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According to AIM there are 13 women in the first generation (see http://aim-med.org/Quarantine.html ).

I estimated a 0.01 probability of infection for each woman and sdstud estimated that the probability was ten times higher than I estimated. For each n (number of infections) the following table shows the probability of infection for that number using my probability estimate and that of sdstud.

n mathes sdsd
- ------ ----
0 0.8775 0.25
1 0.1152 0.37 --- current number with positive HIV test
2 0.0070 0.24
3 0.0003 0.10
4 0.0000 0.03
5 0.0000 0.01

My estimate is consistent with 0 to 1 infections at the 95% confidence level. Sdstud's estimate is consistent with 0 to 4 infections at the 95% confidence level.

The problem with statistics is that 13 is too small a group to say much about probabilities with any certainty.

Assuming that the number of infections holds at one, about the most it is possible to say with any certainty from this data is that the probability of infection in this particular group is greater than 0.00195 (97.5% probability of less than one infection) and less than 0.455 (97.5% probability of more than one infection).

-- Modified on 4/21/2004 1:37:15 AM

For the mathematical among us, could your explain your methods and assumptions.

I have also spent time thinking about the probability of infection for hobbiests and providers given different assumptions.  Have you thought this through as well?

Thanks!

FS

is the report that stated that in the straight porn industry, it has been 5 years since a single positive HIV case has been returned.  My friends, that's an astonishing amount of bareback fucking and sucking without a single case....not even withstanding what goes on off camera.

In my mind, that puts porn performers as the safest group of people on the planet....and the media has the whole world scared shitless about this.  And, let's not forget that this male performer (known to do bareback double anals, with internal cumshots) apparently contracted HIV by having unprotected anal sex in Brazil!!

Food for thought,

Jacksonlips

You can't get infected with HIV if your partner isn't infected.

Working in porn would be perfectly safe (as far as HIV is concerned) if it was a closed community and nobody in the community was having sex with (nontested) individuals outside the community. Of course, no community is completely closed but AIM provides an early detection and rapid response system when HIV is brought into the community from outside.

AIM works because porn is legal and employers know the real names of performers and can verify their HIV status with AIM. Even so the hysteria over the current outbreak may destroy the system (see link).

Nevada uses a half-way system. Providers who work in bordellos must be tested on a regular basis. They do not have to provide real names to clients. Just being in the bordello is sufficient certification. Clients are not tested, but condoms are required to reduce the risk of client to provider infection. This system seems to work. I haven't heard of any HIV outbreak in the Nevada bordellos.

Outside of the Nevada bordellos we trust in condoms and voluntary testing. Many providers and clients are tested on a regular basis. AIM tests civilians. However, nobody really knows that anybody else is safe and there is no response system in place to combat HIV infection.

As long as our hobby remains illegal I do not see a solution for us. Real safety depends on records containing actual names and LE (not to mention the Health Department) can subpoena AIM's records at any time.

I have assumed that infections are random and the probability of infection is constant.

Since the number of exposures is small (13) and the probability of infection is probably small (0.01 to 0.10) a normal distribution cannot be used.

Let
  p = probability of individual infection
  n = number of exposures
  k = number of infections
  P(n,k) = Probability of k infections in n exposures
  C(n,k) = number of combinations of n objects taken k at a time

It is appropriate to calculate P(n,k) using the binomial theorem.

  P(n,k) := C(n,k) * (1 - p) ^ (n - k) * p ^ k

where

  C(n,0) = 1
  C(n,k) = n! / (k! * (n - k)!) for k = 1, 2, ..., n

and ! indicates factorial. (^ indicates exponentiation.)

Thus we have

  P(13,0) := (1 - p) ^ n
  P(13,1) := 13 * (1 - p) ^ (n - 1) * p
  P(13,2) := 78 * (1 - p) ^ (n - 2) * p ^ 2

and so on.

As for my general thoughts on danger of HIV infection for clients and providers see link to previous message.

You may have unintentionally mis-stated sdstud's key assumption used to arrive at the probability number that he speculated.  He seemed to have clearly linked the infection probability to the type of sex that each exposed person had.  If you use sexual behavior (unprotected vaginal, unprotected anal, unprotected sex with wounds to the sex organs, and so on) as a key basis for developing a probability estimate, the infection probality becomes proportional to the type of behavior, as sdstud seemed to have implied.

Therefore I made the assumption of a single act of unprotected anal sex with internal ejaculation but no wounds or other STDs to act as cofactors. I was interested in a more-or-less worse case analysis to set an upper bound on the infection probability.

Sdstud felt that I was still underestimating the infection probability by an order of magnitude. Although the population size of 13 is too small to make a clear determination unless a second infection turns up the fact that one of the 13 is infected means that his estimate is very likely better than mine.

For example, My order of magnitude was based on an assumption that SOME of the participants engaged in EXTREME high risk behavior, such as the Unprotected DP Anal which apparently was the cause of Lara Roxx's infection.  Certainly, NOT EVERYONE in the 1st and 2nd Generation would have been engaged in this type of extreme high risk activity.  My contention was that THOSE types of activities probably had at least an order of magnitude greater transmission probability than conventional Anal, while Mathesar's probabilities were probably reasonable predictors where more conventional unprotected activities occurred.  So in fact, My prediction was 1-2 cases of HIV in the first Generation, and some small number asymptotically approaching zero cases in the second generation.  Three cases in Gen 1 would be an outlier, but not totally implausible, while 4 cases in Gen 1 would be an astoundingly high number, that would lead me to believe that we truly have been underestimating the risk of HIV transmission.  

And to completely clarify my point, I would emphasize that Mathesar's methodology for predicting the number of cases is exactly correct, the only difference being in the initial probability of transmission that he and I each plugged into the formula.  My only issue with his analysis was with the initial probability estimate that he used.  And I'm sure that he'd agree with me, that if one assumed acts like unprotected DP anal, the probabilities he used were too low, just as I'd agree that his estimates were reasonable for more conventional activities.  My only quibble was that I feared (and the Lara Roxx case unfortunately proved) that the typical activities of porn, were pretty far outside the mainstream behavior used to derive the initial estimates that Mathesar plugged into the formula.