# Thread: Urgent: Probability of having Lyme Disease and Bayes theorem

1. ## Urgent: Probability of having Lyme Disease and Bayes theorem

I recently found a deer tick on me (had been there for several days). I have no symptoms. My Dr. says I could ignore it or take a course of antibiotics. Given that the probability that this tick carried lyme is 35% and given that the probability of having Lyme in the absence of symptoms is 50%, what is the probability that I have Lyme and therefore should take the meds? I tried formulating this with Bayes (or is it merely the product of these probabilities .50*.35=17.5%) but I'm not sure I have it right and I need to make a decision today. I'd like to know the answer and how it was derived. Thanks!

2. ## Re: Urgent: Probability of having Lyme Disease and Bayes theorem

Hi,
I think you are missing a parameter, the probability of successfull transmission of the disease if the tick was infected.

regards

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CowboyBear (03-13-2017)

4. ## Re: Urgent: Probability of having Lyme Disease and Bayes theorem

You are right although the probability of successful transmission after 72H (this was >96H) is very high so I will assume 100%.

5. ## Re: Urgent: Probability of having Lyme Disease and Bayes theorem

Originally Posted by ihf
You are right although the probability of successful transmission after 72H (this was >96H) is very high so I will assume 100%.
Imagine 1000 people are bitten by ticks. Out of these 350 will get infected, 175 infected but without symptoms. Also, there are 1000-350 =650 people bitten but without symptoms. If you are without symptoms the probability of being infected will be 175/(650+175)=0.212

regards and good luck

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CowboyBear (03-13-2017)

7. ## Re: Urgent: Probability of having Lyme Disease and Bayes theorem

How prevalent is Lyme disease in your region?

8. ## Re: Urgent: Probability of having Lyme Disease and Bayes theorem

35% likelihood that the deer tick was infected with Lyme.

9. ## Re: Urgent: Probability of having Lyme Disease and Bayes theorem

What is the advantage to not taking the medicine? What is the advantage to taking the medicine?

10. ## Re: Urgent: Probability of having Lyme Disease and Bayes theorem

Let's just assume that there are pros and cons to the meds. Could anyone answer the original question?

Spoiler:

12. ## Re: Urgent: Probability of having Lyme Disease and Bayes theorem

OK. so it is in fact just the product of the probabilities, 17.5%
Thanks!

13. ## Re: Urgent: Probability of having Lyme Disease and Bayes theorem

Just curious, before I run the numbers, what would be an acceptable probability?

14. ## Re: Urgent: Probability of having Lyme Disease and Bayes theorem

This is really a decision theory problem, not just a probability problem. If the expected utility of taking the meds is sufficiently high then you should do so. The probabilities are only half of the equation.

15. ## Re: Urgent: Probability of having Lyme Disease and Bayes theorem

I agree, although determining the expected utility is not simple. The medicine is not 100% effective and there are potential side-effects. The way the Dr. put it was, if you are worried then take the meds as that is the best we course have available (though they may not work). I was trying to put some numbers around it. Seems as if the chance the meds are needed is 17.5% or so.

16. ## Re: Urgent: Probability of having Lyme Disease and Bayes theorem

The attached article covers most topics, not sure if the IDSA has newer information, around page 1097 is where it gets interesting. If you kept the tick, that information can be incorporated into decisions.

Typically literature reports individual risks related to antibiotics are very minimal, though the bigger picture is that the arsenal of viable antibiotics not suspected of resistant to super bugs is getting sparse. There are only a few dozen antibiotics coming down the pipeline and most are analogs. So on the counterpoint is that antibiotics should be used sparingly and for their full course and based on as narrow spectrum as feasible.

17. ## Re: Urgent: Probability of having Lyme Disease and Bayes theorem

I'd take the meds since the sequelae of a lyme infection aren't worth the risk (your doctor likely informed you of the complications without treatment, even some that still can occur with treatment)... by the way, this sounds like a conveniently masked homework problem. It makes me wonder...If it's real then good luck, and like I said, I'd probably take the meds if it were me.

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