figuring the chances of having an STD

[God_of_getting_layed]

chances of having an STD

This post will be useful for those of you have have been tested for STD's or are planning on being tested for STD's.

let's suppose you are getting tested for an STD. The results are either positive or negative for the STD. The test is 95% reliable meaning that 95% of people who really have the STD will turn up positive, and 95% of the people who realy dont have the STD will turn up negative.

Also, 1% of sexually active people have this STD

So you get tested, and the result turns up positive (and your sexually active of course). WHAT IS THE PROBABILITY THAT YOU ACTUALLY HAVE THE STD?

This problem is not a trivial one, and can actually be some helpful knowledge, especially if you get tested for an STD. I know somoene who is a virgin, and got tested for hepatitis and turned up positive for the sexually transmitted one. He beleives there is some mistake in the test. Being a virgin, it would only be logical to come to that conclusion. Of course the doctors didnt beleive he was a virgin, they thought he was lying as a result of being in denial. Of course they knew the tests were very accurate, probably 95% accurate. And the question still remains, does he actually have hepatitis or not?

Im sure some people on this board have been tested for STDs, and turned up negative for STDs which was releaving for them. But the answer to the above question is kind of counterintuitive, and will make you think twice about actually having the STD if you turn up positive for an STD, it will also make you think twice if you turn up negative for an STD. It makes me wonder how many people are out there who were tested negative for HIV actually have it.

first im going to give this post some time and see if anyone can figure out the probability that you have the STD (in this hypothetical problem) just to see what most people's intuition is telling them about this. Then Ill post the answer as well as how to calculate this probability, which will be usefull for those of you who get tested for STDs. becuase a 95% accurate test does not mean it is 95% right, and that there is a 95% chance your negative for the STD if that is what the test resulted, same goes is if it turned up positive(this is what most people's intuition would say) there are other variables that come into play when it comes to determining the probability of having an STD/not having one other than just test accuracy.

 

[Eternal]

Moved to Health and Fitness.

 

[deeloo]

Re: chances of having an STD

Originally posted by God_of_getting_layed
let's suppose you are getting tested for an STD. The results are either positive or negative for the STD. The test is 95% reliable meaning that 95% of people who really have the STD will turn up positive, and 95% of the people who realy dont have the STD will turn up negative.

that made no sense. 95+95=190%...

 

[God_of_getting_layed]

it makes sense, you just didnt comprehend it right.

It means ::IF:: you actually have the STD, there is a 95% chance it will turn up positive. IN THE OPPOSITE SCENARIO ::IF::: you actually DO NOT have the STD there is a 95% chance it will turn up negative.

BTW, based on this logic, you would not add up 95% chance of being positive plus 95% chance of being negative when theyre for 2 different scenarios.

this problem says that all you know is that your test came up positive (in this hypothetical scenario). You dont know if you ACTUALLY HAVE the STD. But you also know another bit of information: 1% of the sexually active population has this STD.

Your trying to figure out the probability that you actually have this STD based on what info you have available, a scenario you will likely to be in if you get tested.

 

[dietzcoi]

I remember something like this when I took probablility and statistics, the professor proved to us that if you come up positive, you actually are MORE likely to be a false positive than a true positive! Had something to do with the fact that only 1% of the people actually have the disease but 5% will have a false positive (Test is only 95% accurate)

5% is obviously larger than 1% so your chance of your positive being false are five times greater than being true

I am sure somebody else can explain it better but it does give you food for thought....

Dietzcoi

 

[God_of_getting_layed]

This is my follow up to my last post "Chances of having an STD"

which can be viewed here:

http://www.sosuave.net/forum/showthread.php?threadid=59485

The post asked a big question that most people on this board will relate to was WHAT ARE THE CHANCES THAT YOU ACTUALLY HAVE AN STD based on:

-Your test result came up positive

-If you actually have the STD, theres a 95% chance the test will come up positive, and a 5% chance it will come up negative.

-If you actually do not have the STD, theres a 5% chance it will come up positive, and a 95% chance it will come up negative.

(the test is 95% accurate)

-Only 1% of the sexually active population has the STD


Most people's intuition would think "well, since the test is 95% accurate, and I came up positive, then theres a 95% chance I have the STD".

But that is the wrong answer, here's the correct answer:

16% chance

Yes, in this scenario, even though the test is 95% accurate, and you came up positive, you only would have a 16% chance of actually having the STD. Yes, it is counter intuitive.

What is the reason for this counter intuitive answer? and How can you calculate this probability should you ever get tested, and want to know the chances of you actually having/not having the STD?

first, lets try to understand why this works out the way it did (If you dont care about why it works out the way it did, and just want to know how to calculate you chances of having an STD, skip this part ):

First, you need to understand that the variables here are dependant on eachother. If the 2 variables were independant, it would be much easier to understand. An example of 2 independant variables are 2 dice, you throw 2 dice at the same time, one die comes up as 6, the other 2. What a given die comes up as does not matter what the other die comes up as. THeyre independant and irrelevant from eachother.

But in this case, your test result is dependant on weither or not you have the disease, and weither or not you have the disease is dependant on a probability statistic.

In this scenario. if you had the disease, there was a 95% chance you would come up positive. So by looking at the disease variable, If the disease is present, we can know know that there is a 95% chance the test result variable will be positive. But the reverse is not true, Just becuase having a disease=95% chance of getting a positive result does not mean we can look at a positive result, and know that there must be a 95% chance that the disease is present. This "asymetricality" in the dependance relationship makes this problem very counterintuitive.

An example is that since the word "the" is the most common word, by looking at the set of the 2 letters "th", we can conclude that the next letter will be an "e" since the probability of "e" following "th" is so high. But that doesnt mean we can find an "e", and conclude that there is a high probability that the letters "th" will precede it.

I could get into more detail about this, but this post is getting long enough as is, so.....

CALCULATING THE PROBABILITY OF HAVING AN STD:

Since the probability you are trying to determine is of dependant variables, youll need to find the "marginal probability" and some information on the variable probabilities and then use "bayes' theorem to calculate the statistic. (explained later)

Basically, you just need to do your homework, and find out the probability that the population has the STD of interest. If you wonder if you have HIV, just find out the statistic on probability that someone in the USA has HIV for example, and note it. this probability will be denoted as the letter "s1" in the equation that will be described later. You also need to fing the probability that the population does not have the STd, which is denoted "s2", you find this by subtracting S1 from 100%. so s2=100%-s1

You will also need to do your homework, and find out the accuracy of the STD test that you are going to take, Find out the probability of it turning up positive if the person actually has the STD, denote this probability as the symbol "b1".

Also note the probability of it turning up negative if you actually have the STD, denoted symbol "B2". This can be calculated easily by subtracting the probability percent of B1 from 100%. so B2=100%-B1.

Youll also need to find out the probability that the test will come up positive if you actually DO NOT have the std, denoted by the symbol "B3".

Then you need to figure out the probability that the test will come up negative if you DO NOT have the std, denoted "B4". This is just 100%-B3=B4.

Once you have all the variables: s1, s2, B1, B2, B3 and B4, you know have enough information to calculate the "marginal probability", and then the final probability of you having the STD using bayes theorem.

REAL EASY EQUATION TO FOLLOW:

to calculate the marginal probability:

Marginal probability= (b1 x s1) + (b3 + s2)

THen take your answer from this equation and plug it into bayes' theorem which is:

(b1 x s1) divided by your answer from the above equation, and youll get the probability that you have the STD!!!!

so thats (b1 x s1)/marginal probability

Now if you ever get tested, you can know the real probability of you actually having the STD or not, and know how accurate your test result is to reality based on probability.

 

[Cheiradawg]

I am not going to argue statistics here because it will do no good. However, if tests in the medical field are only 95% accurate then they usually run the test twice. If the test is ran twice then the possibility of someone being negative and the test comming back positive are very small.

 

[diablo]

Moved to Health & Fitness...

Merged with OP's original thread...

 

[God_of_getting_layed]

even if you run it twice, you still didnt run it enough to where it wount get a positive twice if you were a negative. You should know of the law of large numbers, where the larger your sample is, the closer the stitistic is to the real probability.

In this scenario, the real statistic says, if your actually negative for the STD, then theres a 95% chance that youll come out negative. Keep in mind this is the absolute probability. Your tests are just samples or estimates. You wont see the test results resembling that statistic if your negative untill you get tested alot. The more you get tested, the more you current tests result status will converge on exactly 95% negative results.

example: say you are actually negative for the disease, and you get tested 10 times, you might get 70% negatives, and 30% positive results. THen you try 30 more tests, you might get an average of 89%negatives. Say you try 50 tests, youll get 94% negatives. As you can see, the more tests you do, the closer the average test result converges on the real probability statistic. THe reverse is also true, the lower number of tests you take, the farther, and less accurate the test average will be. So yes, even if you only do 2 tests, it wouldnt be uncommon to get 2 positives in a row, even though your negative, and its 95% accurate. 2 test trials is a very small random sample, and will have a huge margin of error.

But testing over and over AND calculating the probability of having the STD (mentioned above) is a good idea, and is the safest most accurate way to know for sure if you really have the STD or not.

 

[Ricky]

Good old Bayes theorem. I had the urge to crack open my biostats book to verify this one but didn't

 

[I_Only_Live_Once]

I learned this before in Stats, but that was a few years ago.