This post continues the development of Model 3 in Post 381 (
http://www.hungangels.com/vboard/sho...&postcount=381).
Why Model 3? Because (given the clarification in
http://www.cdc.gov/hiv/basics/prep.html ) Model 1 obviously gets the interpretation of “effective” wrong. Model 2’s interpretation of “risk per exposure” is way to rosey (e.g. p = .0000013896). Indeed, I called this a risky calculation in Post 372 (
http://www.hungangels.com/vboard/sho...&postcount=372) because I was wary of the interpretation.
What does Model 3 have going for it?
The interpretation of risk per exposure is straightforward. The CDC reports the risk of transmission for unprotected anal receptive intercourse with an HIV infected partner is 138 per 10000 exposures. Model 3 simply interprets this as: the probability of transmission through one exposure is 138/10000 = 0.0138 = 1.38%. Initially I didn’t go with this interpretation and invented Model 2 instead. Why? Because under this interpretation the probability of transmission after 10000 independent exposures is not 138 chances out of 10000. It was stupid of me to expect it should be. All that one can expect is that 138 be the expected number of transmissions given 10000 independent exposures. And indeed
According to Model 3 the expected number of transmission given 10000 independent exposures 138 (the number measured by the CDC).
So what’s left to do with Model 3 is make a predictive theoretical comparison of PrEP use without condoms to its use with condoms.
The effectiveness of condoms against the transmission of HIV is estimated as being somewhere between 90% to 95% (
http://www.ncbi.nlm.nih.gov/pubmed/9141163) Let’s take the average and round down to 92%. This number just happens to be the effectiveness of PrEP as well (
http://www.cdc.gov/hiv/basics/prep.html).
We saw in my last post that in the case of receptive anal intercourse with an HIV infected partner the probability of transmission through a single exposure for a person using PrEP alone is 0.11%.
Since both PrEP and Condoms have comparable effectiveness against HIV (both 92%) we can also say that in the case of receptive anal intercourse with an HIV infected partner the probability of transmission through a single exposure for a person using condoms alone is 0.11%.
To make Wes happy we’ll also consider the possibility that Truvada(which is a PrEP) is 99% effective. So let’s see, 1.38 is 99% lower than 138. So (using Wes’s report that Truvada is 99% effective) the risk of transmission (for anal receptive intercourse with an HIV partner) is 1.38 per 10000 exposures; i.e. 0.0138%.
For concreteness, once again suppose there are 100 people, each one with a life-long HIV infected partner with whom they have anal receptive intercourse once or twice a day (say 550 times a year).
If the group is on PrEP alone, then after y years the expected number of infected persons is 100[1-(1-.0011)^(550*y)].
If the group is on Wes’s Truvada alone, then after y years the expected number of infected persons is 100[1-(1-.000138)^(550*y)].
If the group is on PrEP and Condoms, then after y years the expected number of infected persons is 100{1-[1-(0.0011)*(0.0011)]^(550*y)}.
Since we’ve been through this a dozen times before I’ll just give a very brief explanation of the last of these. The probability that both the PrEP and the condom fail on the same single exposure is the product of their independent probabilities of failure; i.e. (0.0011)*(0.0011). So [1-(0.0011)*(0.0011)] is the probability that there is no transmission on a single exposure. Consequently [1-(0.0011)*(0.0011)]^(550*y) is the probability of no transmissions after y years. So 1-[1-(0.0011)*(0.0011)]^(550*y) is the probability of at least one transmission before y years are up. Multiply by the group size, in this case 100, to get the expected number of transmission. That’s the quick derivation of the third equation.
So let’s take a look at them. They’re graphed below. Neither form of protection works very well alone. Doubling up a PrEP with condoms has better promise. Condoms can significantly amplify the effectiveness of whatever else you’re using.
Some further points:
Condoms separate the HIV virus from exposure to the PrEP thereby minimizing the risk to the general population of creating resistant strains.
Condoms protect against other STDs as well.
PrEP may have side effects.
Okay. Done. That's my story and I'm stickin' to it.