Odds ratio

We consider two therapies A and B. The success probability of therapy A is $0.41 .$ The odds ratio is $5.76$ relative to therapy A.

Question

What is the success probability of therapy B?

This is an odds ratio.
Convert the success probability of therapy A, $π_{A},$ to the respective odds, ${odds}_{A} = \frac{π_{A}}{1 - π_{A}} .$
Multiply ${odds}_{A}$ by the odds ratio to obtain ${odds}_{B} .$
Back-transform ${odds}_{B}$ to the respective success probability, $π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}} .$

Feedback

Waiting for response...

Solution(s)

The system accepts the following correct response(s)

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = {odds}_{A} OR$
$π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}}$

Correctly identified the problem and the main steps of the calculation.
Correctly determined the odds from $π_{A} .$
Sucessfully calculated ${odds}_{B} .$
Correctly determined the success probability from ${odds}_{B} .$

Incorrect responses

The system detects the following incorrect responses

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = \underset{instead of {odds}_{A} OR}{\underset{⏟}{{odds}_{A} / OR}}$
$π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}}$

Correctly identified the problem and the main steps of the calculation.
Please remember to convert $π_{A}$ to ${odds}_{A} = \frac{π_{A}}{1 - π_{A}} .$
The response matches the inverse result in which ${odds}_{A}$ was divided by the $OR$ rather than multiplied.
Please remember to back-transform ${odds}_{B}$ to $π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}} .$

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = {odds}_{A} OR$
$π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}}$

Correctly identified the problem and the main steps of the calculation.
Please remember to convert $π_{A}$ to ${odds}_{A} = \frac{π_{A}}{1 - π_{A}} .$
Sucessfully calculated ${odds}_{B} .$
Please remember to back-transform ${odds}_{B}$ to $π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}} .$

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = \underset{instead of {odds}_{A} OR}{\underset{⏟}{{odds}_{A} / OR}}$
$π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}}$

Correctly identified the problem and the main steps of the calculation.
Please remember to convert $π_{A}$ to ${odds}_{A} = \frac{π_{A}}{1 - π_{A}} .$
The response matches the inverse result in which ${odds}_{A}$ was divided by the $OR$ rather than multiplied.
Correctly determined the success probability from ${odds}_{B} .$

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = \underset{instead of {odds}_{A} OR}{\underset{⏟}{{odds}_{A} / OR}}$
$π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}}$

Correctly identified the problem and the main steps of the calculation.
Correctly determined the odds from $π_{A} .$
The response matches the inverse result in which ${odds}_{A}$ was divided by the $OR$ rather than multiplied.
Correctly determined the success probability from ${odds}_{B} .$

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = \underset{instead of {odds}_{A} OR}{\underset{⏟}{{odds}_{A} / OR}}$
$π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}}$

Correctly identified the problem and the main steps of the calculation.
Correctly determined the odds from $π_{A} .$
The response matches the inverse result in which ${odds}_{A}$ was divided by the $OR$ rather than multiplied.
Please remember to back-transform ${odds}_{B}$ to $π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}} .$

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = {odds}_{A} OR$
$π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}}$

Correctly identified the problem and the main steps of the calculation.
Please remember to convert $π_{A}$ to ${odds}_{A} = \frac{π_{A}}{1 - π_{A}} .$
Sucessfully calculated ${odds}_{B} .$
Correctly determined the success probability from ${odds}_{B} .$

${odds}_{A} = \frac{π_{A}}{1 - π_{A}}$
${odds}_{B} = {odds}_{A} OR$
$π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}}$

Correctly identified the problem and the main steps of the calculation.
Correctly determined the odds from $π_{A} .$
Sucessfully calculated ${odds}_{B} .$
Please remember to back-transform ${odds}_{B}$ to $π_{B} = \frac{{odds}_{B}}{1 + {odds}_{B}} .$

Traps

Avoid these traps

Make sure to multiply by $OR$ instead of dividing by it.
Do not forget to convert $π_{A}$ to the respective odds.
Do not forget to back-transform ${odds}_{B}$ to the respective probability.