 25, 2014 at 7:44
  • $\begingroup$ There's an issue with the interpretation of "confidence interval" (CI) in this answer, as now explained in stats.stackexchange.com/questions/116711/…. If you had the same population and performed the same study a large number of times, then 95% of hazard ratios would fall within the CI. That's not necessarily the same thing as having 95% certainty that the true hazard ratio is contained in that range. $\endgroup$
    – EdM
    Sep 25, 2014 at 16:54

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