I perfomed and analysis with a simple logistic regression to determine an association between a factor and an outcome, the RR is 0.8 and 95% CI was 0.04-1.02 and the P- Value of 0.03. I am confussed because the CI includes 1 and the P-value is less tha 0.05. Looking at the confidence interval, we can say that the association is not statistically significant but p-value proposes the contrary. Can someone help me how to interpret such results?
You should never use a CI to separate "significant" from "non-significant" results. In so far there is no contradiction. This is your main problem.
CIs can be constructed based on the inversion of a test. But this must not be the case. There are possibly different tests (approximate or exact) and there are also possibly different procedures to construct a CI (eg. based on the likelihood, on the smpling distribution, as inverted test etc. also approximate and exact).
Thanks Rohit Ojah , i am a bit confused about the interpretation of of Confidence interval on its dichotomy character . what i know confidence interval is much more informative than the P value , the P Value intervenes just to verify if the association is the play of chance any way i am going to read the article that you attached so i can have some clarity .
There is little to be confused about.
CIs are NOT INTENDED to be used for dichotomous decisions (like yes/no or significant/non-significant etc.).
CIs provide information about the estimated SIZE of an effect (like a mean differenec or a risk ratio etc) plus additionally a measure of the PRECISION of this estimate. Both pieces of information together can be used to judge the relevance of the observed/estimated effect.
Muhammad Naseer Akhtar,
your statements are not quite correct. I'd like to point this out here to avoid that redaers are put on the wrong interpretations.
"We also noted that the point estimate is the most likely value, based on the observed data"
No. The point estimate is the parameter values (here: the [log] odds ratio) for which the observed data is most likely. There is no statement about how likely the parameter value is. The statement is always about the data.
"and the 95% confidence interval [...] can also be interpreted as the range within which the true value is likely to lie with 95% confidence."
No. Again, all statements are about the data, not about the parameter. The CIs are statistics derived from the data, thes are sample statistics (just like the min, max, median, mean, sd, iqr and whatever is or can be calculated from the observed data). Again, it is not known or controlled how likely such an interval would contain the "true" value. The procedure of calculating such intervals just controls that the probability of the intervals containing the "true" value. Turning this around is not logically justified. Let me give a (stupid) example to make this clear:
We may agree that it is very likely that the president of the USA is a white male person. It would be obviousely very strage to turn this around and conclude that a white person (we observed) is the president of the USA.
Another point to make that clear: Given you have two independent experiments, both give their own CI. It can easily happen that these two CIs don't overlap (or that they overlap only in a small region). If you were correct, then both CIs had a 95% change to cover the "true" value, and the range coverd by both CIs together would then have a more than 100% chance to cover the "true" value. That makes no sense.
"This means that values outside the 95% confidence interval are unlikely to be the true value."
No. This means that the observed data is quite incompatible with hypotheses about the parameter that are outside the 95% confidence interval. Other
"Therefore, if the null value (RR=1.0 or OR=1.0) is not contained within the 95% confidence interval, then the probability that the null is the true value is less than 5%."
No. There is no statement possible about the probability that a hypothesis is true or false (such a statement would make no sene for point-nulls anyway!). This only means that for hypotheses outside of the CI, the observed data is less likely than 5%.
"Conversely, if the null is contained within the 95% confidence interval, then the null is one of the values that is consistent with the observed data"
Yes. But it would be clearer to turn this around: "... then the data is consistent with the null (hypothesis)"
Any p value can come from a z value. The 0 of z statistics can be aligned on either H0 or H1.
In classical statistics, H0 is the alignment point and H1 is threshold for definition of p value. In forest plot of meta-analysis it may be vice versa.
However, if the z distribution is the same, p H1 = p H0 = p value.
If your CI is not fit with p value, the reason is that you have used a different z distribution for calculation of CI (H1).
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