Package {LongitudinalEvalue}

COVID example dataset

Description

The Covidexample dataset is a data frame with 30 observations and 5 variables. It contains daily cumulative incidence data of SARS-CoV-2 infections in November 2020 for municipalities under regional lockdown and comparable municipalities without lockdown.

In addition, the dataset includes a temporal average treatment effect (TATE) for the regional lockdown and a hypothetical average treatment effect (ATE) under the assumption of no unmeasured confounding.

Usage

Covidexample

Format

A data frame with 30 rows and 5 variables:

time

Date of the observation.

incidencelockdown

Cumulative incidence in the lockdown municipalities.

incidencenolockdown

Cumulative incidence in the non-lockdown municipalities.

TATE

Temporal average treatment effect on the absolute scale.

ATE

Hypothetical temporal average treatment effect under no unmeasured confounding.

Details

This dataset includes the daily cumulative incidence of SARS Covid-19 in November 2020 for the municipalities which experienced the regional lockdown and those which did not. It also includes the temporal average treatment of the regional lockdown and the hypothetical averagetreatment effect if a confounder could explain the effect of the regional lockdown

Source

Ege, F. (2024). Short, stringent lockdowns halted SARS-CoV-2 transmissions in Danish municipalities.

Examples

"Covidexample"

Sensitivity analysis for unmeasured time-invariant confounders

Description

A launcher for the LongitudinalEvalueApp.

Usage

LongitudinalEvalueApp()

Details

The app is also available online at https://andreaskpedersen.shinyapps.io/LongitudinalEvalue/

The Shiny app contains the following inputs:

• Effects_sizes: Vector of observed temporal average treatment effects (TATE)

• Order: Differencing order of the TATE process

• X_axis: X-axis limits

• Y_axis: Y-axis limits

• Legendtitle: Legend title and labels

• Plot_type: Type of plot ("Confounder" or "Difference-In-Difference")

Value

Launches the Shiny application. The app allows users to explore and download sensitivity curves describing the strength of association that an unmeasured time-invariant confounder would need to have with both exposure and outcome to fully explain the observed causal effect.

The exposure–confounder association is modeled on a ratio scale, while the confounder–outcome association is expressed on the same scale as the TATE.

Examples

if(interactive()){
LongitudinalEvalueApp()
}

Simulating a time-varying confounder (non-parametric approach)

Description

The SDEconfounderNonparametric is a non-parametric method simulate the confounder which could explain the discrepancy between the observed and causal average treatment. It has a similar syntax to SDEconfounderYuima1d but utilizes the observed data instead of of the fit from qmle from the yuima package

Usage

SDEconfounderNonparametric(
  Observed,
  ATE,
  time,
  EFXU,
  EFUY,
  custom_time = NULL,
  bayesianXU = "No",
  bayesianUY = "No",
  nbayes = 100,
  priors = list(sigmaUY = 1, sigmaXU = 1),
  alpha = 0.05,
  bw_drift = NULL,
  bw_diffusion = NULL,
  bwmethod_drift = "cv.aic",
  bwmethod_diffusion = "cv.aic",
  scheme = "no",
  stiff = "no",
  tol = 1e-08,
  iteration_solver = 5,
  frozenJacobi = TRUE,
  seed = NULL
)

Arguments

Value

A list of two data frames:

• A full set of simulated confounder trajectories.

• The mean trajectory with corresponding 100(1 - \alpha)\% credibility intervals.

Note

The kernel regression predictions are conditional on the observed values of the TATE. This is because we condition on the dataset, where the most expected value of the dataset is the observed value

References

Kloeden, P. E., & Platen, E. (1992). Numerical Solution of Stochastic Differential Equations (1st ed.).

Hutzenthaler, M., Jentzen, A., & Kloeden, P. E. Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. arXiv preprint.

Examples

## Simulate and plot a latent time-varying confounder where the two 
## assocations from the confounder are both 1.5 and the bandwidth for the 
## kernel regression is based on  least-squares cross-validation and the 
## scheme is based on the explicit Euler-Maruyama scheme.
U_t <- SDEconfounderNonparametric(
  Covidexample$TATE,
  ATE = Covidexample$ATE,
  time = Covidexample$time,
  EFXU = 1.5,
  EFUY = 1.5,
  bwmethod_drift = "cv.ls",
  bwmethod_diffusion = "cv.ls",
  scheme = "Euler-Maruyama"
)
plot(U_t)

S4 class for SDEconfounderResult used by SDEconfounderNonparametric

Description

S4 class for SDEconfounderResult used by SDEconfounderNonparametric

Slots

data

A data frame containing simulated trajectories

trajectories

A matrix of simulated paths

hasCI

Logical indicating whether confidence intervals are included

S4 class for SDEconfounderResultYuima used by SDEconfounderYuima1d

Description

S4 class for SDEconfounderResultYuima used by SDEconfounderYuima1d

Slots

data

A data frame containing simulated trajectories

Simulating time-varying confounder parametrically

Description

SDEconfounderYuima1d uses the fit from the qmle function in the yuima package to simulate the confounder which could explain the discrepancy between the observed and causal average treat ment.

Usage

SDEconfounderYuima1d(
  fit,
  time,
  EFXU,
  EFUY,
  bayesianXU = "No",
  bayesianUY = "No",
  nbayes = 200,
  initial.value = 0,
  priors = list(sigmaUY = 1, sigmaXU = 1),
  alpha = 0.05
)

Arguments

Value

A data frame containing the simulated confounder trajectory along with corresponding 100(1 - \alpha)\% credibility intervals.

Note

The simulation is based on parameter estimates obtained from the qmle function in the yuima package.

References

Iacus, S. M. (2018). Simulation and Inference for Stochastic Processes with YUIMA: A Comprehensive R Framework for SDEs and Other Stochastic Processes (1st ed.). Springer Nature. https://doi.org/10.1007/978-3-319-55569-0

Examples

## Simulate and plot the trajectory of the unmeasured confounder based on the
## fit object from the qmle function from the yuima package.
## For information on how to use the qmle-function we refer to the 
## yuima-package, Iacus, S. M. (2018) and the accompanying vignette for this 
## package.
Delta<-1/3
Covidexample$t<-1:30
mod<-yuima::setModel(drift="a/TATE+c*TATE", diffusion="sigma", 
state.var="TATE", time.var = "t", 
             solve.var = "TATE",xinit = 5.425966)
model<-yuima::setYuima(model=mod, 
data=yuima::setData(zoo::zoo(Covidexample$TATE, order.by = Covidexample$t),
                                       delta=Delta))
fit <- yuima::qmle(model,start = list(a=-5,c = 5,sigma = 0.2),
           lower = list(a=-10,c = -10,sigma = 0), 
           upper = list(a=0,c = 10,sigma =1))

U_t <- SDEconfounderYuima1d(
  fit,
  time = Covidexample$time,
  EFXU = 2,
  EFUY = 1,
  alpha = 0.05
)
plot(U_t)

Plot method for SDEconfounderNonparametric

Description

Plot method for SDEconfounderNonparametric

Usage

## S4 method for signature 'SDEconfounderResult,ANY'
plot(x)

Arguments

Value

A ggplot object showing the confounder trajectory with corresponding credibility intervals if they are specified.

Plot method for SDEconfounderYuima1d

Description

Plot method for SDEconfounderYuima1d

Usage

## S4 method for signature 'SDEconfounderResultYuima,ANY'
plot(x)

Arguments

Value

A ggplot object showing the confounder trajectory with corresponding credibility intervals if they are specified.