Title: Statistical Modelling for Infectious Disease Management
Version: 1.0
Description: Statistical models for specific coronavirus disease 2019 use cases at German local health authorities. All models of Statistical modelling for infectious disease management 'smidm' are part of the decision support toolkit in the 'EsteR' project. More information is published in Sonja Jäckle, Rieke Alpers, Lisa Kühne, Jakob Schumacher, Benjamin Geisler, Max Westphal "'EsteR' – A Digital Toolkit for COVID-19 Decision Support in Local Health Authorities" (2022) <doi:10.3233/SHTI220799> and Sonja Jäckle, Elias Röger, Volker Dicken, Benjamin Geisler, Jakob Schumacher, Max Westphal "A Statistical Model to Assess Risk for Supporting COVID-19 Quarantine Decisions" (2021) <doi:10.3390/ijerph18179166>.
License: BSD_3_clause + file LICENSE
Encoding: UTF-8
RoxygenNote: 7.2.1
Imports: dplyr, extraDistr, stats, methods
Suggests: testthat (≥ 3.0.0), covr, xml2, knitr, rmarkdown, tidyr, hdrcde, ggplot2, scales
Config/testthat/edition: 3
VignetteBuilder: knitr
URL: https://gitlab.cc-asp.fraunhofer.de/ester/smidm
BugReports: https://gitlab.cc-asp.fraunhofer.de/ester/smidm/-/issues
NeedsCompilation: no
Packaged: 2022-08-26 12:12:44 UTC; sjaeckle
Author: Max Westphal ORCID iD [aut], Stefanie Grimm [aut], Sonja Jäckle ORCID iD [aut, cre], Rieke Alpers ORCID iD [aut], Hong Phuc Truong [aut], Amelie Lucker [ctb], Fraunhofer MEVIS [cph], Fraunhofer ITWM [cph]
Maintainer: Sonja Jäckle <sonja.jaeckle@mevis.fraunhofer.de>
Repository: CRAN
Date/Publication: 2022-08-27 08:40:02 UTC

Overall likelihood

Description

Calculates vector of probabilities that zero positive tests are observed given different numbers of infected.

Usage

calculate_likelihood_negative_tests(
  test_infos,
  test_types,
  negative_persons,
  subgroup_size,
  info
)

Arguments

test_infos

Matrix with column number of test days and a column for each test with the testday relative to event date, the rows are the groups.

test_types

Matrix with test day (columns) of each group (rows) and whe informations about test types.

negative_persons

Number of people without the infectious persons.

subgroup_size

Array with the number of persons per test group.

info

Dataframe, this is a placeholder

Value

Vector of probabilities calculated.

Examples

test_infos <- matrix(nrow = 2, ncol = 3)
test_infos[1,] <- c(1, 2, NA)
test_infos[2,] <- c(2, 4, 6)

test_types <- matrix(nrow = 2, ncol = 2)
test_types[1,] <- c("PCR", NA)
test_types[2,] <- c("PCR", "Antigen")

calculate_likelihood_negative_tests(test_infos = test_infos,
                                    test_types = test_types,
                                    negative_persons = 23,
                                    subgroup_size = c(3, 5))

Likelihood K

Description

Calculates the probability that zero positive tests are observed given K of the group are infected.

Usage

calculate_likelihood_negative_tests_k(
  infected_group_size,
  information_data,
  test_infos,
  test_types,
  info,
  combination_infected,
  number_group_peoples,
  number_subgroups
)

Arguments

infected_group_size

Number of infected Persons in the group.

information_data

Matrix with columns person ID, tested (T/F), result(F/NA), testNumbers, groupNumber

test_infos

Matrix with column number of test days and a column for each test with the testday relative to event date, the rows are the groups.

test_types

Matrix with test day (columns) of each group (rows) and whe informations about test types.

info

Dataframe with the day specific information about sensitivity and specificity.

combination_infected

Matrix of all possible combinations how K infected are distributed among subgroups.

number_group_peoples

Vector with the number of people per group.

number_subgroups

Number of subgroups including group of untested (if existent).

Value

The probability.

Negative analysis probability

Description

Calculates the probability that nobody is infected given the negative tests.

Usage

calculate_posterior_no_infections(
  negative_persons,
  infected_persons,
  event,
  test_infos,
  test_types,
  subgroup_size,
  distribution = NULL,
  info
)

Arguments

negative_persons

Number of people without the infectious persons.

infected_persons

Number of infectious persons.

event

Characters, the name of the event, currently: "school" or "day_care_center".

test_infos

Matrix with testing information; each row gives the number of tests (1. column) and each test date (following columns) for each test group

test_types

Matrix with test day (columns) of each group (rows) and the informations about test types.

subgroup_size

Array with the number of persons per test group.

distribution

Vector, this is a placeholder

info

Dataframe, this is a placeholder

Details

The probability is based on Bayes' theorem.

Value

The probability p.

See Also

calculate_prior_infections, generate_data_extended, get_test_sensitivities and calculate_likelihood_negative_tests.

Examples

test_infos <- matrix(nrow = 2, ncol = 3)
test_infos[1,] <- c(1, 2, NA)
test_infos[2,] <- c(2, 4, 6)

test_types <- matrix(nrow = 2, ncol = 2)
test_types[1,] <- c("PCR", NA)
test_types[2,] <- c("PCR", "Antigen")

calculate_posterior_no_infections(negative_persons = 23,
                                  infected_persons = 2,
                                  event = "school",
                                  test_infos = test_infos,
                                  test_types = test_types,
                                  subgroup_size = c(3, 5))

A priori probability of further Infections

Description

Calculates the a priori probability of how many people are infected in one event.

Usage

calculate_prior_infections(
  negative_persons,
  infected_persons,
  event,
  p_one = NULL,
  infect_average = NULL
)

Arguments

negative_persons

Number of people without the infectious persons.

infected_persons

Number of infected people.

event

Characters, event type given as characters, currently: "school" or "day_care_center".

p_one

Number, this is a placeholder

infect_average

Number, this is a placeholder

Details

The probability is beta-binomial distributed. The values for p1 and infection_average for the events "school" and "day_care_center" are from Schoeps et al. (2021).

Value

The a priori probability y.

References

Schoeps A et al. (2021) "Surveillance of SARS-CoV-2 transmission in educational institutions, August to December 2020, Germany". Epidemiology and Infection 149, E213: 1-9.

Examples

calculate_prior_infections(negative_persons = 23,
                           infected_persons = 2,
                           event = "school")

Generate data extended

Description

Creates a dataframe suitable as input for calculate_likelihood_negative_tests.

Usage

generate_data_extended(
  M = 20,
  d = matrix(data = 1, nrow = 1, ncol = 2),
  S = c(12)
)

Arguments

M

The size of the group without infected, default is twenty.

d

A matrix with the test dates, default is matrix(data = 1, nrow = 1, ncol = 2).

S

A vector with the sizes of the subgroups, default is c(12).

Value

The dataframe.

Expected number of total symptomatic infections

Description

Calculates the expected total number of symptomatic infections after a group event, based on the observed infections so far.

Usage

get_expected_total_infections(
  group_size,
  last_day_reported_infection,
  total_reported_infections,
  meanlog = 1.69,
  sdlog = 0.55
)

Arguments

group_size

integer, size of the group.

last_day_reported_infection

Number of days the last infection was reported after the event (0 = event day).

total_reported_infections

Number of reported symptomatic infections so far.

meanlog

Number, the parameter of mean from the log-normal distribution.

sdlog

Number, the parameter of sd from the log-normal distribution.

Details

meanlog and sdlog are the log-normal distribution parameters derived from the incubation period characteristics described in Xin et al. (2021). Note that the function often clearly overestimates the number of symptomatic infections if last_day_reported_infections is less than 3.

Value

The total number of expected symptomatic infections.

Examples

get_expected_total_infections(25, 5, 4)

Vector of day-specific probabilities of disease outbreak

Description

Creates a vector containing the probabilities of the disease outbreak for the days 1 to maxi after the infection.

Usage

get_incubation_day_distribution(max_days, meanlog = 1.69, sdlog = 0.55)

Arguments

max_days

Number, the maximum length of the incubation time, defined as number.

meanlog

Number, the parameter of mean from the log-normal distribution.

sdlog

Number, the parameter of sd from the log-normal distribution.

Details

meanlog and sdlog are the log-normal distribution parameters derived from the incubation period characteristics described in Xin et al. (2021).

Value

Vector of day-specific probabilities of disease outbreak.

References

Xin H, Wong JY, Murphy C et al. (2021) "The Incubation Period Distribution of Coronavirus Disease 2019: A Systematic Review and Meta-Analysis". Clinical Infectious Diseases, 73(12): 2344-2352.

Examples

get_incubation_day_distribution(10)
get_incubation_day_distribution(10, meanlog = 1.69, sdlog = 0.55)

Dataframe with dates and probability of infection

Description

Creates a dataframe containing probability of infection occurring at a particular date/time, given the symptom_begin_date.

Usage

get_infection_density(
  symptom_begin_date,
  max_incubation_days = 14,
  meanlog = 1.69,
  sdlog = 0.55
)

Arguments

symptom_begin_date

Date, when the person gets symptoms.

max_incubation_days

Number of incubation days.

meanlog

Number, the parameter of mean from the log-normal distribution.

sdlog

Number, the parameter of sd from the log-normal distribution.

Details

meanlog and sdlog are the log-normal distribution parameters derived from the incubation period characteristics described in Xin et al. (2021).

Value

Dataframe with dates and probability of infection.

References

Xin H, Wong JY, Murphy C et al. (2021) "The Incubation Period Distribution of Coronavirus Disease 2019: A Systematic Review and Meta-Analysis". Clinical Infectious Diseases, 73(12): 2344-2352.

Examples

get_infection_density(as.Date("2022-03-22"))
get_infection_density(as.Date("2022-03-22"), max_incubation_days = 14, meanlog = 1.69, sdlog = 0.55)

Dataframe with dates and infectiousness probability

Description

Creates a dataframe containing infectiousness at a particular date/time, given the symptom_begin_date.

Usage

get_infectiousness_density(
  symptom_begin_date,
  infectiousness_shift = 12.272481,
  max_infectious_days = 24,
  shape_infectiousness_gamma = 20.516508,
  rate_infectiousness_gamma = 1.592124
)

Arguments

symptom_begin_date

Date, when the person gets symptoms.

infectiousness_shift

Number of days with the largest contagions before the first symptoms.

max_infectious_days

Number of the infectious days.

shape_infectiousness_gamma

Number, the shape parameter for the gamma distribution.

rate_infectiousness_gamma

Number, the rate parameter for the gamma distribution.

Details

infectiousness_shift, shape_infectiousness_gamma and rate_infectiousness_gamma are the distribution parameters for the infectious period from He et al. (2020).

Value

Dataframe with dates and infectiousness probability.

References

He, X et al. (2020) "Temporal dynamics in viral shedding and transmissibility of COVID-19". Nature Medicine, 26: 672–675.

Examples

get_infectiousness_density(as.Date("2022-03-22"))
get_infectiousness_density(as.Date("2022-03-22"), infectiousness_shift = 12.272481,
                           max_infectious_days = 24, shape_infectiousness_gamma = 20.516508,
                           rate_infectiousness_gamma = 1.592124)

Dataframe with dates and probability of infection

Description

Creates a dataframe containing probability of infection occurring at a particular dates/times, given the symptom_begin_dates and number_of_persons per date.

Usage

get_misc_infection_density(
  symptom_begin_dates,
  number_of_persons,
  max_incubation_days = 17,
  meanlog = 1.69,
  sdlog = 0.55
)

Arguments

symptom_begin_dates

Dates, when the persons get symptoms.

number_of_persons

Number of persons who get symptoms on each date.

max_incubation_days

Number of incubation days.

meanlog

Number, the parameter of mean from the log-normal distribution.

sdlog

Number, the parameter of sd from the log-normal distribution.

Details

meanlog and sdlog are the log-normal distribution parameters derived from the incubation period characteristics described in Xin et al. (2021).

Value

Dataframe with dates and probability of infection.

References

Xin H, Wong JY, Murphy C et al. (2021) "The Incubation Period Distribution of Coronavirus Disease 2019: A Systematic Review and Meta-Analysis". Clinical Infectious Diseases, 73(12): 2344-2352.

Examples

symptom_begin_dates <- c(as.Date("2022-03-22"), as.Date("2022-03-26"))
number_of_persons <- c(3,1)
get_misc_infection_density(symptom_begin_dates, number_of_persons)

Dataframe with dates and contact symptom begin probability

Description

Creates a dataframe containing probability that a contact will start showing symptoms (serial interval) at a particular date/time, given the symptom_begin_date.

Usage

get_serial_interval_density(
  symptom_begin_date,
  max_serial_interval_days = 20,
  shape_serial = 2.154631545,
  rate_serial = 0.377343528
)

Arguments

symptom_begin_date

Date, when the index person got symptoms.

max_serial_interval_days

Number of serial interval days.

shape_serial

Number, the shape parameter for the gamma distribution.

rate_serial

Number, the rate parameter for the gamma distribution.

Details

shape_serial and rate_serial are the parameters of the gamma distribution for the serial interval derived from Najafi et al. (2020).

Value

Dataframe with dates and contact symptom begin probability.

References

Najafi F et al. (2020) "Serial interval and time-varying reproduction number estimation for COVID-19 in western Iran.". New Microbes and New Infections, 36: 100715.

Examples

get_serial_interval_density(as.Date("2022-03-22"))
get_serial_interval_density(as.Date("2022-03-22"), max_serial_interval_days = 20,
                            shape_serial = 2.15, rate_serial = 0.38)

Generate info

Description

Creates a dataframe with day specific test sensitivity and specificity of PCR and Antigen tests.

Usage

get_test_sensitivities(df)

Arguments

df

Dataframe, this is a placeholder

Value

The dataframe.

Examples

get_test_sensitivities()
df <- data.frame(
             "PCR" = c(0, 0, 0, 0.04, 0.34, 0.64, 0.76, 0.79, 0.80, 0.79,
                      0.77, 0.74, 0.71, 0.67, 0.62, 0.58, 0.54, 0.49, 0.44,
                      0.40, 0.37, 0.33),
             "Antigen" = c(0, 0, 0, 0.03, 0.13, 0.40,  0.64, 0.69, 0.70, 0.69,
                          0.62, 0.52, 0.40, 0.29, 0.21, 0.17, 0.13, 0.11,
                          0.08, 0.07, 0.05, 0.04)
                )
get_test_sensitivities(df)

One more primary a priori probability

Description

Calculates the a priori probability y for one primary case more by using the current prior distribution and the prior distribution of one single primary case.

Usage

p_onePrimaryMore(yCurrent, y1)

Arguments

yCurrent

The current prior distribution.

y1

The prior distribution of one single primary case.

Value

The a priori probability y.

Prediction of future infections per day

Description

Predicts how many people are expected to develop symptoms on each day after the last reported infection after a group event.

Usage

predict_future_infections(
  last_day_reported_infection,
  total_reported_infections,
  total_expected_infections,
  meanlog = 1.69,
  sdlog = 0.55
)

Arguments

last_day_reported_infection

Number of days the last infection was reported after the event (0 = event day).

total_reported_infections

Number of reported symptomatic infections so far.

total_expected_infections

Number of expected symptomatic infections in total.

meanlog

Number, the parameter of mean from the log-normal distribution.

sdlog

Number, the parameter of sd from the log-normal distribution.

Details

meanlog and sdlog are the log-normal distribution parameters derived from the incubation period characteristics described in Xin et al. (2021).

Value

Vector with expected future infections per day after the event.

References

Xin H, Wong JY, Murphy C et al. (2021) "The Incubation Period Distribution of Coronavirus Disease 2019: A Systematic Review and Meta-Analysis". Clinical Infectious Diseases, 73(12): 2344-2352.

Examples

predict_future_infections(last_day_reported_infection = 3,
                          total_reported_infections = 5,
                          total_expected_infections = 15)