Package 'incidental' reference manual

Title:	Implements Empirical Bayes Incidence Curves
Description:	Make empirical Bayes incidence curves from reported case data using a specified delay distribution.
Authors:	Andrew Miller [aut], Lauren Hannah [aut, cre], Nicholas Foti [aut], Joseph Futoma [aut], Apple, Inc. [cph]
Maintainer:	Lauren Hannah <[email protected]>
License:	MIT + file LICENSE
Version:	0.1
Built:	2024-11-21 06:46:45 UTC
Source:	CRAN

Compute expected cases

Description

This function computes expected cases given incidence curve parameters and a delay distribution.

Usage

compute_expected_cases(beta, Q, lnPmat, Tobs)
compute_expected_cases(beta, Q, lnPmat, Tobs)

Arguments

`beta`	parameter vector of num_params
`Q`	spline basis matrix, of size Tmod x num_params
`lnPmat`	matrix size Tobs x Tobs, log of make_likelihood_matrix
`Tobs`	maximum observed time point

Value

A Tobs-length vector that models expected cases

Compute log likelihood of incidence model

Description

This function computes log likelihood of incidence model given parameters and observations.

Usage

compute_log_incidence(beta, Q, Tobs)
compute_log_incidence(beta, Q, Tobs)

Arguments

`beta`	parameter vector of num_params
`Q`	spline basis matrix, of size Tmod x num_params
`Tobs`	maximum observed time point

Value

I Tobs-length vector that models log incidence curve

Delay distribution from COVID-19 pandemic.

Description

Daily case, hospitalization, and death proportions.

Usage

covid_delay_dist
covid_delay_dist

Format

A data frame with 61 entries and 4 columns.

days: number of days since infection
case: proportion of cases confirmed by a test that are recorded on that day
hospitalization: proportion of cases that become hospitalized that are hospitalized on that day
death: proportion of cases that result in death that die on that day

Source

Time from incidence to symptoms: Lauer et al., "Estimated Incubation Period of COVID-19", ACC (2020). https://www.acc.org/latest-in-cardiology/journal-scans/2020/05/11/15/18/the-incubation-period-of-coronavirus-disease.

Time from symptoms to recorded cases: Case line data from Florida through 2020-07-14 with same day waits removed. https://open-fdoh.hub.arcgis.com/datasets/florida-covid19-case-line-data.

Time from symptoms to hospitalization: Wang et al., "Clinical Characteristics of 138 Hospitalized Patients With 2019 Novel Coronavirus–Infected Pneumonia in Wuhan, China", JAMA (2020). https://jamanetwork.com/journals/jama/fullarticle/2761044.

Time from hospitalization to death: Lewnard et al. "Incidence, clinical outcomes, and transmission dynamics of severe coronavirus disease 2019 in California and Washington: prospective cohort study", BJM (2020). https://www.bmj.com/content/369/bmj.m1923.long

New York City data from the COVID-19 pandemic.

Description

Daily case, hospitalization, and death proportions by borough through 2020-06-30.

Usage

covid_new_york_city
covid_new_york_city

Format

A data frame with 615 entries and 5 columns.

date: record date
borough: record borough: Brooklyn, Bronx, Manhattan, Queens, and Staten Island
case: number of recorded cases
hospitalization: number of new hospital admissions
death: number of recorded deaths

Source

New York City Department of Health https://raw.githubusercontent.com/nychealth/coronavirus-data/master/boro/boroughs-case-hosp-death.csv.

Input data check

Description

Check input data for:

minimum length of reported
integer for reported
positivity for delay_dist and reported
sums to 1 for delay_dist

Throw an error if any conditions are violated.

Usage

data_check(reported, delay_dist)
data_check(reported, delay_dist)

Arguments

`reported`	An integer vector of reported cases.
`delay_dist`	A positive vector that sums to one, which describes the delay distribution.

Data processing wrapper

Description

Does basic checks for reported data and delay distribution, front pads, and makes AR extrapolation.

Usage

data_processing(
  reported,
  delay_dist,
  num_ar_steps = 10,
  num_ar_samps = 100,
  seed = 1,
  linear_tail = 14,
  front_pad_size = 10,
  extrapolation_prior_precision = 2
)
data_processing(
  reported,
  delay_dist,
  num_ar_steps = 10,
  num_ar_samps = 100,
  seed = 1,
  linear_tail = 14,
  front_pad_size = 10,
  extrapolation_prior_precision = 2
)

Arguments

`reported`	An integer vector of reported cases.
`delay_dist`	A positive vector that sums to one, which describes the delay distribution.
`num_ar_steps`	An integer number of AR steps after last observation.
`num_ar_samps`	An integer number of AR samples.
`seed`	Seed for RNG.
`linear_tail`	An integer number of days used to fit linear model on tail to be used as a mean for AR extrapolation.
`front_pad_size`	An integer for initial number of 0's before first observation.
`extrapolation_prior_precision`	A positive scalar for extrapolation slope shrinkage prior precision.

Value

A list with elements:

extrap = a matrix of size (num_ar_samps x n + num_ar_steps + front_pad_size)
original = a vector of logicals for whether in original time series range

Transpose of the 1st difference operator

Description

This function computes a transpose of the 1st difference operator.

Usage

diff_trans(a)
diff_trans(a)

Arguments

`a`	A vector of inputs

Value

The transpose of the first difference operator

Fit incidence curve to reported data

Description

This is a function that fits an incidence curve to a set of reported cases and delay distribution using an empirical Bayes estimation method, which fits parameters for a spline basis. All hyper parameter tuning and data processing are done within this function.

Usage

fit_incidence(
  reported,
  delay_dist,
  dof_grid = seq(6, 20, 2),
  dof_method = "aic",
  lam_grid = 10^(seq(-1, -8, length.out = 20)),
  lam_method = "val",
  percent_thresh = 2,
  regularization_order = 2,
  num_ar_steps = 10,
  num_ar_samps = 100,
  linear_tail = 14,
  front_pad_size = 10,
  extrapolation_prior_precision = 10,
  frac_train = 0.75,
  fisher_approx_cov = TRUE,
  end_pad_size = 50,
  num_samps_per_ar = 10,
  val_restarts = 2,
  seed = 1
)
fit_incidence(
  reported,
  delay_dist,
  dof_grid = seq(6, 20, 2),
  dof_method = "aic",
  lam_grid = 10^(seq(-1, -8, length.out = 20)),
  lam_method = "val",
  percent_thresh = 2,
  regularization_order = 2,
  num_ar_steps = 10,
  num_ar_samps = 100,
  linear_tail = 14,
  front_pad_size = 10,
  extrapolation_prior_precision = 10,
  frac_train = 0.75,
  fisher_approx_cov = TRUE,
  end_pad_size = 50,
  num_samps_per_ar = 10,
  val_restarts = 2,
  seed = 1
)

Arguments

`reported`	An integer vector of reported cases.
`delay_dist`	A positive vector that sums to one, which describes the delay distribution.
`dof_grid`	An integer vector of degrees of freedom for the spline basis.
`dof_method`	Metric to choose "best" spline degrees of freedom: 'aic': Akaike information criterion, 'bic': Bayesian information criterion, 'val': validation likelihood.
`lam_grid`	A vector of regularization strengths to scan.
`lam_method`	metric to choose "best" regularization strength lambda: 'aic': Akaike information criterion, 'bic': Bayesian information criterion, 'val': validation likelihood.
`percent_thresh`	If using validation likelihood to select best, the largest (strongest) lambda that is within 'percent_thresh' of the highest validation lambda will be selected. Default is 2. Must be greater than 0.
`regularization_order`	An integer (typically 0, 1, 2), indicating differencing order for L2 regularization of spline parameters. Default is 2 for second derivative penalty.
`num_ar_steps`	An integer number of AR steps after last observation.
`num_ar_samps`	An integer number of AR samples.
`linear_tail`	An integer number of days used to fit linear model on tail to be used as a mean for AR extrapolation.
`front_pad_size`	An integer for initial number of 0's before first observation.
`extrapolation_prior_precision`	A positive scalar for extrapolation slope shrinkage prior precision.
`frac_train`	A numeric between 0 and 1 for fraction of data used to train lambda validation.
`fisher_approx_cov`	A flag to use either the Fisher Information (TRUE) or the Hessian (FALSE) to approx posterior covariance over parameters.
`end_pad_size`	And integer number of steps the spline is defined beyond the final observation.
`num_samps_per_ar`	An integer for the number of Laplace samples per AR fit.
`val_restarts`	An integer for the number of times to refit hyperparameters if 'val' is used for either. Set to 1 for faster but more unstable fits.
`seed`	Seed for RNG.

Value

A list with the following entries:

Isamps – sample of the incidence curve from a Laplace approximation per AR sample;
Ihat – MAP incidence curve estimate;
Chat – expected cases given MAP incidence curve estimate;
beta_hats – matrix of beta's per AR sample;
best_dof – best degrees of freedom from tuning;
best_lambda – best regularization parameter from tuning; and
reported – a copy of reported values used for fitting.

Examples


indiana_model <- fit_incidence(
                  reported = spanish_flu$Indiana, 
                  delay_dist = spanish_flu_delay_dist$proportion) 
indiana_model <- fit_incidence(
                  reported = spanish_flu$Indiana, 
                  delay_dist = spanish_flu_delay_dist$proportion)

Pad reported data with zeros in front

Description

Add zeros in front of reported data avoid infections from before first reported date all being placed on first reported date.

Usage

front_zero_pad(reported, size)
front_zero_pad(reported, size)

Arguments

`reported`	An integer vector of reported cases
`size`	An integer size of zero-padding

Value

An integer vector of cases with size 0's in front

Export incidence model to data frame

Description

Export the output of fit_incidence to a data frame with an optional addition of a time index.

Usage

incidence_to_df(x, times = NULL, low_quantile = 0.05, high_quantile = 0.95)
incidence_to_df(x, times = NULL, low_quantile = 0.05, high_quantile = 0.95)

Arguments

`x`	An "incidence_spline_model" output from `fit_incidence`.
`times`	An optional vector of time indices.
`low_quantile`	A scalar that specifies the low quantile value for the output CI.
`high_quantile`	A scalar that specifies the high quantile value for the output CI.

Value

A data frame with the following entries:

Time – a time index; if 'ts' is 'NULL' it is the observation number;
Reported – the value of 'reported';
Ihat – MAP incidence curve estimate;
Chat – expected cases given MAP incidence curve estimate;
LowCI – lower pointwise credible interval bands around the incidence curve; and
HighCI – higher pointwise credible interval bands around the incidence curve.

Examples


indiana_model <- fit_incidence(
                  reported = spanish_flu$Indiana, 
                  delay_dist = spanish_flu_delay_dist$proportion)
 indiana_df <- incidence_to_df(indiana_model, times = spanish_flu$Date)

indiana_model <- fit_incidence(
                  reported = spanish_flu$Indiana, 
                  delay_dist = spanish_flu_delay_dist$proportion)
 indiana_df <- incidence_to_df(indiana_model, times = spanish_flu$Date)

Initialize spline parameters (beta)

Description

Initialize spline parameters (beta) using a standard Gaussian distribution.

Usage

init_params(num_params)
init_params(num_params)

Arguments

num_params

Integer size of desired parameter vector

Value

vector of size num_params

Make AR samples for extrapolation past end point

Description

Make auto-regressive (AR) samples for extrapolation past end point to help with right-censoring problems.

Usage

make_ar_extrap_samps(
  reported,
  num_ar_steps = 10,
  num_ar_samps = 50,
  seed = 1,
  linear_tail = 14,
  extrapolation_prior_precision = 2
)
make_ar_extrap_samps(
  reported,
  num_ar_steps = 10,
  num_ar_samps = 50,
  seed = 1,
  linear_tail = 14,
  extrapolation_prior_precision = 2
)

Arguments

`reported`	An integer vector of reported cases.
`num_ar_steps`	An integer number of AR steps after last observation.
`num_ar_samps`	An integer number of AR samples.
`seed`	Seed for RNG.
`linear_tail`	An integer number of days used to fit linear model on tail to be used as a mean for AR extrapolation.
`extrapolation_prior_precision`	A positive scalar for extrapolation slope shrinkage prior precision.

Value

A matrix of size (num_ar_samps x n + num_ar_steps)

Make delay likelihood matrix

Description

This function creates a matrix such that P[t, s] = P(C = t | I = s) = theta_t-s for s <= t and 0 otherwise.

Usage

make_likelihood_matrix(delay_dist)
make_likelihood_matrix(delay_dist)

Arguments

delay_dist

A positive vector that sums to one, which describes the delay distribution.

Value

A matrix of size n x n

Create spline basis matrix

Description

This function creates basis matrix for spline model using cubic splines.

Usage

make_spline_basis(dof, tgrid)
make_spline_basis(dof, tgrid)

Arguments

`dof`	An integer degrees of freedom.
`tgrid`	A grid of time values.

Value

A matrix of cubic spline basis values with 'length(tgrid)' x 'dof' entries.

Marginal log likelihood This function computes the marginal probability of Pr(reported | beta). Note that lnPmat must be zero padded enough (or censored) to match the length of reported cases vector.

Description

Marginal log likelihood This function computes the marginal probability of Pr(reported | beta). Note that lnPmat must be zero padded enough (or censored) to match the length of reported cases vector.

Usage

marg_loglike_poisson(beta, reported, Q, lnPmat)
marg_loglike_poisson(beta, reported, Q, lnPmat)

Arguments

`beta`	spline parameter vector length num_params
`reported`	An integer vector of reported cases.
`Q`	spline basis matrix Tmod x num_params
`lnPmat`	matrix size Tobs x Tobs, log of make_likelihood_matrix

Value

A scalar log likelihood value.

Marginal log likelihood Fisher information matrix

Description

This function computes the Fisher information matrix log likelihood term with respect to beta.

Usage

marg_loglike_poisson_fisher(beta, reported, Q, lnPmat)
marg_loglike_poisson_fisher(beta, reported, Q, lnPmat)

Arguments

`beta`	A spline parameter vector length num_params.
`reported`	An integer vector of reported cases.
`Q`	A spline basis matrix Tmod x num_params.
`lnPmat`	A matrix size Tobs x Tobs, log of make_likelihood_matrix.

Value

A numeric vector, gradient of log likelihood value with respect to beta.

Marginal log likelihood gradient

Description

This function computes the gradient of the log likelihood term with respect to beta.

Usage

marg_loglike_poisson_grad(beta, reported, Q, lnPmat)
marg_loglike_poisson_grad(beta, reported, Q, lnPmat)

Arguments

`beta`	spline parameter vector length num_params
`reported`	An integer vector of reported cases.
`Q`	spline basis matrix Tmod x num_params
`lnPmat`	matrix size Tobs x Tobs, log of make_likelihood_matrix

Value

A numeric vector, gradient of log likelihood value with respect to beta.

Plot model from fit_incidence

Description

Plot time, reported cases, incidence curve with credible interval, and implied case curve.

Usage

## S3 method for class 'incidence_spline_model'
plot(x, ...)
## S3 method for class 'incidence_spline_model'
plot(x, ...)

Arguments

x

An "incidence_spline_model" output from fit_incidence.

...

Other parameters that can be included:

'times': an optional vector of time indices.
'plot_Chat': a logical for whether Chat should be plotted.
'plot_reported': a logical for whether reported cases should be plotted.
'plot_CI': a logical for whether CI should be plotted.

Examples


indiana_model <- fit_incidence(
                  reported = spanish_flu$Indiana, 
                  delay_dist = spanish_flu_delay_dist$proportion)
 plot(indiana_model, times = spanish_flu$Date)

indiana_model <- fit_incidence(
                  reported = spanish_flu$Indiana, 
                  delay_dist = spanish_flu_delay_dist$proportion)
 plot(indiana_model, times = spanish_flu$Date)

Poisson objective function

Description

This function computes Poisson objective function including regularizer.

Usage

poisson_objective(beta, lam, reported, Q, lnPmat, regularization_order)
poisson_objective(beta, lam, reported, Q, lnPmat, regularization_order)

Arguments

`beta`	spline parameter vector length num_params
`lam`	positive scalar regularization strength
`reported`	An integer vector of reported cases.
`Q`	spline basis matrix Tmod x num_params
`lnPmat`	matrix size Tobs x Tobs, log of make_likelihood_matrix
`regularization_order`	An integer (typically 0, 1, 2), indicating differencing order for L2 regularization of spline parameters. Default is 2 for second derivative penalty.

Value

scalar objective function value

Poisson objective function gradient

Description

This function computes the Poisson objective function (including regularizer) gradient.

Usage

poisson_objective_grad(beta, lam, reported, Q, lnPmat, regularization_order)
poisson_objective_grad(beta, lam, reported, Q, lnPmat, regularization_order)

Arguments

`beta`	spline parameter vector length num_params
`lam`	positive scalar regularization strength
`reported`	An integer vector of reported cases.
`Q`	spline basis matrix Tmod x num_params
`lnPmat`	matrix size Tobs x Tobs, log of make_likelihood_matrix
`regularization_order`	An integer (typically 0, 1, 2), indicating differencing order for L2 regularization of spline parameters. Default is 2 for second derivative penalty.

Value

scalar objective function value

Compute Fisher information matrix for Poisson objective

Description

This function computes the Fisher information matrix for a regularized Poisson objective function.

Usage

poisson_objective_post_cov_approx(
  beta,
  lam,
  reported,
  Q,
  lnPmat,
  regularization_order
)
poisson_objective_post_cov_approx(
  beta,
  lam,
  reported,
  Q,
  lnPmat,
  regularization_order
)

Arguments

`beta`	A vector of spline parameters.
`lam`	A regularization penalty parameter.
`reported`	A vector of reported values.
`Q`	A spline basis matrix.
`lnPmat`	A matrix size Tobs x Tobs, log of make_likelihood_matrix.
`regularization_order`	An integer that specifies the regularization order.

Value

Fisher information matrix of a regularized Poisson objective function.

Beta regularization function

Description

This function computes regularization penalty term based on the betas and a difference.

Usage

regfun(beta, regularization_order = 2)
regfun(beta, regularization_order = 2)

Arguments

`beta`	A spline parameter vector length num_params.
`regularization_order`	An integer (typically 0, 1, 2), indicating differencing order for L2 regularization of spline parameters. Default is 2 for second derivative penalty.

Value

A scalar regularization value.

Beta regularization function gradient

Description

This function computes regularization penalty term gradient based on the betas and difference order.

Usage

regfun_grad(beta, regularization_order = 2)
regfun_grad(beta, regularization_order = 2)

Arguments

`beta`	spline parameter vector length num_params
`regularization_order`	An integer (typically 0, 1, 2), indicating differencing order for L2 regularization of spline parameters. Default is 2 for second derivative penalty.

Value

scalar regularization value

Beta regularization function Hessian

Description

This function computes regularization penalty term Hessian based on the betas and differencing order.

Usage

regfun_hess(beta, regularization_order = 2)
regfun_hess(beta, regularization_order = 2)

Arguments

`beta`	spline parameter vector length num_params
`regularization_order`	An integer (typically 0, 1, 2), indicating differencing order for L2 regularization of spline parameters. Default is 2 for second derivative penalty.

Value

scalar regularization value

Generate Laplace samples of incidence

Description

This function generates Laplace samples of posterior distribution for a vector of reported incidence.

Usage

sample_laplace_log_incidence_poisson(
  beta_hat,
  beta_cov,
  reported,
  Q,
  num_samps_per_ar = 10
)
sample_laplace_log_incidence_poisson(
  beta_hat,
  beta_cov,
  reported,
  Q,
  num_samps_per_ar = 10
)

Arguments

`beta_hat`	Maximum likelihood solution for beta parameter.
`beta_cov`	Covariance of objective solution (either Fisher information or Hessian inverse).
`reported`	An integer vector of reported cases.
`Q`	Spline basis matrix.
`num_samps_per_ar`	Number of Laplace samples to return for each AR path.

Value

A matrix of 'num_samps_per_ar' log incidence curve samples from laplace approximation of distribution.

Scan spline degrees of freedom

Description

This function holds the regularization parameter value fixed and scans spline degrees of freedom.

Usage

scan_spline_dof(
  reported,
  delay_dist,
  dof_grid,
  method = "bic",
  lam = 0,
  regularization_order = 2,
  reported_val = NULL,
  end_pad_size = 0,
  fisher_approx_cov = FALSE
)
scan_spline_dof(
  reported,
  delay_dist,
  dof_grid,
  method = "bic",
  lam = 0,
  regularization_order = 2,
  reported_val = NULL,
  end_pad_size = 0,
  fisher_approx_cov = FALSE
)

Arguments

`reported`	An integer vector of reported cases.
`delay_dist`	A positive vector that sums to one, which describes the delay distribution.
`dof_grid`	An integer vector of degrees of freedom for the spline basis.
`method`	Metric to choose "best" dof: 'aic', 'bic', 'val'. If method='val', reported_val must be non NULL and match reported size.
`lam`	A fixed value for the beta parameter regularization strength.
`regularization_order`	An integer (typically 0, 1, 2), indicating differencing order for L2 regularization of spline parameters. Default is 2 for second derivative penalty.
`reported_val`	Validation time series of equal size to reported vector for use with 'val' method. Default is NULL.
`end_pad_size`	And integer number of steps the spline is defined beyond the final observation.
`fisher_approx_cov`	A flag to use either the Fisher Information (TRUE) or the Hessian (FALSE) to approx posterior covariance over parameters.

Value

A list of degree of freedom fit statistics:

best_dof = best degrees of freedom
dof_resdf = data frame of fit statistics (lambda, dof, aic, bic, val_lls, train_lls)

Scan spline regularization parameter

Description

This function holds degrees of freedom fixed and scans regularization parameter values.

Usage

scan_spline_lam(
  reported,
  delay_dist,
  lam_grid,
  method = "val",
  percent_thresh = 2,
  dof = 10,
  regularization_order = 2,
  reported_val = NULL,
  end_pad_size = 0,
  fisher_approx_cov = TRUE
)
scan_spline_lam(
  reported,
  delay_dist,
  lam_grid,
  method = "val",
  percent_thresh = 2,
  dof = 10,
  regularization_order = 2,
  reported_val = NULL,
  end_pad_size = 0,
  fisher_approx_cov = TRUE
)

Arguments

`reported`	An integer vector of reported cases.
`delay_dist`	A positive vector that sums to one, which describes the delay distribution.
`lam_grid`	A vector of regularization strengths to scan.
`method`	Metric to choose "best" dof: 'aic', 'bic', 'val'. If method='val', reported_val must be non NULL and match reported size.
`percent_thresh`	If using validation likelihood to select best, the largest (strongest) lambda that is within 'percent_thresh' of the highest validation lambda will be selected. Default is 2. Must be greater than 0.
`dof`	Degrees of freedom for spline basis.
`regularization_order`	An integer (typically 0, 1, 2), indicating differencing order for L2 regularization of spline parameters. Default is 2 for second derivative penalty.
`reported_val`	Validation time series of equal size to reported vector for use with 'val' method. Default is NULL.
`end_pad_size`	And integer number of steps the spline is defined beyond the final observation.
`fisher_approx_cov`	A flag to use either the Fisher Information (TRUE) or the Hessian (FALSE) to approx posterior covariance over parameters.

Value

List of outputs:

best_lam = best lambda
lam_resdf = data frame of fit statistics (lambda, dof, aic, bic, val_lls, train_lls)

Daily flu mortality from 1918 flu pandemic.

Description

Daily mortality data from 1918-09-01 through 1918-12-31 in Indiana, Kansas, and Philadelphia

Usage

spanish_flu
spanish_flu

Format

A data frame with 122 entries for 3 locations

Date: date
Indiana: daily deaths for all of Indiana
Kansas: daily deaths for all of Kansas
Philadelphia: daily deaths for Philadelphia

Source

Rogers SL (1920). Special Tables of Mortality from Influenza and Pneumonia, in Indiana, Kansas, and Philadelphia, PA (U.S. Dept Commerce, Washington, DC).

Delay distribution from 1918 flu pandemic.

Description

Daily death proportions.

Usage

spanish_flu_delay_dist
spanish_flu_delay_dist

Format

A data frame with 31 entries and 3 columns.

days: number of days since infection
proportion: proportion of deaths that happen on that day

Source

Goldstein E, et al. (2009). Reconstructing influenza incidence by deconvolution of daily mortality time series (PNAS). https://www.pnas.org/content/pnas/106/51/21825.full.pdf

Train and validate model on reported data

Description

This function fit models with selected hyperparameters on reported data and return a matrix of posterior Laplace samples.

Usage

train_and_validate(
  reported,
  delay_dist,
  lam,
  dof,
  beta0 = NULL,
  regularization_order = 2,
  reported_val = NULL,
  end_pad_size = 0,
  fisher_approx_cov = TRUE,
  num_samps_per_ar = 10
)
train_and_validate(
  reported,
  delay_dist,
  lam,
  dof,
  beta0 = NULL,
  regularization_order = 2,
  reported_val = NULL,
  end_pad_size = 0,
  fisher_approx_cov = TRUE,
  num_samps_per_ar = 10
)

Arguments

`reported`	An integer vector of reported cases.
`delay_dist`	A positive vector that sums to one, which describes the delay distribution.
`lam`	A fixed value for the beta parameter regularization strength.
`dof`	Degrees of freedom for spline basis.
`beta0`	(optional) Initial setting of spline parameters (before optimization)
`regularization_order`	An integer (typically 0, 1, 2), indicating differencing order for L2 regularization of spline parameters. Default is 2 for second derivative penalty.
`reported_val`	Validation time series of equal size to reported vector for use with 'val' method. Default is NULL.
`end_pad_size`	And integer number of steps the spline is defined beyond the final observation.
`fisher_approx_cov`	A flag to use either the Fisher Information (TRUE) or the Hessian (FALSE) to approx posterior covariance over parameters.
`num_samps_per_ar`	An integer for the number of Laplace samples per AR fit.

Value

A list of results of train and validate, including:

train_ll = training log likelihood
val_ll = validation log likelihood (if 'reported_val' is not 'NULL')
Isamps = samples of the incidence curve from a Laplace approximation
Ihat = MAP estimate of the incidence curve
Chat = expected cases given MAP incidence curve
beta_hat = MAP estimate of spline parameters
beta_cov = covariance of spline parameters
beta_hess = Hessian of spline parameters

Split reported case data

Description

Split reported case integer time series into train and validate time series through thinning.

Usage

train_val_split(reported, frac_train = 0.75)
train_val_split(reported, frac_train = 0.75)

Arguments

`reported`	An integer vector of reported cases.
`frac_train`	A numeric between 0 and 1 for fraction of data used to train lambda validation.

Value

A list(reported_train, reported_val) where the elements reported_train and reported_val are both length, Tobs, and 'frac_train' of the counts fall in reported_train, the rest in reported_val.

Package 'incidental'

Help Index

Compute expected cases

Description

Usage

Arguments

Value

Compute log likelihood of incidence model

Description

Usage

Arguments

Value

Delay distribution from COVID-19 pandemic.

Description

Usage

Format

Source

New York City data from the COVID-19 pandemic.

Description

Usage

Format

Source

Input data check

Description

Usage

Arguments

Data processing wrapper

Description

Usage

Arguments

Value

Transpose of the 1st difference operator

Description

Usage

Arguments

Value

Fit incidence curve to reported data

Description

Usage

Arguments

Value

Examples

Pad reported data with zeros in front

Description

Usage

Arguments

Value

Export incidence model to data frame

Description

Usage

Arguments

Value

Examples

Initialize spline parameters (beta)

Description

Usage

Arguments

Value

Make AR samples for extrapolation past end point

Description

Usage

Arguments

Value

Make delay likelihood matrix

Description

Usage

Arguments

Value

Create spline basis matrix

Description

Usage

Arguments

Value

Marginal log likelihood This function computes the marginal probability of Pr(reported | beta). Note that lnPmat must be zero padded enough (or censored) to match the length of reported cases vector.

Description

Usage

Arguments

Value

Marginal log likelihood Fisher information matrix

Description