Your P-value and OR are not inconsistent with each other.  When evaluating an OR, the null value is 1, not 0.   An OR of 1 in this study would mean no association between diet and cancer.  When the 95% CI of the OR does not include 1, we conclude it is a significant association.  In this context ORs < 1 are protective, > 1 are harmful.  Thus an OR of .44 signifies a .44 odds of cancer in the diet 1 vs diet 2 group.  If we flip the order of the two groups, and then invert  the OR and the two bounds of the CI, we get OR=2.27 (1.05-5.0); this expresses the harm of diet 2 relative to diet 1, and for me,is  more intuitive to interpret: the odds of those on diet 2 having cancer is a bit more than 2x that on diet 1.  If we want to be very conservative, we look at the lower bound of the CI.  It tells us, that at the very LEAST, those on diet 2 have 5% (1.05) increased odds of having cancer. The explicit interpretation of your P-value is that you are running a 3.5% risk (

Sometimes p-values and CI for odds ratios lead to different results because the standard formula for CI for odds ratios is based on a Gaussian approximation that may not be valid.

Since your CI for the odds ratio does not contain the value 1 your CI for odds ratio shows association just like the p-value. Maybe I did not understand your setup, so, please, provide the exact counts. 

"the P value shows association but the odd ratio does not."

In principle, the P value never shows association. This is not the purpose of a P value. The P values shows you how likely you would expect "more extreme data" than the observed data under your model with a given restriction. This is a complicated and quite weird thing and usually not helpful for the scientist.

The odds ratio is a measure that shows how strong the association is. The estimate you have (0.44) is obtained as that value for which your observed data in your model would be most likely. This as well as the meaning of the CI is actually as weird as the P value, but it can give same more or less vague idea about a sensible value of the odds ratio how certain we may be about this. This means: given only your data we would believe that odds ratios below 0.2 or above 0.95 would be rather bad choices to describe the association between diet and cancer, and that values close to 0.44 would be rather good choices. Actually, such conclusions are based on some prior opinion about the association, therefore I said that it gives only a "vague" idea.

Mathematically, P-value and CI show two aspects of the same thing. The 95%-CI will just scratch the tested values (i.e.: odds ratio = 1) when the P-value is 0.05, and it will include it, when P>0.05.  In your case the P-value is

Thank you Peter for your replay.

If I understood what you requested, here is part of the results,

24 out of 71 patients eats (the specific diet we are testing its association to cancer) and 47 doesn’t. 13 out of 71 of the controls eat this type of food and 58 don’t . Statistical analysis showed p value of 0.035, OR 95% CI of 0.44(0.20 to 0.95).

Here is my way of interpretation of your findings:

Let, Number of controls having the specific diet = a = 13

Number of Controls not having the specific diet = b = 58

Number of cancer patients having the specified diet = c = 24

Number of cancer patients not having the specified diet = d = 47

So, Odds Ratio = (a/b)/(c/d) = (13/58)/(24/47)

It can also be written as (a x d)/(b x c) = (13 x 47)/ (58 x 24)

Your answer is 0.44 which is less than 1.

Regarding CI, go through whatever Sir Jochen has described. That's the best explanation.

CI doesn't include 1 which indicates there is good association between selection of diet and risk of getting cancer but OR below 1 indicates that the numerator in the formula weighs lesser than the denominator, i.e. a x d < b x c. The components contributing to the numerator is weaker in product value than that of the denominator. This indicates that the specified diet is the risk factor for occurrence of Cancer.

p-value merely helps you to accept or reject the null hypothesis. For interpretation of Odds ratio data I don't think p-value is of that importance. In addition, both (p-value and Confidence Interval) are significant in your data.

I hope this answer will help you to some extent.

I do not understand what could be the problem in this study. Would it be due to the small sample size?

Where do you see a problem? Why should there be a problem?

This mean both odd ratio and P value indicated association between this type of diet and cancer? I am so sorry for my confusion but as far as I know, when odd ratio is less than 1 it means there is no association, and when P value is more than 0.05 it means also no association. Here althugh P value is less than 0.05, odd ratio shows no association. I wonder why?

Your P-value and OR are not inconsistent with each other.  When evaluating an OR, the null value is 1, not 0.   An OR of 1 in this study would mean no association between diet and cancer.  When the 95% CI of the OR does not include 1, we conclude it is a significant association.  In this context ORs < 1 are protective, > 1 are harmful.  Thus an OR of .44 signifies a .44 odds of cancer in the diet 1 vs diet 2 group.  If we flip the order of the two groups, and then invert  the OR and the two bounds of the CI, we get OR=2.27 (1.05-5.0); this expresses the harm of diet 2 relative to diet 1, and for me,is  more intuitive to interpret: the odds of those on diet 2 having cancer is a bit more than 2x that on diet 1.  If we want to be very conservative, we look at the lower bound of the CI.  It tells us, that at the very LEAST, those on diet 2 have 5% (1.05) increased odds of having cancer. The explicit interpretation of your P-value is that you are running a 3.5% risk (

Thank you Emet, but here I am testing only one type of diet against cancer.

Hi Mona,

My interpretation of your finding is, as previously mentioned by others, there is no discrepancy between Odds Ratio (OR) and P value. Both of them indicate a significant association. I guess the source of confusion coming from your idea of OR has to be more than 1 to be considered significant, which is not the case. In fact, OR can be significant even when it is less than 1, as far as the confidence interval (CI) does not contain 1; in your case the CI is 0.20 to 0.95. The interpretation of OR when its value is more than 1 is your test group (cancer patients) have more risk than the control group, however you obtained an OR less 1 which can be interpreted as the cancer patients have lower risk than the controls. In other words the diet seem to have protective effect on the patients compared to the controls and this association is significant based on both OR and P values. Although you have this significant association but I have the same concern, as you, of low sample size.

best

Waleed

I agree with Waleed but I just want to add that if your p-value is less than your level of significance (alpha), you reject  or vice versa

I have some doubt over Waleed's conclusion. The statement you have written is

"The interpretation of OR when its value is more than 1 is your test group (cancer patients) have more risk than the control group"

The above statement holds true if the ratio is calculated as cancer : control (as it should be, in general) but Mona has calculated it the other way. Hence, the conclusion should be that the specified diet has causative effect on the cancer patients.

If the ratio is calculated as Cancer : control (as it should be calculated) then the result would be more than 2, which again indicates that the specified diet is positively associated with occurrence of cancer, as per the statement made by Waleed.

I would request you to review your answer and rectify me if I am incorrect anywhere.

odds ratio

RR, OR = 1 ⇒ no association ======= RR, OR > 1 ⇒ postive association ====== RR, OR < 1 ⇒ negative association • Relative risks and odds ratios are the most common measures of association used in epidemiologic studies. • Use of the relative risk or odds ratio implies preference for a multiplicative model as opposed to an additive model. In other words, we prefer to describe by what factor the risk or odds is increased or decreased rather than by what absolute amount.

So how can I explain this P value of 0.8 and OR of 1.233 and 95% CI of 0.40 -2.87?

P value of 0.00 but odd ration 0.159 and the 95% CI 0.08 to 0.40?

Mona look at your confidence intervals for OR not the mean or median OD

the first scenario - it crosses 1 --- ( 0.4 ----1 -----2.87 )

the second scenario - it does not cross 1 -- (0.08 ----0.4)....................1

Ok, I understood, thank you for you all guys for your help.

Hi Mona,

you can read this manuscript. I think it will be helpful.

Article Explaining Odds Ratio

please see the attached file

The p value answers the question, “What is the probability, if the relative risk is 1.0, that a study might give a result as far as this or farther from 1.0?”

Thus, the p value is the probability, conditional on the null hypothesis, of observing as strong an association as was observed or a stronger one.

Hello guys good morning.

I carried out a study which has to look at prevalence of hepatitis B infection among pregnant women.

I calculated the odds to determine the association between the infection and the age categories of the study participants taking >40 years as reference. Now each odds calculated for the other age groups gives me a p-value.

Now the Chi-sqaure p-value for all the age groups put together is different from the individual p-values from the odds for each age category.

My problem is, what is the difference between the chi-square p-value and the odds ratio p-value?

Will be glad to get a quick response.

Thank you.