Measures of Effect

Major Concepts

1. Risk

1. • Probability of an event occurring given specific conditions

   • Ex: probability of an event in control group is C/(C+D)

2. Relative Risk

   • Risk of an event occurring in the treatment group compared to the risk of an event occurring in the control group

   • RR = (Risk of an event occurring in treatment)/(Risk of an event occurring in control)=(Risk of failing after getting tutoring)/(Risk of failing after not getting tutoring)= (A/(A+B))/(C/(C+D))

3. Odds

   • Event in a group divided by no event

   • Ex: odds of an event in treatment group is A/B

   • Ex: odds of an even in control group C/D

4. Odds Ratio

   • Odds of an event compared to the odds of no event

   • OR = (odds of an event in treatment group) / (odds of event in control group) = (A/B) / (C/D) = (AD/BC)

5. Conversion between odds and risk

   • Risk to odds: OR = R / (1-R)

Positive Predictive ValueOdds Ratio

Risk Ratio

Relative Risk Reduction

Absolute Risk Reduction

Number Needed to Treat

Confidence Interval

Risk: Just a more foreboding term for the probability of something happening. For example, the risk of failing after getting tutoring is a/(a+b)

Relative Risk (RR): This can be defined as the risk of an event occurring in the treatment group compared to the risk of an event occurring in the control group. Or put in a formula.

RR = (Risk of an event occuring in treatment)/(Risk ofan event occuring in control)=(Risk of failing after getting tutoring)/(Risk of failing after not getting tutoring)= (a/(a+b))/(c/(c+d))

Odds Ratio (OR): This refers to the Based on our sample table above, this means it’s the odds of a student failing compared to the odds of a student passing. But that still begs the question: what are odds? Simply put they are the n. For example, if we’re looking at the odds of failing.

〖Odds〗_tutoring=(number of students who failed)/(number of students who passed) =a/b

〖Odds〗_(no-tutoring)=(number of students who failed)/(number of students who passed) =c/d

Now, as said above, odds ratio is just odds of event over odds of no event. So here:

OR=〖Odds〗_tutoring/〖Odds〗_(no-tutoring) =(a/b)/(c/d)=ad/bc

Fun fact about Odds Ratio: It can also be written as the probability of an event over the probability of a non-event. As probabilities of every possible outcome always add up to 1, this is also written as . The more you know!

HOW ARE THESE USED?!

Easy peasy way of remembering. There’s a CASE in the OR. Case control usually use odds ratio. Relative risk is used in cohort. I don’t have pneumonic for that. In my defense, I’m a historian and public health practitioner – my friends are facts and stats, neither of which require much creativity.