Per-Exposure Risk: What Transmission Probability Estimates Actually Mean

The key distinction is one covered in our guide to Bayes' theorem: the probability of an outcome given a condition isn't the same as the probability of the condition given the outcome. Here, the probability of infection given an exposure is a different quantity from the probability that a particular exposure was the source given that an infection occurred.

What a per-exposure estimate is

A per-exposure (or per-act) probability is the estimated chance that one exposure results in transmission under specified conditions. The HIV risk and prevention estimates give them per 10,000 exposures to a partner with HIV:

• receptive anal intercourse: 138 per 10,000
• needle sharing during injection drug use: 63 per 10,000
• insertive anal intercourse: 11 per 10,000
• receptive penile-vaginal intercourse: 8 per 10,000
• insertive penile-vaginal intercourse: 4 per 10,000

These are population averages for exposures without the prevention measures that change the risk. The CDC notes that other STDs, acute infection and high viral load can raise transmission risk. Condoms, male circumcision, antiretroviral treatment and pre-exposure prophylaxis can lower it. It also states that people with HIV who achieve and maintain viral suppression through treatment do not transmit HIV through sex. So these estimates shouldn't be applied unchanged to exposures involving effective prevention.

Converting per-act risk to cumulative risk

A common question is what happens over repeated exposures. The clearest framing uses conditional probability.

Let p be the probability of infection at an exposure, given that the person was still uninfected before it. If that conditional probability is the same at every exposure, the probability of remaining uninfected after n exposures is (1 − p)^n. The probability of infection by exposure n is:

More generally, if each exposure has its own conditional probability pᵢ, the expression becomes:

Worked example

Take p = 0.0008 (8 per 10,000) and n = 100 exposures.

Here the result is close to the simple product n × p = 8%, because the cumulative risk is still relatively small. The approximation 1 − (1 − p)^n ≈ np only holds when np is small, not merely when p is. A tiny per-exposure probability can still add up to substantial cumulative risk over enough exposures.

With p = 0.0138 (138 per 10,000), the gap is clear:

Multiplying p by n would give 69% for 50 exposures. Simply adding per-exposure probabilities treats the events as mutually exclusive. The complement calculation accounts for the fact that infection can only happen once: once someone is infected, later exposures can't infect them again.

What the formula assumes

The cumulative formula depends on how each p is defined. It needs the probability of infection at each exposure, conditional on the person still being uninfected. In practice, those conditional probabilities differ from one exposure to the next, depending on the partner's viral load and treatment, co-infections, and the prevention used.

That's why a population-average estimate can't simply be substituted for the individual conditional probabilities in the general formula. The average describes many exposures across many people. It doesn't describe the risk of a specific exposure between specific partners.

Two different ideas are easy to confuse here:

• Variation in underlying risk: real differences between people and exposures, such as viral suppression versus high viral load, or prevention used versus not used.
• Uncertainty in the estimate: how precisely researchers have measured an average risk, reflected in confidence intervals around published figures.

Pooling data doesn't erase either one. When researchers combine observations from different people, shared unmeasured risk factors can create dependence between exposures that a simple model ignores. Systematic reviews, such as the 2014 review estimating per-act HIV transmission risk, summarize the evidence and its uncertainty. They don't turn an average into a precise individual probability.

Why per-exposure probability alone cannot identify an individual source

The hardest limit is attribution. A per-exposure probability describes how often infection follows exposure across many exposures. Attribution asks the reverse question: given that an infection occurred, how likely is it that a specific exposure caused it? Answering that requires Bayes' theorem and inputs that per-exposure figures don't supply.

Suppose someone had exposures with two partners during the same period. To estimate the relative likelihood of each source, you'd need each partner's infection status at the time, their viral load and treatment, the timing and type of each exposure, and whether the person was already infected before any of them. Without those, per-exposure estimates can't point to a source, though statistical inference combined with other evidence can still narrow the possibilities.

The same gap between population probability and individual cause shows up in civil claims, and it's one reason legal guides note that STD cases can be hard to prove. Depending on the jurisdiction and the legal claim, the relevant issues may include what the defendant knew or reasonably should have known, their conduct, and evidence connecting that conduct to the infection. A transmission probability can describe the risk of an exposure, but it can't establish that connection on its own.

Reading transmission estimates correctly

A few habits keep per-exposure figures from being misused:

• check what each estimate is conditioned on, including exposure type, partner status and prevention
• keep variation in underlying risk separate from uncertainty in the estimate
• use the complement calculation rather than adding probabilities for cumulative risk
• state which conditional probabilities a cumulative calculation assumes
• don't use population averages to assign cause in an individual case