Hello everyone, I saw a lot of equations on how to convert odds ratio into probability but still do not know which one to apply.
In my case, I used regression to get the odds ratio whether a predictor can impact the injury, but I want the probability of that certain predictor.
Edit: failure rate is 14.76%
Is there a formula on how to convert odds ratio into probability?
Thanks
Lachin is the leading work in the field. It is shown in the attachment. Best wishes David Booth
You're interested in the meaning of the regression coefficient that you mentioned.. look up the type of regression you did and there you find a way to convert the regression coefficient to probability. Best wishes David Booth
Another good reference is is Rosner Fundamentals of Biostatistics D Booth
A simple answer is no you can't go from odds ratio (OR) to probability without additional information. You can go from odds (o) to probabilities (p) fairly easily by:
p = o / (o + 1)
The difficulty with the OR is that its the ratio of two odds and you need additional information to find the relevant odds. However, its likely that's provided in your regression output, but it requires a good understanding of the regression model in question (and also depends on whether predictors are categorical or continuous and what's happening to any other predictors in the model).
I'm assuming you are working with logistic regression. In arguably the simplest case you have a single categorical predictor x coded 0/1 and a binary 0/1 outcome. This gives you an equation like:
ln(P/(1-P) = y ~ b0 + b1 * x
e^b0 gives the odds of the outcome when x is 0 (because b0 is the intercept) and e^(b0 + b1 * 1) gives the odds of the outcome when x = 1. This can be covered to probability of each outcome using p = o / (o + 1).
Its a bit more complicated if there are other predictors or if x is continuous or if you have a more complex model (e.g., an ordinal logistic regression).
Thank you very much for both answers;
David Eugene Booth I will check the university library for a copy of the book
Thom Baguley I have two linear regressions and one binary logistic regression. two contineous depandant variables (Linear regression) whether the number of people rescuded go up or down and the dammage increase or decrease and one categorical variable (Binary) whether the predictors impact casualty (fatal/non fatal and no casualties). As for the predictors, they are all contineous variables.
Kindly read from this link: https://yury-zablotski.netlify.app/post/from-odds-to-probability/@
Armitage and Berry Statistical Methods in Medical Research is also a good book, but mine is falling apart as the glue disintegrated on the binding & I just took it somewhere to use, now I'm not sure where it is, but I very detailed book.
Divide the odds by one plus the odds to convert the odds to a probability. Therefore, to convert 1/7 odds to a probability, divide 1/7 by 10/7 to get 0.10 as the result.
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