# My Dominant Hemisphere

The Official Weblog of 'The Basilic Insula'

## Decision Tree Questions In Genetics And The USMLE

Just a quick thought. It just occurred to me that some of the questions on the USMLE involving pedigree analysis in genetics, are actually typical decision tree questions. The probability that a certain individual, A, has a given disease (eg: Huntington’s disease) purely by random chance is simply the disease’s prevalence in the general population. But what if you considered the following questions:

• How much genetic code do A and B share if they are third cousins?
• If you suddenly knew that B has Huntington’s disease, what is the new probability for A?
• What is the disease probability for A‘s children, given how much genetic code they share with B?

When I’d initially written about decision trees, it did not at all occur to me at the time how this stuff was so familiar to me already!

Apply a little Bayesian strategy to these questions and your mind is suddenly filled with all kinds of probability questions ripe for decision tree analysis:

• If the genetic test I utilize to detect Huntington’s disease has a false-positive rate x and a false-negative rate y, now what is the probability for A?
• If the pre-test likelihood is m and the post-test likelihood is n, now what is the probability for A?

I find it truly amazing how so many geneticists and genetic counselors accomplish such complex calculations using decision trees without even realizing it! Don’t you 🙂 ?

Written by Firas MR

September 3, 2009 at 4:07 pm

## Does Changing Your Anwer In The Exam Help? One of the 3 doors hides a car. The other two hide a goat each. In search of a new car, the player picks a door, say 1. The game host then opens one of the other doors, say 3, to reveal a goat and offers to let the player pick door 2 instead of door 1. Is there an advantage if the the player decides to switch? (Courtesy: Wikipedia)

Hola amigos! Yes, I’m back! It’s been eons and I’m sure many of you may have been wondering why I was MIA. Let’s just say it was academia as usual.

So what the heck are decision trees anyway? They are basically conceptual tools that help you make the right decisions given a couple of known probabilities. You draw a line to represent a decision, and explicitly label it with a corresponding probability. To find the final probability for a number of decisions (or lines) in sequence, you multiply or add their individual probabilities. It takes skill and a critical mind to build a correct tree, as I learned. But once you have a tree in front of you, its easier to see the whole picture.

Let’s just ignore decision trees completely for the moment and think in the usual sense. How good an idea is it to change an answer on an MCQ exam such as the USMLE? The Kaplan lecture notes will tell you that your chances of being correct are better off if you don’t. Let’s analyze this. If every question has 1 correct option and 4 incorrect options (the total number of options being 5), then any single try on a random choice gives you a probability of 20% for the correct choice and 80% for the incorrect choice. The odds are higher that on any given attempt, you’ll get the answer wrong. If your choice was correct the first time, it still doesn’t change these basic odds. You are still likely to pick the incorrect choice 80% of the time. Borrowing from the concept of “regression towards the mean” (repeated measurements of something, yield values closer to said thing’s mean), we can apply the same reasoning to this problem. Since the outcomes in question are categorical (binomial to be exact), the measure of central tendency used is the Mode (defined as the most commonly or frequently occurring thing in a series). In a categorical series – cat, dog, dog, dog, cat – the mode is ‘dog’. Since the Mode in this case happens to be the category “incorrect”, if you pick a random answer and repeat this multiple times, you are more likely to pick an incorrect answer! See, it all make sense 🙂 ! It’s not voodoo after all 😀 !

Coming back to decision analysis, just as there’s a way to prove the solution to the Monty Hall Paradox using decision trees, there’s also a way to prove our point on the MCQ problem using decision trees. While I study to polish my understanding of decision trees, building them for either of these problems will be a work in progress. And when I’ve figured it all out, I’ll put them up here. A decision tree for the Monty Hall Paradox can be accessed here.

To end this post, I’m going to complicate our main question a little bit and leave it out in the void. What if on your initial attempt you have no idea which of the answers is correct or incorrect but on your second attempt, your mind suddenly focuses on a structure flaw in one or more of the options? Assuming that an option with a structure flaw can’t be correct, wouldn’t this be akin to Monty showing the goat? One possible structure flaw, could be an option that doesn’t make grammatical sense when combined with the stem of the question. Does that mean you should switch? Leave your comments below!

Hope you’ve found this post interesting. Adios for now!

Coleman-Liau index: 8.5
Gunning fog index: 11.4
SMOG index: 10.7 Intuitive Biostatistics, by Harvey Motulsky The Monty Hall Problem: The Remarkable Story Of Math’s Most Contentious Brain Teaser, by Jason Rosenhouse

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