## What is point estimation?

A point estimate is a single numeric calculation of risk. The particular input parameter values chosen for exposure and dose response correspond to the desired interpretation. One common point estimate is to select the most likely values of the various inputs and calculate a single "best estimate" of risk. Alternatively, one might choose values of inputs that are plausible but conservative (tend to result in higher risk estimates) in order to make a point estimate of the maximum reasonable exposure, or 'worst credible case'.

Point estimation is relatively simple to implement. Multiple point estimates across different scenarios and inputs can help to characterize uncertainty. For more complex models and more detailed analyses, probabilistic risk assessment methods (link to PRA content) are recommended. However, point estimates remain useful for teaching examples or 'back of the envelope' risk characterizations.

### Example: Cryptosporidiosis risk

If Cryptosporidium is present in a water body, what is the risk of infection from swimming in this water? What are the risks of illness or death? Point estimates of these risks can be quickly calculated using likely exposure and dose response parameter values.

#### Exposure assessment

• Assume 10 infective oocysts/liter in a particular water body
• 0.13 liters ingested per swim, 7 swims per year 
• Dose = contact rate x concentration: 0.13 liters/swim x 10 oocyst/liter = 1.3 oocysts ingested per swim

The number of swims per year will be used later.

#### Dose response

A dose response function can be used to convert the mean dose of oocysts into a risk of infection.

• Risk = 1 - exp(-k x dose)
• k = 0.0572, with infection as the response
• Risk = 1 - exp(-1.3 x 0.0572) = 0.072

The risk is defined here as the probability of infection per swim.

#### Risk characterization

The probability of infection per swim can be modified to reflect other risks. If the probability of infection per swim is 0.072, and we suppose that people swim 7 times/year on average, the yearly risk of one or more infections would be:

• 1 - (1 - 0.072)^7 = 0.41

Risks of illness and death can also be easily estimated, since these risks are often viewed as independent of dose given that infection has occurred. The probabilities of illness or death resulting from an infection are assumed to be:

• Prob[illness|infection] = 0.39
• Prob[death|illness] = ~0.001
• Risk of illness from a single swim = Prob[illness|infection] x Prob[infection] = 0.39 x 0.072 = 0.028
• Yearly risk of illness (assuming 7 swims) = 1 - (1 - 0.028)^7 = 0.18
• Risk of death from a single swim = Prob[death|illness] x Prob[illness] = 0.001 x 0.028 = 2.8x10-5
• Yearly risk of death (assuming 7 swims) = 1 - (1 - 2.8x10-5)^7 = 2.0x10-4