arlCusum

Calculates the average run length (ARL) for an upward CUSUM scheme for discrete
 distributions (i.e. Poisson and binomial) using the Markov chain approach.

models

Statistical methods for the modeling and monitoring of time series
of counts, proportions and categorical data, as well as for the modeling
of continuous-time point processes of epidemic phenomena.
The monitoring methods focus on aberration detection in count data time
series from public health surveillance of communicable diseases, but
applications could just as well originate from environmetrics,
reliability engineering, econometrics, or social sciences. The package
implements many typical outbreak detection procedures such as the
(improved) Farrington algorithm, or the negative binomial GLR-CUSUM
method of Hoehle and Paul (2008) <doi:10.1016/j.csda.2008.02.015>.
A novel CUSUM approach combining logistic and multinomial logistic
modeling is also included. The package contains several real-world data
sets, the ability to simulate outbreak data, and to visualize the
results of the monitoring in a temporal, spatial or spatio-temporal
fashion. A recent overview of the available monitoring procedures is
given by Salmon et al. (2016) <doi:10.18637/jss.v070.i10>.
For the retrospective analysis of epidemic spread, the package provides
three endemic-epidemic modeling frameworks with tools for visualization,
likelihood inference, and simulation. hhh4() estimates models for
(multivariate) count time series following Paul and Held (2011)
<doi:10.1002/sim.4177> and Meyer and Held (2014) <doi:10.1214/14-AOAS743>.
twinSIR() models the susceptible-infectious-recovered (SIR) event
history of a fixed population, e.g, epidemics across farms or networks,
as a multivariate point process as proposed by Hoehle (2009)
<doi:10.1002/bimj.200900050>. twinstim() estimates self-exciting point
process models for a spatio-temporal point pattern of infective events,
e.g., time-stamped geo-referenced surveillance data, as proposed by
Meyer et al. (2012) <doi:10.1111/j.1541-0420.2011.01684.x>.
A recent overview of the implemented space-time modeling frameworks
for epidemic phenomena is given by Meyer et al. (2017)
<doi:10.18637/jss.v077.i11>.

Sebastian Meyer

surveillance

Temporal and Spatio-Temporal Modeling and Monitoring of Epidemic
Phenomena

Andrea Riebler

Daniel Sabanes Bove

Stefan Steiner

Mikko Virtanen

Wei Wei

Valentin Wimmer

R Core Team 

Howard Burkom

Thais Correa

Mathias Hofmann

Christian Lang

Juliane Manitz

Dirk Schumacher

Leonhard Held

Michael Hoehle

Michaela Paul

Maelle Salmon

arlCusum function

<dl> <dt>h</dt>
<dd>decision interval</dd> <dt>k</dt>
<dd>reference value</dd> <dt>theta</dt>
<dd>distribution parameter for the cumulative distribution function
 (cdf) \(F\), i.e. rate
 \(\lambda\) for Poisson variates or probability \(p\)
 for binomial variates</dd> <dt>distr</dt>
<dd><code>"poisson"</code> or <code>"binomial"</code></dd>
 </dl>

<dl> <dt>W</dt>
<dd>Winsorizing value <code>W</code> for a robust CUSUM,
 to get a nonrobust CUSUM set 
 <code>W</code> &gt; <code>k</code>+<code>h</code>. If <code>NULL</code>, a nonrobust CUSUM is used.</dd> <dt>digits</dt>
<dd><code>k</code> and <code>h</code> are rounded to <code>digits</code> decimal places</dd> <dt>...</dt>
<dd>further arguments for the distribution function, i.e. number of trials <code>n</code>
 for binomial cdf</dd></dl>

Arguments

Calculation of Average Run Length for discrete CUSUM schemes — arlCusum

<dl>

 <dt>h</dt>
<dd>decision interval</dd>

 <dt>k</dt>
<dd>reference value</dd>

 <dt>theta</dt>
<dd>distribution parameter for the cumulative distribution function
 (cdf) \(F\), i.e. rate
 \(\lambda\) for Poisson variates or probability \(p\)
 for binomial variates</dd>

 <dt>distr</dt>
<dd><code>"poisson"</code> or <code>"binomial"</code></dd>
 </dl>

<dl>

 <dt>W</dt>
<dd>Winsorizing value <code>W</code> for a robust CUSUM,
 to get a nonrobust CUSUM set 
 <code>W</code> &gt; <code>k</code>+<code>h</code>. If <code>NULL</code>, a nonrobust CUSUM is used.</dd>

 <dt>digits</dt>
<dd><code>k</code> and <code>h</code> are rounded to <code>digits</code> decimal places</dd>

 <dt>...</dt>
<dd>further arguments for the distribution function, i.e. number of trials <code>n</code>
 for binomial cdf</dd>

</dl>

Calculation of Average Run Length for discrete CUSUM schemes

arlCusum: Calculation of Average Run Length for discrete CUSUM schemes

Description

Usage

Value

Arguments