# Help with Odds ratio and confidence interval

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#1
I am writing my exam on liver biopsies and the chance for bleeding. One article has researched this and has presented their results in form of odds ratio and confidence interval. I have no idea what they mean.

They make a scoring system in order to predict bleeding. They write: "Platelet count was divided into bands of <50000/uL and >50000/uL". Platelet count had a significant predictor of risk (p=0.01) with odds ratio of 3.12 (95% confidence interval of 3.75-29.12)
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2 years ago
#2
Before i start, don’t get too upset as everyone hates odds ratio and it is hard to understand.
You should link the full study. I’m assuming the low platlet group are more likely to bleed out in my explanation:
Therefore, the odds ratio represents the odds that a patient will bleed out if they have low platelet count compared to the other group.

Odds ratio which is greater than 1 shows a positive association - which means that the risk factor, in this case low platelet has greater odds to bleed than high platelet.

So the study divided people into 2 groups :

1. those under <50000/uL
2. those above >50000/uL

And we are measuring 2 possible outcomes:
1. They bleed
2. They don’t bleed

If we now combine the possible outcomes and groups:

A. Those UNDER <50000/u who BLEED
B. Those UNDER <50000/u who DO NOT BLEED
C. Those ABOVE >50000/uL who BLEED.
D. Those ABOVE >50000/uL who DO NOT BLEED.

Not lets assign some number (100 participants to each of the two platelet groups= 200 people total):
those UNDER <50000/uL
100 people
Group A - 70 BLEEDERS
Group B - 30 NON-BLEEDERS

Those ABOVE >50000/uL
100 people
Group C - 40 BLEEDERS
Group D - 60 NON-BLEEDERS

Before even doing a calculation, you can see by looking at the numbers that the group under <50000/uL has more bleeders.

The equation to calculate ODDS ratio:
OR = (A/B)/(C/D)
70/30 = 2.333333
40/60 = 0.6666666
2.33333/ 0.6666 = 3.5 odds ratio.

The odds ratio does NOT mean “the under <50000/uL/ group is 3.5 times more likely to bleed out”

But that “ the odds of the under <50000/uL groups bleeding out is 3.5 times greater than the above >50000/uL group bleeding”

This is extremely confusing for most people so don’t be alarmed! To say how ’likely’ something is we need to calculate relative risk.

Lets calculate the relative risk:
Relative RISK (RR) = ((A/(A+B))/(C/(C+D))
70/100 = 0.7
40/100 = 0.4
0.7/0.4 = 1.75
Relative RISK = 1.75

We can say that “ under <50000/uL platelet group are 1.75 times more likely to bleed out than the over <50000/uL group”

Now for p value p=0.01
This is the probability that results of the study was due to chance. 0.01= 1/100, so there is a 1% chance that the same result or greater could happen due to random chance, very unlikely. Therefore the platelet count is most likely the factor which increased odds of bleeding and not simply random chance.

Confidence intervals
Basically using what we call ‘normal distribution’ we can say that 95% of the time we would get p value within the quoted range. You have made an error in your text as the lower part of confidence interval cannot be greater than the odds ratio.

Using my example we get: odds ratio = 3.5 (95% confidence interval 1.9 - 6.2)
So if we repeat the study somewhere else, 95% of the time, we would get an odds ratio of between 1.9 - 6.2
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