Odds Ratio & Relative Risk Calculation & Definition, Probability & Odds

ERRATA: At about the 3:00 mark the slide says "10,00" when it is really supposed to say "10,000." I added a pop up box to fix it. Thanks to Mehdi Hedjazi for pointing this typo out

The terms odds and probability are used interchangeably in everyday life. However, in the setting of Biostats they are two different things. Generally speaking they both represent how likely something is, but they are calculated differently and used in different situations. Probability is essentially the same things as percentage. You are comparing the number of occurrences of a certain outcome to the number of total events measured. Probability ranges between zero and one. Odds is a ratio of the likelihood of an event happening compared to the likelihood of an event not happening. Odds can be zero or any positive number (not just values between 0 and 1).

So the probability of rolling a 4 on one attempt with one six faced die is 1_6. The odds of rolling a 4 are 1_5. Here is another example. If 13 people of a 60 person sample have lung cancer the probability of a person in that group having lung cancer is 13_60 and the odds of a person in that group having lung cancer is 13_ 47.

When we are talking about common events the difference between odds and probability is high. For example, flipping a coin one time gives you pretty different results. You have 1_1 odds of getting head and 1_2 probability of getting heads. However, as an event gets more and more rare the difference between odds and probability gets very small. Pretend there is a drawing with one winner and 10,000 people entered. The odds of winning are 1_9,999 (0.0001) and the probability of winning is 1_10,000 (0.0001). In this case, odds and probability are essentially identical.

The difference between odds and probability is important because Relative Risk is calculated with probability and Odds Ratio is calculated with odds. Relative Risk (RR) is a ratio of probabilities or put another way it is one probability divided by another. Odds Ratio (OR) is a ratio or proportion of odds. I just remember that odds ratio is a ratio of odds and probability isn't a ratio of odds (AKA it is the other option).
Relative Risk = Probability _ Probability
Odds Ratio = Odds _ Odds

Now that you have a general idea of what odds ratio and relative risk are you need to know when to use them. They don't always just ask you to calculate one or the other. Sometimes questions on Step 1 also require you to figure out which type of calculation is needed based on the situation. In clinical trials and cohort studies we use relative risk to compare the incidence of health outcomes between groups of differing exposure or treatment. For case-control trials we use odds ratio to compare the "incidence" of past exposures or treatments.

Cohort Studies (and clinical trials) = Relative Risk
Case-Control studies = Odds Ratio

I remember this by thinking about a group of pirates (group = cohort) all saying "aRRrrr!". That reminds you that cohort studies use RR and the "other one" uses OR.

Now that we understand the research setting for each term we can redefine RR & OR. I should note that I think memorizing these definitions is unnecessary because if you understand the simpler definitions you should be able to create these based on the scenario presented in the question.

An RR or OR of 1 means there is no difference between the two groups being compared with respect to what you are measuring. In this case the treatment or risk factor being study has no effect on the rate of outcome development. Similarly, an OR or RR of 2 means whatever you are measuring is two times as likely to occur in the group being studied when compared with the control group. 0.5 means it is half as likely and so on. Later in the chapter we will cover how confidence intervals are applied to RR & OR.

[Napricorn_]

you the real MVP, for real. Just my luck I find you as I'm attempting to finish my final epidemiology assignment. I've been reading the textbooks, slides, listening to lectures on repeat, and a few simple videos just made me understand something I was ready to give up on and just take the L. Thank you sir! Do you do any other medical classes? I'm subbing anyway thanks for saving me, your my hero.

[lalu]

finally someone who can explain the different usage scenarios for both and not only limit to a broad description of the calculation. thank you so much

[smileyface]

Thank you so much, odds ratio makes so much sense now, the dice bit was gold!

[ntimifrank]

This video has been great and very useful for me. Thanks very much for the clear explanation

[nurhafizsahzaimey]

hi! I just wanna thank you for this video. I just finished my epidemiology paper today and I couldn't do it if its not because of you. thank you so much for your videos. you're the real MVP. =)

[alexhamble]

Extremely good thanks for your time, ive told others about your channel ;)

[bangaliwala]

thank you. :) appreciate all that you do

[tukeicathy]

Thank u from Uganda. U just saved my life.

[Drspraker]

Thanks so much.. it can't get any better..

[Nickllllllllll]

You, sir, are awesome. Very clear explanations :)

[manerwal]

Super. You made it so simple. loved it.

[jmrjmr]

Great video, but I am still confused about the interpretation. So the interpretation of RR and OR is the same? Because if seen some websites that say that RR should be interpreted as the way you explained it but not the OR. 

[DavePSmith-ykbe]

hi thanks. These videos are so fascinating and educative.

[malesh]

top stuff dude! this helped me lot!
i hope you achieve all your goals and dreams
God bless

[vmedicoschannel]

Thank u.. Informative vedio
One zero is missing in probability denominator.. ??

[kabidahmed]

Thank u so much. Its very much useful to me .

[saniyaa]

Hi
just a quick question what actually is a odds ratio and a relative risk? when are they used and what information do they give in regards to the information collected from respective studies ?
thank you so much for the videos!

[Theoryverse]

Thank you so much for your helpful video :)

[Pln]

great job !
are the same biostat topics tested in step 3 ?

[Fungus_Pilot]

yay <3 thank you for this useful video :3