Package 'rtestim'

Canadian Incident COVID-19 Cases

Description

This dataset contains 3+ years of incident COVID-19 case counts as reported by opencovid.ca as of July 4, 2023.

Usage

cancovid

Format

A data frame with 1,253 rows and 2 columns:

date

The observed date. A Date object.

incident_cases

The number of new recorded cases for this date.

Source

This data is available under the CC-BY-4.0 License.

See:

Berry, I., O’Neill, M., Sturrock, S. L., Wright, J. E., Acharya, K., Brankston, G., Harish, V., Kornas, K., Maani, N., Naganathan, T., Obress, L., Rossi, T., Simmons, A. E., Van Camp, M., Xie, X., Tuite, A. R., Greer, A. L., Fisman, D. N., & Soucy, J.-P. R. (2021). A sub-national real-time epidemiological and vaccination database for the COVID-19 pandemic in Canada. Scientific Data, 8(1). doi:10.1038/s41597-021-00955-2

---

Add confidence bands to estimated Rt or incidence curves

Description

Create an approximate confidence band for the Rt or incidence estimate. Note that the variance computation is approximate.

Usage

confband(object, lambda, level = 0.95, type = c("Rt", "Yt"), ...)

Arguments

object	a poisson_rt or cv_poisson_rt object.
lambda	the selected lambda. May be a scalar value, or in the case of cv_poisson_rt objects, "lambda.min" or "lambda.max".
level	the desired confidence level(s). These will be sorted if necessary.
type	the type Rt or Yt for confidence intervals of fitted Rt or fitted incident cases
...	additional arguments for methods. Unused.

Value

A data.frame containing the estimates Rt or Yt at the chosen lambda, and confidence limits corresponding to level

Examples

y <- c(1, rpois(100, dnorm(1:100, 50, 15) * 500 + 1))
out <- estimate_rt(y, nsol = 10)
head(confband(out, out$lambda[2]))
head(confband(out, out$lambda[2], level = c(0.95, 0.8, 0.5)))

cv <- cv_estimate_rt(y, nfold = 3, nsol = 30)
head(confband(cv, "lambda.min", c(0.5, 0.9)))

---

Rt estimation algorithm configuration

Description

Rt estimation algorithm configuration

Usage

configure_rt_admm(
  rho = -1,
  alpha = 0.5,
  gamma = 0.9,
  tolerance = 1e-04,
  maxiter_newton = 50L,
  maxiter_line = 20L,
  verbose = 0,
  ...
)

Arguments

rho	Double. An ADMM parameter; coefficient of augmented term in the Lagrangian function.
alpha	Double. A parameter adjusting upper bound in line search algorithm in prox_newton algorithm.
gamma	Double. A parameter adjusting step size in line search algorithm in prox_newton algorithm.
tolerance	Double. Tolerance of ADMM convergence.
maxiter_newton	Integer. Maximum number of iterations for the outer Newton iteration.
maxiter_line	Integer. Maximum number of iterations for the linesearch algorithm in the proximal Newton method.
verbose	Integer.
...	space for future extensions

Value

a list of model parameters with class rt_admm_configuration

Examples

configure_rt_admm()
configure_rt_admm(tolerance = 1e-6, verbose = 1L)

---

Leave-kth-out cross validation for choosing a optimal parameter lambda

Description

Leave-kth-out cross validation for choosing a optimal parameter lambda

Usage

cv_estimate_rt(
  observed_counts,
  korder = 3L,
  dist_gamma = c(2.5, 2.5),
  nfold = 3L,
  error_measure = c("deviance", "mse", "mae"),
  x = 1:n,
  lambda = NULL,
  maxiter = 1000000L,
  delay_distn = NULL,
  delay_distn_periodicity = NULL,
  regular_splits = FALSE,
  invert_splits = FALSE,
  ...
)

Arguments

observed_counts	vector of the observed daily infection counts
korder	Integer. Degree of the piecewise polynomial curve to be estimated. For example, korder = 0 corresponds to a piecewise constant curve.
dist_gamma	Vector of length 2. These are the shape and scale for the assumed serial interval distribution. Roughly, this distribution describes the probability of an infectious individual infecting someone else after some period of time after having become infectious. As in most literature, we assume that this interval follows a gamma distribution with some shape and scale.
nfold	Integer. This number of folds to conduct the leave-kth-out cross validation. For leave-kth-out cross validation, every kth observed_counts and their corresponding position (evenly or unevenly spaced) are placed into the same fold. The first and last observed_counts are not assigned to any folds. Smallest allowable value is nfold = 2.
error_measure	Metric used to calculate cross validation scores. Must be choose from mse, mae, and deviance. mse calculates the mean square error; mae calculates the mean absolute error; deviance calculates the deviance
x	a vector of positions at which the counts have been observed. In an ideal case, we would observe data at regular intervals (e.g. daily or weekly) but this may not always be the case. May be numeric or Date.
lambda	Vector. A user supplied sequence of tuning parameters which determines the balance between data fidelity and smoothness of the estimated Rt; larger lambda results in a smoother estimate. The default, NULL results in an automatic computation based on nlambda, the largest value of lambda that would result in a maximally smooth estimate, and lambda_min_ratio. Supplying a value of lambda overrides this behaviour. It is likely better to supply a decreasing sequence of lambda values than a single (small) value. If supplied, the user-defined lambda sequence is automatically sorted in decreasing order.
maxiter	Integer. Maximum number of iterations for the estimation algorithm.
delay_distn	in the case of a non-gamma delay distribution, a vector or matrix (or Matrix::Matrix()) of delay probabilities may be passed here. For a vector, these will be coerced to sum to 1, and padded with 0 in the right tail if necessary. If a time-varying delay matrix, it must be lower-triangular. Each row will be silently coerced to sum to 1. See also vignette("delay-distributions").
delay_distn_periodicity	Controls the relationship between the spacing of the computed delay distribution and the spacing of x. In the default case, x would be regular on the sequence 1:length(observed_cases), and this would be 1. But if x is a Date object or spaced irregularly, the relationship becomes more complicated. For example, weekly data when x is a date in the form YYYY-MM-DD requires specifying delay_distn_periodicity = "1 week". Or if observed_cases were reported on Monday, Wednesday, and Friday, then delay_distn_periodicity = "1 day" would be most appropriate.
regular_splits	Logical. If TRUE, the folds for k-fold cross-validation are chosen by placing every kth point into the same fold. The first and last points are not included in any fold and are always included in building the predictive model. As an example, with 15 data points and kfold = 4, the points are assigned to folds in the following way: $0 \; 1 \; 2 \; 3 \; 4 \; 1 \; 2 \; 3 \; 4 \; 1 \; 2 \; 3 \; 4 \; 1 \; 0$ where 0 indicates no assignment. Therefore, the folds are not random and running cv_estimate_rt() twice will give the same result.
invert_splits	Logical. Typical K-fold CV would use K-1 folds for the training set while reserving 1 fold for evaluation (repeating the split K times). Setting this to true inverts this process, using a much smaller training set with a larger evaluation set. This tends to result in larger values of lambda that minimize CV.
...	additional parameters passed to estimate_rt() function

Value

An object with S3 class "cv_poisson_rt". Among the list components:

• full_fit An object with S3 class "poisson_rt", fitted with all observed_counts and lambda

• cv_scores leave-kth-out cross validation scores

• cv_se leave-kth-out cross validation standard error

• lambda.min lambda which achieved the optimal cross validation score

• lambda.1se lambda that gives the optimal cross validation score within one standard error.

• lambda the value of lambda used in the algorithm.

Examples

y <- c(1, rpois(100, dnorm(1:100, 50, 15) * 500 + 1))
cv <- cv_estimate_rt(y, korder = 3, nfold = 3, nsol = 30)
cv

---

Calculate the total infectiousness at each observed time point.

Description

The total infectiousness at each observed time point is calculated by $\sum_{s=1}^t I_{t-s}w_s$, where $I$ denotes the vector containing observed incidence, and $w$ denotes the generation interval distribution. Typically, the generation interval is challenging to estimate from data, so the serial interval is used instead. The serial interval distribution expresses the probability of a secondary infection caused by a primary infection which occurred $s$ days earlier.

Usage

delay_calculator(
  observed_counts,
  x = NULL,
  dist_gamma = c(2.5, 2.5),
  delay_distn = NULL,
  delay_distn_periodicity = NULL,
  xout = x
)

Arguments

observed_counts	vector of the observed daily infection counts
x	a vector of positions at which the counts have been observed. In an ideal case, we would observe data at regular intervals (e.g. daily or weekly) but this may not always be the case. May be numeric or Date.
dist_gamma	Vector of length 2. These are the shape and scale for the assumed serial interval distribution. Roughly, this distribution describes the probability of an infectious individual infecting someone else after some period of time after having become infectious. As in most literature, we assume that this interval follows a gamma distribution with some shape and scale.
delay_distn	in the case of a non-gamma delay distribution, a vector or matrix (or Matrix::Matrix()) of delay probabilities may be passed here. For a vector, these will be coerced to sum to 1, and padded with 0 in the right tail if necessary. If a time-varying delay matrix, it must be lower-triangular. Each row will be silently coerced to sum to 1. See also vignette("delay-distributions").
delay_distn_periodicity	Controls the relationship between the spacing of the computed delay distribution and the spacing of x. In the default case, x would be regular on the sequence 1:length(observed_cases), and this would be 1. But if x is a Date object or spaced irregularly, the relationship becomes more complicated. For example, weekly data when x is a date in the form YYYY-MM-DD requires specifying delay_distn_periodicity = "1 week". Or if observed_cases were reported on Monday, Wednesday, and Friday, then delay_distn_periodicity = "1 day" would be most appropriate.
xout	a vector of positions at which the results should be returned. By default, this will be the same as x, but in the case that observations are unequally spaced, alternatives may be desired. Note that xout must satisfy min(x) <= min(xout) and max(x) >= max(xout).

Value

A vector containing the total infectiousness at each point xout.

Examples

delay_calculator(c(3, 2, 5, 3, 1), dist_gamma = c(2.5, 2.5))

---

Compute the discretized density function for gamma distribution

Description

The serial interval distribution expresses the probability of the symptom onset of a secondary infection occurred a given number of days after the primary infection. The serial interval distribution is commonly represented by a discretized Gamma distribution in literature, parametrized by the shape and scale parameters.

Usage

discretize_gamma(x, shape = 2.5, scale = 2.5, rate = 1/scale)

Arguments

x	locations (times) where cases are observed. Must be nonnegative.
shape, scale	shape and scale parameters. Must be positive, scale strictly.
rate	an alternative way to specify the scale.

Value

probability mass of the discretized gamma distribution

Examples

discretize_gamma(1:30, shape = 1, scale = 1)

---

Estimate Rt using smoothness-penalized Poisson likelihood

Description

The Effective Reproduction Number $R_t$ of an infectious disease can be estimated by solving the smoothness penalized Poisson regression (trend filtering) of the form:

$\hat{\theta} = \arg\min_{\theta} \frac{1}{n} \sum_{i=1}^n (w_i e^{\theta_i} - y_i\theta_i) + \lambda\Vert D^{(k+1)}\theta\Vert_1,$

where $R_t = e^{\theta}$, $y_i$ is the observed case count at day $i$, $w_i$ is the weighted past counts at day $i$, $\lambda$ is the smoothness penalty, and $D^{(k+1)}$ is the $(k+1)$-th order difference matrix.

Usage

estimate_rt(
  observed_counts,
  korder = 3L,
  dist_gamma = c(2.5, 2.5),
  x = 1:n,
  lambda = NULL,
  nsol = 50L,
  delay_distn = NULL,
  delay_distn_periodicity = NULL,
  lambdamin = NULL,
  lambdamax = NULL,
  lambda_min_ratio = 1e-04,
  maxiter = 1e+05,
  init = configure_rt_admm()
)

Arguments

observed_counts	vector of the observed daily infection counts
korder	Integer. Degree of the piecewise polynomial curve to be estimated. For example, korder = 0 corresponds to a piecewise constant curve.
dist_gamma	Vector of length 2. These are the shape and scale for the assumed serial interval distribution. Roughly, this distribution describes the probability of an infectious individual infecting someone else after some period of time after having become infectious. As in most literature, we assume that this interval follows a gamma distribution with some shape and scale.
x	a vector of positions at which the counts have been observed. In an ideal case, we would observe data at regular intervals (e.g. daily or weekly) but this may not always be the case. May be numeric or Date.
lambda	Vector. A user supplied sequence of tuning parameters which determines the balance between data fidelity and smoothness of the estimated Rt; larger lambda results in a smoother estimate. The default, NULL results in an automatic computation based on nlambda, the largest value of lambda that would result in a maximally smooth estimate, and lambda_min_ratio. Supplying a value of lambda overrides this behaviour. It is likely better to supply a decreasing sequence of lambda values than a single (small) value. If supplied, the user-defined lambda sequence is automatically sorted in decreasing order.
nsol	Integer. The number of tuning parameters lambda at which to compute Rt.
delay_distn	in the case of a non-gamma delay distribution, a vector or matrix (or Matrix::Matrix()) of delay probabilities may be passed here. For a vector, these will be coerced to sum to 1, and padded with 0 in the right tail if necessary. If a time-varying delay matrix, it must be lower-triangular. Each row will be silently coerced to sum to 1. See also vignette("delay-distributions").
delay_distn_periodicity	Controls the relationship between the spacing of the computed delay distribution and the spacing of x. In the default case, x would be regular on the sequence 1:length(observed_cases), and this would be 1. But if x is a Date object or spaced irregularly, the relationship becomes more complicated. For example, weekly data when x is a date in the form YYYY-MM-DD requires specifying delay_distn_periodicity = "1 week". Or if observed_cases were reported on Monday, Wednesday, and Friday, then delay_distn_periodicity = "1 day" would be most appropriate.
lambdamin	Optional value for the smallest lambda to use. This should be greater than zero.
lambdamax	Optional value for the largest lambda to use.
lambda_min_ratio	If neither lambda nor lambdamin is specified, the program will generate a lambdamin by lambdamax * lambda_min_ratio. A multiplicative factor for the minimal lambda in the lambda sequence, where lambdamin = lambda_min_ratio * lambdamax. A very small value will lead to the solution Rt = log(observed_counts). This argument has no effect if there is a user-defined lambda sequence.
maxiter	Integer. Maximum number of iterations for the estimation algorithm.
init	a list of internal configuration parameters of class rt_admm_configuration.

Value

An object with S3 class poisson_rt. Among the list components:

• observed_counts the observed daily infection counts.

• x a vector of positions at which the counts have been observed.

• weighted_past_counts the weighted sum of past infection counts.

• Rt the estimated effective reproduction rate. This is a matrix with each column corresponding to one value of lambda.

• lambda the values of lambda actually used in the algorithm.

• korder degree of the estimated piecewise polynomial curve.

• dof degrees of freedom of the estimated trend filtering problem.

• niter the required number of iterations for each value of lambda.

• convergence if number of iterations for each value of lambda is less than the maximum number of iterations for the estimation algorithm.

Examples

y <- c(1, rpois(100, dnorm(1:100, 50, 15) * 500 + 1))
out <- estimate_rt(y)
out
plot(out)

out0 <- estimate_rt(y, korder = 0L, nsol = 40)
out0
plot(out0)

---

Fitted cv_poisson_rt

Description

Fitted cv_poisson_rt

Usage

## S3 method for class 'cv_poisson_rt'
fitted(object, which_lambda = c("lambda.min", "lambda.1se"), ...)

Arguments

object	result of cross validation of type cv_poisson_rt
which_lambda	select which Rt's to output. If not provided, all Rt's are returned. If provided a list of lambda,the corresponding Rt estimation will be returned. If provided a string, it must be either one of lambda.min or lambda.1se. If provided lambda.min, return Rt which is generated from the lambda that minimizes the cross validation score. If provided lambda.1se, return Rt which is generated from the lambda whose corresponding cross validation score is 1 standard error away of the minimal cross validation score.
...	not used.

Value

Rt's estimated from provided lambda

Examples

y <- c(1, rpois(100, dnorm(1:100, 50, 15) * 500 + 1))
cv <- cv_estimate_rt(y, korder = 3, nfold = 3, nsol = 30)
f <- fitted(cv)
f <- fitted(cv, which_lambda = cv$lambda[1])
f <- fitted(cv, which_lambda = "lambda.1se")
f <- fitted(cv, which_lambda = NULL)

---

Interpolate (or extrapolate) Rt estimates to intermediate design points

Description

Interpolate (or extrapolate) Rt estimates to intermediate design points

Usage

interpolate_rt(object, xout, ...)

## S3 method for class 'cv_poisson_rt'
interpolate_rt(object, xout, which_lambda = c("lambda.min", "lambda.1se"), ...)

## S3 method for class 'poisson_rt'
interpolate_rt(object, xout, lambda = NULL, ...)

Arguments

object	A fitted object produced by estimate_rt() or cv_estimate_rt().
xout	a vector of new positions at which Rt should be produced, but where counts may not have been observed.
...	additional arguments passed to methods.
which_lambda	Select which lambdas from the object to use. If not provided, all Rt's are returned. Note that new lambdas not originally used in the estimation procedure may be provided, but the results will be calculated by linearly interpolating the estimated Rt's. The strings lambda.min or lambda.1se are allowed to choose either the lambda that minimizes the cross validation score or the largest lambda whose corresponding cross validation score is within 1 standard error of the minimal cross validation score.
lambda	Vector. A user supplied sequence of tuning parameters which determines the balance between data fidelity and smoothness of the estimated Rt; larger lambda results in a smoother estimate. The default, NULL results in an automatic computation based on nlambda, the largest value of lambda that would result in a maximally smooth estimate, and lambda_min_ratio. Supplying a value of lambda overrides this behaviour. It is likely better to supply a decreasing sequence of lambda values than a single (small) value. If supplied, the user-defined lambda sequence is automatically sorted in decreasing order.

Value

A vector or matrix of interpolated Rt estimates.

Examples

y <- c(1, rpois(100, dnorm(1:100, 50, 15) * 500 + 1))
out <- estimate_rt(y)

# originally estimated at
out$x

# get the Rt at 3 new points (for all estimated lambdas)
int <- interpolate_rt(out, c(10.5, 11.5, 12.5))

# get the Rt at a single value of lambda
interpolate_rt(out, c(10.5, 11.5, 12.5), lambda = out$lambda[20])

y <- c(1, rpois(100, dnorm(1:100, 50, 15) * 500 + 1))
out <- estimate_rt(y, nsol = 10)
interpolate_rt(out, xout = c(1.5, 2.5))

---

Plot cv_poisson_rt

Description

Plot cv_poisson_rt

Usage

## S3 method for class 'cv_poisson_rt'
plot(x, which_lambda = c("cv_scores", "lambda.min", "lambda.1se"), ...)

Arguments

x	result of cv_estimate_rt of class cv_poisson_rt
which_lambda	select which Rt's to plot. If not provided, the cross validation score will be plotted. If provided a list of lambda, the corresponding Rt estimation will be plotted. If provided a string, it must be either one of lambda.min, lambda.1se, or cv_scores. If provided lambda.min, plot Rt which is generated from the lambda that minimizes the cross validation score. If provided lambda.1se, plot Rt which is generated from the lambda whose corresponding cross validation score is 1 standard error away of the minimal cross validation score. If provided cv_scores, plot the cross validation score. If NULL, all estimated Rt values are plotted.
...	Not used.

Value

a ggplot2::ggplot

Examples

y <- c(1, rpois(100, dnorm(1:100, 50, 15) * 500 + 1))
cv <- cv_estimate_rt(y, korder = 1, nfold = 3, nsol = 30)
plot(cv)
plot(cv, which_lambda = cv$lambda[1])
plot(cv, which_lambda = "lambda.min")
plot(cv, which_lambda = "lambda.1se")
plot(cv, NULL)

---

Plot estimated Rt values from a poisson_rt object

Description

Produces a figure showing some or all estimated Rt values for different values of the penalty. The result is a ggplot2::ggplot(). Additional user modifications can be added as desired.

Usage

## S3 method for class 'poisson_rt'
plot(x, lambda = NULL, ...)

Arguments

x	output of the function estimate_rt() of class poisson_rt
lambda	select which Rt's to plot. If not provided, all Rt's are plotted.
...	Not used.

Value

a ggplot2::ggplot

Examples

y <- c(1, rpois(100, dnorm(1:100, 50, 15) * 500 + 1))
out <- estimate_rt(y, lambda = log(c(1.1, 1.3, 1.5)))
plot(out)

---

Plot estimated confidence bands for an estimate of Rt

Description

Produces a figure showing a single estimated Rt value along with approximate confidence bands. The result is a ggplot2::ggplot(). Additional user modifications can be added as desired.

Usage

## S3 method for class 'rt_confidence_band'
plot(x, colour = "#3A448F", ...)

Arguments

x	An object of class rt_confidence_band as produced by confband().
colour	The colour of the desired plot
...	Not used.

Value

A ggplot2::ggplot().

Examples

y <- c(1, rpois(100, dnorm(1:100, 50, 15) * 500 + 1))
out <- estimate_rt(y, nsol = 10)
cb <- confband(out, out$lambda[2], level = c(0.95, 0.8, 0.5))
plot(cb)
cb_y <- confband(out, out$lambda[2], level = c(0.95, 0.8, 0.5), type = "Yt")
plot(cb_y)

---

Predict observed data using estimated Rt

Description

Given an object of class poisson_rt produced with estimate_rt(), calculate predicted observed cases for the estimated Rt values. Note: This function is not intended for "new x" or to produce forecasts, but rather to examine how Rt relates to observables.

Usage

## S3 method for class 'cv_poisson_rt'
predict(object, which_lambda = c("lambda.min", "lambda.1se"), ...)

Arguments

object	result of cross validation of type cv_poisson_rt
which_lambda	Select which lambdas from the object to use. If not provided, all Rt's are returned. Note that new lambdas not originally used in the estimation procedure may be provided, but the results will be calculated by linearly interpolating the estimated Rt's. The strings lambda.min or lambda.1se are allowed to choose either the lambda that minimizes the cross validation score or the largest lambda whose corresponding cross validation score is within 1 standard error of the minimal cross validation score.
...	not used.

Value

A vector or matrix of predicted case counts.

Examples

y <- c(1, rpois(100, dnorm(1:100, 50, 15) * 500 + 1))
cv <- cv_estimate_rt(y, korder = 3, nfold = 3, nsol = 30)
p <- predict(cv)
p <- predict(cv, which_lambda = cv$lambda[1])
p <- predict(cv, which_lambda = "lambda.1se")
p <- predict(cv, which_lambda = NULL)
plot(y)
matlines(p, lty = 2)

---

Predict observed data using estimated Rt

Description

Given an object of class poisson_rt produced with estimate_rt(), calculate predicted observed cases for the estimated Rt values. Note: This function is not intended for "new x" or to produce forecasts, but rather to examine how Rt relates to observables.

Usage

## S3 method for class 'poisson_rt'
predict(object, lambda = NULL, ...)

Arguments

object	An object of class poisson_rt produced with estimate_rt().
lambda	Select which lambdas from the object to use. If not provided (the default), all are returned. Note that new lambdas not originally used in the estimation procedure may be provided, but the results will be calculated by linearly interpolating the estimated Rt's.
...	Not used.

Value

A vector or matrix of predicted case counts.

Examples

y <- c(1, rpois(100, dnorm(1:100, 50, 15) * 500 + 1))
out <- estimate_rt(y, nsol = 10)
preds <- predict(out)
plot(y)
matlines(preds, lty = 1)

---