This is the first entry I have transformed into a webpage from my research notebook.

## Tasks

### [DONE]{.done .DONE} Read through this case study

CLOSED: [2016-07-19 Tue 10:02] <2016-06-10 Fri 10:21>

- The source can be found on github

## Readings

### Documenting disease freedom in swine by combination of surveillance programmes using information from multiple non-survey-based sources [[scenario]{.smallcaps}]{.tag tag-name=“scenario”} [[tree]{.smallcaps}]{.tag tag-name=“tree”}

<2016-06-10 Fri 10:46>

- Report for International EpiLab
- Provides case studies on scenario tree modelling, so a good place to start reading in this area, even though it\’s a little old (2003)
- The ultimate goal is to estimate the
*surveillance process\’s sensitivity*- this is the probability of detecting an infected unit, given the area is infected (under some design prevalence)
- $\Pr\left(\geq 1\text{ infected unit }\big|\text{ country infected}\right)$

- If there is a positive (confirmed) test on a unit, then clearly the area is not free from disease!
- Layman\’s summary for scenario tree:
- Combines probabilities in each step of the surveillance system to output an overall probability that the surveillance system will detect the disease if present

- For a scenario tree, they define conditional probabilities by
considering preconditions
- That is, all parent nodes to the current node

- Confidence = overall sensitivity
- Use hypothesis testing as a framework
- Hence the
*design prevalence*^{1}as the*null*hypothesis - We then compare output based on the assumed design prevalence

- Hence the
- Suggest in S2.3.3 that Bayesian probabilities can be used at the end
of modelling to produce a probability of freedom from disease
- As opposed to the probability of detection as above

- All nodes in a scenario tree are
*conditional*on all parent nodes - Unit of analysis is important
- []{#crops}What happens with variable size units? E.g. crops or herds?

- Ordering of nodes is not important
- as opposed to graphical models?
- it does affect the conditional probabilities though, so keeps them easier to specify

- Factors to include are those that influence the probability of
infection or detection
- So in response to above, variable sizing would need to be included somehow
- This would then suggest for a continuous measure like crop size (e.g. in Ha), it would be better to go to a more flexible modelling tool that allows a continuous node
- They suggest with the note, capturing variability

- Recommend stochastic modelling, with each branch probability having
uncertainty in the form of an appropriate probability distribution
- How that stochastic modelling is done is what I\’m interested in mainly

- Branch probabilities
- They say you need to use data!
- Of course, but that\’s the hard part
- Need to use data from similar diseases or geographies for a large part of this
- Otherwise, expert opinion, which the go in to

- Surveillance systems with incomplete coverage (e.g. targeted
surveillance) require two model fits
- That using the actual data using design prevalence
- One using a
*representative*surveillance process, which uses estimated prevalence, and simulated data/units- With the same number of units as in the actual data

- Estimating the probability of freedom from infection is then easily done using Bayes theorem, and law of total probability
- Sensitivity analysis should be performed
- But doesn\’t say how in S2.5.2.3.8

- Provides a brief excursion into expert opinion
- Including the gathering and analysis of such data to provide node probability distributions

- Doesn\’t really go in to how the probabilities are traced through
the tree
- I\’m wondering whether this is the process:
- For any of the nodes that have a distribution attached, make a draw from them
- Calculate the final node probabilities (for positive, i.e. infected animal) by multiplying together all of the conditional probabilities that trace to that node
- Sum all these probabilities to produce the probability of detecting a positive animal
- Repeat
`nreps`

times to give a distribution of estimates for the probability of detecting a positive animal - Calculate required sensitivities

- I\’m wondering whether this is the process:

## Footnotes

*Design*refers to the fact that this prevalence is a part of the design of the model/system and is not related to any actual prevalence within the system.^{[return]}