Reporting Odds RAtio

 

When Odds ratio is above 2, then it is simply put as XX times higher likelihood (XX=odds ratio). If odds ratio is 2.5, then there is a 2.5 times higher likelihood of having the outcome compared to the comparison group. From the above example, one might say “The odds of having a postoperative infection is 3.5 times higher if the patient experienced a complication during the surgery as opposed to not experiencing the complication”. Here the odds ratio would be 3.5.

When the odds ratio is lower than 1, the likelihood of having the outcome is XX% lower (XX% = 1-Odds ratio). For e.g. if odds ratio is 0.70, then there is a 30% lower likelihood of having the outcome. In the above example related to surgical infection, you might say “The odds of having a postoperative infection is 20% lower if the patient was given prophylactic antibiotics during the surgery as opposed to not getting the antibiotic”. Here the odds ratio would be 0.80.

The odds ratio also shows the strength of the association between the variable and the outcome. Simply put, an odds ratio of 5 (i.e. 5 times greater likelihood) shows a much stronger association than odds ratio of 3, which in turn is stronger than an odds ratio of 1.5. Lastly, the odds ratio tells us the direction of the association between the factor and the outcome. For example, an odds ratio of greater than 1 shows us a positive association between the outcome (e.g. infection) and the associated factor (e.g. surgical complication) i.e. complication is associated with a higher likelihood of infection and administering an antibiotic is associated with a lower risk of association. The direction of association may come intuitively to you but statistical backing makes a difference and shows that your data is robust enough.

Having said this, we also need to understand whether the association is statistically significant or not. Odds ratios are accompanied with a p value and a 95% confidence interval, both of which tell us the statistical significance. The P value of <0.05 usually signifies a significant association. Since the odds ratio shows the strength and direction of association, it is important that we report the odds ratio even if it is not statistically significant. You can read a more detailed discussion about the P value here.

Importance of 95% Confidence interval with odds ratios:

The 95% confidence interval is perhaps more important than the p value in interpreting the statistical significance of odds ratios. Simply put, it is an expression of the spread of the odds ratio in 95% of the study population. If the Odds ratio of 1 means no increase or decrease of likelihood of the event, then a 95% CI on either side of 1 means that there is both a higher and lower odds of the outcome occurring which doesn’t really make sense. Hence a 95% confidence interval spanning across 1 can never be statistically significant i.e. will never be accompanied by a p value of <0.05.


In the above example, a more complete sentence will be “The odds of having a postoperative infection is 65% higher (Odds ratio=1.65, 95% CI=1.36 – 1.96, p=0.02) if the patient experienced a complication during the surgery as opposed to not experiencing the complication”. On the other hand, you may come across the sentence “The odds of having a postoperative infection is 65% higher (Odds ratio=1.65, 95% CI=0.36 – 1.96, p=0.31) where, though the odds ratio shows an association, the 95% CI spans across 1 on either side and hence the p value is >0.05”. If authors of a manuscript are manipulating data, they may change the odds ratio and the p value to <0.05 to suit their conclusions but usually do not alter the 95% confidence interval appropriately, thus giving away the fact that the data might have been manipulated. I hope this is easy to understand. The confidence interval also tells us the upper and lower limits of the strength of association, which helps us understand the strength of association even better than the odds ratio itself.

Also note that I have used the word “likelihood” throughout the write up and never interchanged it with “risk” or “chance”. Logistic regression and its output i.e. odds ratio is based on the statistical principles of likelihood ratios and differ from risk ratio and other similar and related statistical measures. Clinical studies usually employ logistic regression with Odds ratios and Epidemiologic studies employ risk ratios, but this is not the rule. Another caveat is that look for the sample size used in the logistic regression. Remember that even if entry for one variable is missing in your datasheet, the entire patient will be dropped from the analysis. Hence, if the datasheet is shoddy, you may see that only 50% of the sample is used for the logistic regression which is never good. Lastly, odds ratios are more reliable and thus believable and applicable if performed on a sample of 100 observations or more.


 

ambil dari sini

https://senguptasresearchacademy.com/odds-ratio/

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