knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )
This is a work in progress. Please consider submitting a PR to improve it.
This model deals with the problem of nowcasting, or adjusting for right-truncation in reported count data. This occurs when the quantity being observed, for example cases, hospitalisations or deaths, is reported with a delay, resulting in an underestimation of recent counts. The estimate_truncation()
model attempts to infer parameters of the underlying delay distributions from multiple snapshots of past data. It is designed to be a simple model that can integrate with the other models in the package and therefore may not be ideal for all uses. For a more principled approach to nowcasting please consider using the epinowcast package.
Given snapshots $C^{i}{t}$ reflecting reported counts for time $t$ where $i=1\ldots S$ is in order of recency (earliest snapshots first) and $S$ is the number of past snapshots used for estimation, we try to infer the parameters of a discrete truncation distribution $\zeta(\tau | \mu{\zeta}, \sigma_{\zeta})$ with corresponding probability mass function $Z(\tau | \mu_{\zeta}$).
The model assumes that final counts $D_{t}$ are related to observed snapshots via the truncation distribution such that
\begin{equation} C^{i < S){t}\sim \mathcal{NegBinom}\left(Z (T_i - t | \mu_{Z}, \sigma_{Z}) D(t) + \sigma, \varphi\right) \end{equation}
where $T_i$ is the date of the final observation in snapshot $i$, $Z(\tau)$ is defined to be zero for negative values of $\tau$ and $\sigma$ is an additional error term.
The final counts $D_{t}$ are estimated from the most recent snapshot as
\begin{equation} D_t = \frac{C^{S}}{Z (T_\mathrm{S} - t | \mu_{Z}, \sigma_{Z})} \end{equation}
Relevant priors are:
\begin{align} \mu_\zeta &\sim \mathrm{Normal}(0, 1)\ \sigma_\zeta &\sim \mathrm{HalfNormal}(0, 1)\ \varphi &\sim \mathrm{HalfNormal}(0, 1)\ \sigma &\sim \mathrm{HalfNormal}(0, 1) \end{align}
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