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

### [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

### 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 prevalence1 as the null hypothesis
• We then compare output based on the assumed design prevalence
• 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
1. That using the actual data using design prevalence
2. 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:
1. For any of the nodes that have a distribution attached, make a draw from them
2. Calculate the final node probabilities (for positive, i.e. infected animal) by multiplying together all of the conditional probabilities that trace to that node
3. Sum all these probabilities to produce the probability of detecting a positive animal
4. Repeat nreps times to give a distribution of estimates for the probability of detecting a positive animal
5. Calculate required sensitivities

## Footnotes

1. 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.

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