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update paper link to delay best practice #163

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2 changes: 1 addition & 1 deletion episodes/delays-refresher.Rmd
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- From the [serial interval](reference.md#serialinterval) distribution we can optimize contact tracing. We can evaluate the need to expand the number of days pre-onset to consider in the contact tracing to include more backwards contacts ([Claire Blackmore, 2021](https://www.paho.org/sites/default/files/backward_contact_tracing_v3_0.pdf); [Davis et al., 2020](https://assets.publishing.service.gov.uk/media/61e9ab3f8fa8f50597fb3078/S0523_Oxford_-_Backwards_contact_tracing.pdf)).

![A schematic of the relationship of different time periods of transmission between a primary case and a secondary case in a transmission pair. Adapted from [Zhao et al, 2021](https://www.sciencedirect.com/science/article/pii/S1755436521000359#fig0005)](fig/delays-adapted.png)

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[image missing alt-text]: fig/delays-adapted.png

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When we calculate the *serial interval*, we see that not all case pairs have the same time length. We will observe this variability for any case pair and individual time period.

![Serial intervals of possible case pairs in (a) COVID-19 and (b) MERS-CoV. Pairs represent a presumed infector and their presumed infectee plotted by date of symptom onset ([Althobaity et al., 2022](https://www.sciencedirect.com/science/article/pii/S2468042722000537#fig6)).](fig/serial-interval-pairs.jpg)

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[image missing alt-text]: fig/serial-interval-pairs.jpg

To summarise these data from individual and pair time periods, we can find the **statistical distributions** that best fit the data ([McFarland et al., 2023](https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2023.28.27.2200806)).

<!-- add a reference about good practices to estimate distributions -->

![Fitted serial interval distribution for (a) COVID-19 and (b) MERS-CoV based on reported transmission pairs in Saudi Arabia. We fitted three commonly used distributions, Log normal, Gamma, and Weibull distributions, respectively ([Althobaity et al., 2022](https://www.sciencedirect.com/science/article/pii/S2468042722000537#fig5)).](fig/seria-interval-fitted-distributions.jpg)

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[image missing alt-text]: fig/seria-interval-fitted-distributions.jpg

Statistical distributions are summarised in terms of their **summary statistics** like the *location* (mean and percentiles) and *spread* (variance or standard deviation) of the distribution, or with their **distribution parameters** that inform about the *form* (shape and rate/scale) of the distribution. These estimated values can be reported with their **uncertainty** (95% confidence intervals).

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**Estimating epidemiological delays is CHALLENGING!**

Epidemiological delays need to account for biases like censoring, right truncation, or epidemic phase ([Charniga et al., 2024](https://arxiv.org/abs/2405.08841)).
Epidemiological delays need to account for biases like censoring, right truncation, or epidemic phase ([Charniga et al., 2024](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1012520)).
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Additionally, at the beginning of an outbreak, limited data or resources exist to perform this during a real-time analysis. Until we have more appropriate data for the specific disease and region of the ongoing outbreak, we can **reuse delays from past outbreaks** from the same pathogens or close in its phylogeny, independent of the area of origin.

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