Package 'npDoseResponse' reference manual

Title:	Nonparametric Estimation and Inference on Dose-Response Curves
Description:	A novel integral estimator for estimating the causal effects with continuous treatments (or dose-response curves) and a localized derivative estimator for estimating the derivative effects. The inference on the dose-response curve and its derivative is conducted via nonparametric bootstrap. The reference paper is Zhang, Chen, and Giessing (2024) <doi:10.48550/arXiv.2405.09003>.
Authors:	Yikun Zhang [aut, cre] , Yen-Chi Chen [aut]
Maintainer:	Yikun Zhang <[email protected]>
License:	MIT + file LICENSE
Version:	0.1
Built:	2025-02-13 05:43:11 UTC
Source:	https://github.com/cran/npDoseResponse

The proposed localized derivative estimator.

Description

This function implements our proposed estimator for estimating the derivative of a dose-response curve via Nadaraya-Watson conditional CDF estimator.

Usage

DerivEffect(
  Y,
  X,
  t_eval = NULL,
  h_bar = NULL,
  kernT_bar = "gaussian",
  h = NULL,
  b = NULL,
  C_h = 7,
  C_b = 3,
  print_bw = TRUE,
  degree = 2,
  deriv_ord = 1,
  kernT = "epanechnikov",
  kernS = "epanechnikov",
  parallel = TRUE,
  cores = 6
)
DerivEffect(
  Y,
  X,
  t_eval = NULL,
  h_bar = NULL,
  kernT_bar = "gaussian",
  h = NULL,
  b = NULL,
  C_h = 7,
  C_b = 3,
  print_bw = TRUE,
  degree = 2,
  deriv_ord = 1,
  kernT = "epanechnikov",
  kernS = "epanechnikov",
  parallel = TRUE,
  cores = 6
)

Arguments

`Y`	The input n-dimensional outcome variable vector.
`X`	The input n*(d+1) matrix. The first column of X stores the treatment/exposure variables, while the other d columns are confounding variables.
`t_eval`	The m-dimensional vector for evaluating the derivative. (Default: t_eval = NULL. Then, t_eval = `X[,1]`, which consists of the observed treatment variables.)
`h_bar`	The bandwidth parameter for the Nadaraya-Watson conditional CDF estimator. (Default: h_bar = NULL. Then, the Silverman's rule of thumb is applied. See Chen et al. (2016) for details.)
`kernT_bar`	The name of the kernel function for the Nadaraya-Watson conditional CDF estimator. (Default: "gaussian".)
`h`, `b`	The bandwidth parameters for the treatment/exposure variable and confounding variables in the local polynomial regression. (Default: h = NULL, b = NULL. Then, the rule-of-thumb bandwidth selector in Eq. (A1) of Yang and Tschernig (1999) is used with additional scaling factors C_h and C_b, respectively.)
`C_h`, `C_b`	The scaling factors for the rule-of-thumb bandwidth parameters.
`print_bw`	The indicator of whether the current bandwidth parameters should be printed to the console. (Default: print_bw = TRUE.)
`degree`	Degree of local polynomials. (Default: degree = 2.)
`deriv_ord`	The order of the estimated derivative of the conditional mean outcome function. (Default: deriv_ord = 1. It shouldn't be changed in most cases.)
`kernT`, `kernS`	The names of kernel functions for the treatment/exposure variable and confounding variables. (Default: kernT = "epanechnikov", kernS = "epanechnikov".)
`parallel`	The indicator of whether the function should be parallel executed. (Default: parallel = TRUE.)
`cores`	The number of cores for parallel execution. (Default: cores = 6.)

Value

The estimated derivative of the dose-response curve evaluated at points t_eval.

Author(s)

Yikun Zhang, [email protected]

References

Zhang, Y., Chen, Y.-C., and Giessing, A. (2024) Nonparametric Inference on Dose-Response Curves Without the Positivity Condition. https://arxiv.org/abs/2405.09003.

Hall, P., Wolff, R. C., and Yao, Q. (1999) Methods for Estimating A Conditional Distribution Function. Journal of the American Statistical Association, 94 (445): 154-163.

Examples


  library(parallel)
  set.seed(123)
  n <- 300

  S2 <- cbind(2 * runif(n) - 1, 2 * runif(n) - 1)
  Z2 <- 4 * S2[, 1] + S2[, 2]
  E2 <- 0.2 * runif(n) - 0.1
  T2 <- cos(pi * Z2^3) + Z2 / 4 + E2
  Y2 <- T2^2 + T2 + 10 * Z2 + rnorm(n, mean = 0, sd = 1)
  X2 <- cbind(T2, S2)

  t_qry2 = seq(min(T2) + 0.01, max(T2) - 0.01, length.out = 100)
  chk <- Sys.getenv("_R_CHECK_LIMIT_CORES_", "")
  if (nzchar(chk) && chk == "TRUE") {
    # use 2 cores in CRAN/Travis/AppVeyor
    num_workers <- 2L
  } else {
    # use all cores in devtools::test()
    num_workers <- parallel::detectCores()
  }
  theta_est2 = DerivEffect(Y2, X2, t_eval = t_qry2, h_bar = NULL,
                           kernT_bar = "gaussian", h = NULL, b = NULL,
                           C_h = 7, C_b = 3, print_bw = FALSE,
                           degree = 2, deriv_ord = 1, kernT = "epanechnikov",
                           kernS = "epanechnikov", parallel = TRUE, cores = num_workers)
  plot(t_qry2, theta_est2, type="l", col = "blue", xlab = "t", lwd=5,
       ylab="(Estimated) derivative effects")
  lines(t_qry2, 2*t_qry2 + 1, col = "red", lwd=3)
  legend(-2, 5, legend=c("Estimated derivative", "True derivative"),
         fill = c("blue","red"))


library(parallel)
  set.seed(123)
  n <- 300

  S2 <- cbind(2 * runif(n) - 1, 2 * runif(n) - 1)
  Z2 <- 4 * S2[, 1] + S2[, 2]
  E2 <- 0.2 * runif(n) - 0.1
  T2 <- cos(pi * Z2^3) + Z2 / 4 + E2
  Y2 <- T2^2 + T2 + 10 * Z2 + rnorm(n, mean = 0, sd = 1)
  X2 <- cbind(T2, S2)

  t_qry2 = seq(min(T2) + 0.01, max(T2) - 0.01, length.out = 100)
  chk <- Sys.getenv("_R_CHECK_LIMIT_CORES_", "")
  if (nzchar(chk) && chk == "TRUE") {
    # use 2 cores in CRAN/Travis/AppVeyor
    num_workers <- 2L
  } else {
    # use all cores in devtools::test()
    num_workers <- parallel::detectCores()
  }
  theta_est2 = DerivEffect(Y2, X2, t_eval = t_qry2, h_bar = NULL,
                           kernT_bar = "gaussian", h = NULL, b = NULL,
                           C_h = 7, C_b = 3, print_bw = FALSE,
                           degree = 2, deriv_ord = 1, kernT = "epanechnikov",
                           kernS = "epanechnikov", parallel = TRUE, cores = num_workers)
  plot(t_qry2, theta_est2, type="l", col = "blue", xlab = "t", lwd=5,
       ylab="(Estimated) derivative effects")
  lines(t_qry2, 2*t_qry2 + 1, col = "red", lwd=3)
  legend(-2, 5, legend=c("Estimated derivative", "True derivative"),
         fill = c("blue","red"))

Nonparametric bootstrap inference on the derivative effect via our localized derivative estimator.

Description

This function implements the nonparametric bootstrap inference on the derivative of a dose-response curve via our localized derivative estimator.

Usage

DerivEffectBoot(
  Y,
  X,
  t_eval = NULL,
  boot_num = 500,
  alpha = 0.95,
  h_bar = NULL,
  kernT_bar = "gaussian",
  h = NULL,
  b = NULL,
  C_h = 7,
  C_b = 3,
  print_bw = TRUE,
  degree = 2,
  deriv_ord = 1,
  kernT = "epanechnikov",
  kernS = "epanechnikov",
  parallel = TRUE,
  cores = 6
)
DerivEffectBoot(
  Y,
  X,
  t_eval = NULL,
  boot_num = 500,
  alpha = 0.95,
  h_bar = NULL,
  kernT_bar = "gaussian",
  h = NULL,
  b = NULL,
  C_h = 7,
  C_b = 3,
  print_bw = TRUE,
  degree = 2,
  deriv_ord = 1,
  kernT = "epanechnikov",
  kernS = "epanechnikov",
  parallel = TRUE,
  cores = 6
)

Arguments

`Y`	The input n-dimensional outcome variable vector.
`X`	The input n*(d+1) matrix. The first column of X stores the treatment/exposure variables, while the other d columns are confounding variables.
`t_eval`	The m-dimensional vector for evaluating the derivative. (Default: t_eval = NULL. Then, t_eval = `X[,1]`, which consists of the observed treatment variables.)
`boot_num`	The number of bootstrapping times. (Default: boot_num = 500.)
`alpha`	The confidence level of both the uniform confidence band and pointwise confidence interval. (Default: alpha = 0.95.)
`h_bar`	The bandwidth parameter for the Nadaraya-Watson conditional CDF estimator. (Default: h_bar = NULL. Then, the Silverman's rule of thumb is applied. See Chen et al. (2016) for details.)
`kernT_bar`	The name of the kernel function for the Nadaraya-Watson conditional CDF estimator. (Default: kernT_bar = "gaussian".)
`h`, `b`	The bandwidth parameters for the treatment/exposure variable and confounding variables in the local polynomial regression. (Default: h = NULL, b = NULL. Then, the rule-of-thumb bandwidth selector in Eq. (A1) of Yang and Tschernig (1999) is used with additional scaling factors C_h and C_b, respectively.)
`C_h`, `C_b`	The scaling factors for the rule-of-thumb bandwidth parameters.
`print_bw`	The indicator of whether the current bandwidth parameters should be printed to the console. (Default: print_bw = TRUE.)
`degree`	Degree of local polynomials. (Default: degree = 2.)
`deriv_ord`	The order of the estimated derivative of the conditional mean outcome function. (Default: deriv_ord = 1. It shouldn't be changed in most cases.)
`kernT`, `kernS`	The names of kernel functions for the treatment/exposure variable and confounding variables. (Default: kernT = "epanechnikov", kernS = "epanechnikov".)
`parallel`	The indicator of whether the function should be parallel executed. (Default: parallel = TRUE.)
`cores`	The number of cores for parallel execution. (Default: cores = 6.)

Value

A list that contains four elements.

`theta_est`	The estimated derivative of the dose-response curve evaluated at points `t_eval`.
`theta_est_boot`	The estimated derivative of the dose-response curve evaluated at points `t_eval` for all the bootstrap samples.
`theta_alpha`	The width of the uniform confidence band.
`theta_alpha_var`	The widths of the pointwise confidence bands at evaluation points `t_eval`.

Author(s)

Yikun Zhang, [email protected]

References

Zhang, Y., Chen, Y.-C., and Giessing, A. (2024) Nonparametric Inference on Dose-Response Curves Without the Positivity Condition. https://arxiv.org/abs/2405.09003.

Examples


  set.seed(123)
  n <- 300

  S2 <- cbind(2 * runif(n) - 1, 2 * runif(n) - 1)
  Z2 <- 4 * S2[, 1] + S2[, 2]
  E2 <- 0.2 * runif(n) - 0.1
  T2 <- cos(pi * Z2^3) + Z2 / 4 + E2
  Y2 <- T2^2 + T2 + 10 * Z2 + rnorm(n, mean = 0, sd = 1)
  X2 <- cbind(T2, S2)

  t_qry2 = seq(min(T2) + 0.01, max(T2) - 0.01, length.out = 100)
  chk <- Sys.getenv("_R_CHECK_LIMIT_CORES_", "")
  if (nzchar(chk) && chk == "TRUE") {
    # use 2 cores in CRAN/Travis/AppVeyor
    num_workers <- 2L
  } else {
    # use all cores in devtools::test()
    num_workers <- parallel::detectCores()
  }

  # Increase bootstrap times "boot_num" to a larger integer in practice
  theta_boot2 = DerivEffectBoot(Y2, X2, t_eval = t_qry2, boot_num = 3, alpha = 0.95,
                               h_bar = NULL, kernT_bar = "gaussian", h = NULL,
                               b = NULL, C_h = 7, C_b = 3, print_bw = FALSE,
                               degree = 2, deriv_ord = 1, kernT = "epanechnikov",
                               kernS = "epanechnikov", parallel = TRUE,
                               cores = num_workers)


set.seed(123)
  n <- 300

  S2 <- cbind(2 * runif(n) - 1, 2 * runif(n) - 1)
  Z2 <- 4 * S2[, 1] + S2[, 2]
  E2 <- 0.2 * runif(n) - 0.1
  T2 <- cos(pi * Z2^3) + Z2 / 4 + E2
  Y2 <- T2^2 + T2 + 10 * Z2 + rnorm(n, mean = 0, sd = 1)
  X2 <- cbind(T2, S2)

  t_qry2 = seq(min(T2) + 0.01, max(T2) - 0.01, length.out = 100)
  chk <- Sys.getenv("_R_CHECK_LIMIT_CORES_", "")
  if (nzchar(chk) && chk == "TRUE") {
    # use 2 cores in CRAN/Travis/AppVeyor
    num_workers <- 2L
  } else {
    # use all cores in devtools::test()
    num_workers <- parallel::detectCores()
  }

  # Increase bootstrap times "boot_num" to a larger integer in practice
  theta_boot2 = DerivEffectBoot(Y2, X2, t_eval = t_qry2, boot_num = 3, alpha = 0.95,
                               h_bar = NULL, kernT_bar = "gaussian", h = NULL,
                               b = NULL, C_h = 7, C_b = 3, print_bw = FALSE,
                               degree = 2, deriv_ord = 1, kernT = "epanechnikov",
                               kernS = "epanechnikov", parallel = TRUE,
                               cores = num_workers)

The proposed integral estimator.

Description

This function implements our proposed integral estimator for estimating the dose-response curve.

Usage

IntegEst(
  Y,
  X,
  t_eval = NULL,
  h_bar = NULL,
  kernT_bar = "gaussian",
  h = NULL,
  b = NULL,
  C_h = 7,
  C_b = 3,
  print_bw = TRUE,
  degree = 2,
  deriv_ord = 1,
  kernT = "epanechnikov",
  kernS = "epanechnikov",
  parallel = TRUE,
  cores = 6
)
IntegEst(
  Y,
  X,
  t_eval = NULL,
  h_bar = NULL,
  kernT_bar = "gaussian",
  h = NULL,
  b = NULL,
  C_h = 7,
  C_b = 3,
  print_bw = TRUE,
  degree = 2,
  deriv_ord = 1,
  kernT = "epanechnikov",
  kernS = "epanechnikov",
  parallel = TRUE,
  cores = 6
)

Arguments

`Y`	The input n-dimensional outcome variable vector.
`X`	The input n*(d+1) matrix. The first column of X stores the treatment/exposure variables, while the other d columns are confounding variables.
`t_eval`	The m-dimensional vector for evaluating the dose-response curve. (Default: t_eval = NULL. Then, t_eval = `X[,1]`, which consists of the observed treatment variables.)
`h_bar`	The bandwidth parameter for the Nadaraya-Watson conditional CDF estimator. (Default: h_bar = NULL. Then, the Silverman's rule of thumb is applied. See Chen et al. (2016) for details.)
`kernT_bar`	The name of the kernel function for the Nadaraya-Watson conditional CDF estimator. (Default: "gaussian".)
`h`, `b`	The bandwidth parameters for the treatment/exposure variable and confounding variables in the local polynomial regression. (Default: h = NULL, b = NULL. Then, the rule-of-thumb bandwidth selector in Eq. (A1) of Yang and Tschernig (1999) is used with additional scaling factors C_h and C_b, respectively.)
`C_h`, `C_b`	The scaling factors for the rule-of-thumb bandwidth parameters.
`print_bw`	The indicator of whether the current bandwidth parameters should be printed to the console. (Default: print_bw = TRUE.)
`degree`	Degree of local polynomials. (Default: degree = 2.)
`deriv_ord`	The order of the estimated derivative of the conditional mean outcome function. (Default: deriv_ord = 1. It shouldn't be changed in most cases.)
`kernT`, `kernS`	The names of kernel functions for the treatment/exposure variable and confounding variables. (Default: kernT = "epanechnikov", kernS = "epanechnikov".)
`parallel`	The indicator of whether the function should be parallel executed. (Default: parallel = TRUE.)
`cores`	The number of cores for parallel execution. (Default: cores = 6.)

Value

The estimated dose-response curve evaluated at points t_eval.

Author(s)

Yikun Zhang, [email protected]

References

Zhang, Y., Chen, Y.-C., and Giessing, A. (2024) Nonparametric Inference on Dose-Response Curves Without the Positivity Condition. https://arxiv.org/abs/2405.09003.

Examples


  set.seed(123)
  n <- 300

  S2 <- cbind(2*runif(n) - 1, 2*runif(n) - 1)
  Z2 <- 4 * S2[, 1] + S2[, 2]
  E2 <- 0.2 * runif(n) - 0.1
  T2 <- cos(pi * Z2^3) + Z2 / 4 + E2
  Y2 <- T2^2 + T2 + 10 * Z2 + rnorm(n, mean = 0, sd = 1)
  X2 <- cbind(T2, S2)

  t_qry2 = seq(min(T2) + 0.01, max(T2) - 0.01, length.out = 100)
  chk <- Sys.getenv("_R_CHECK_LIMIT_CORES_", "")
  if (nzchar(chk) && chk == "TRUE") {
    # use 2 cores in CRAN/Travis/AppVeyor
    num_workers <- 2L
  } else {
    # use all cores in devtools::test()
    num_workers <- parallel::detectCores()
  }
  m_est2 = IntegEst(Y2, X2, t_eval = t_qry2, h_bar = NULL, kernT_bar = "gaussian",
                    h = NULL, b = NULL, C_h = 7, C_b = 3, print_bw = FALSE,
                    degree = 2, deriv_ord = 1, kernT = "epanechnikov",
                    kernS = "epanechnikov", parallel = TRUE, cores = num_workers)

  plot(t_qry2, m_est2, type="l", col = "blue", xlab = "t", lwd=5,
       ylab="(Estimated) dose-response curves")
  lines(t_qry2, t_qry2^2 + t_qry2, col = "red", lwd=3)
  legend(-2, 6, legend=c("Estimated curve", "True curve"), fill = c("blue","red"))


set.seed(123)
  n <- 300

  S2 <- cbind(2*runif(n) - 1, 2*runif(n) - 1)
  Z2 <- 4 * S2[, 1] + S2[, 2]
  E2 <- 0.2 * runif(n) - 0.1
  T2 <- cos(pi * Z2^3) + Z2 / 4 + E2
  Y2 <- T2^2 + T2 + 10 * Z2 + rnorm(n, mean = 0, sd = 1)
  X2 <- cbind(T2, S2)

  t_qry2 = seq(min(T2) + 0.01, max(T2) - 0.01, length.out = 100)
  chk <- Sys.getenv("_R_CHECK_LIMIT_CORES_", "")
  if (nzchar(chk) && chk == "TRUE") {
    # use 2 cores in CRAN/Travis/AppVeyor
    num_workers <- 2L
  } else {
    # use all cores in devtools::test()
    num_workers <- parallel::detectCores()
  }
  m_est2 = IntegEst(Y2, X2, t_eval = t_qry2, h_bar = NULL, kernT_bar = "gaussian",
                    h = NULL, b = NULL, C_h = 7, C_b = 3, print_bw = FALSE,
                    degree = 2, deriv_ord = 1, kernT = "epanechnikov",
                    kernS = "epanechnikov", parallel = TRUE, cores = num_workers)

  plot(t_qry2, m_est2, type="l", col = "blue", xlab = "t", lwd=5,
       ylab="(Estimated) dose-response curves")
  lines(t_qry2, t_qry2^2 + t_qry2, col = "red", lwd=3)
  legend(-2, 6, legend=c("Estimated curve", "True curve"), fill = c("blue","red"))

Nonparametric bootstrap inference on the dose-response curve via our integral estimator.

Description

This function implements the nonparametric bootstrap inference on the dose-response curve via our integral estimator.

Usage

IntegEstBoot(
  Y,
  X,
  t_eval = NULL,
  boot_num = 500,
  alpha = 0.95,
  h_bar = NULL,
  kernT_bar = "gaussian",
  h = NULL,
  b = NULL,
  C_h = 7,
  C_b = 3,
  print_bw = TRUE,
  degree = 2,
  deriv_ord = 1,
  kernT = "epanechnikov",
  kernS = "epanechnikov",
  parallel = TRUE,
  cores = 4
)
IntegEstBoot(
  Y,
  X,
  t_eval = NULL,
  boot_num = 500,
  alpha = 0.95,
  h_bar = NULL,
  kernT_bar = "gaussian",
  h = NULL,
  b = NULL,
  C_h = 7,
  C_b = 3,
  print_bw = TRUE,
  degree = 2,
  deriv_ord = 1,
  kernT = "epanechnikov",
  kernS = "epanechnikov",
  parallel = TRUE,
  cores = 4
)

Arguments

`Y`	The input n-dimensional outcome variable vector.
`X`	The input n*(d+1) matrix. The first column of X stores the treatment/exposure variables, while the other d columns are confounding variables.
`t_eval`	The m-dimensional vector for evaluating the dose-response curve (Default: t_eval = NULL. Then, t_eval = `X[,1]`, which consists of the observed treatment variables.)
`boot_num`	The number of bootstrapping times. (Default: boot_num = 500.)
`alpha`	The confidence level of both the uniform confidence band and pointwise confidence interval. (Default: alpha = 0.95.)
`h_bar`	The bandwidth parameter for the Nadaraya-Watson conditional CDF estimator. (Default: h_bar = NULL. Then, the Silverman's rule of thumb is applied. See Chen et al. (2016) for details.)
`kernT_bar`	The name of the kernel function for the Nadaraya-Watson conditional CDF estimator. (Default: kernT_bar = "gaussian".)
`h`, `b`	The bandwidth parameters for the treatment/exposure variable and confounding variables in the local polynomial regression. (Default: h = NULL, b = NULL. Then, the rule-of-thumb bandwidth selector in Eq. (A1) of Yang and Tschernig (1999) is used with additional scaling factors C_h and C_b, respectively.)
`C_h`, `C_b`	The scaling factors for the rule-of-thumb bandwidth parameters.
`print_bw`	The indicator of whether the current bandwidth parameters should be printed to the console. (Default: print_bw = TRUE.)
`degree`	Degree of local polynomials. (Default: degree = 2.)
`deriv_ord`	The order of the estimated derivative of the conditional mean outcome function. (Default: deriv_ord = 1. It shouldn't be changed in most cases.)
`kernT`, `kernS`	The names of kernel functions for the treatment/exposure variable and confounding variables. (Default: kernT = "epanechnikov", kernS = "epanechnikov".)
`parallel`	The indicator of whether the function should be parallel executed. (Default: parallel = TRUE.)
`cores`	The number of cores for parallel execution. (Default: cores = 6.)

Value

A list that contains four elements.

`m_est`	The estimated dose-response curve evaluated at points `t_eval`.
`m_est_boot`	The estimated dose-response curve evaluated at points `t_eval` for all the bootstrap samples.
`m_alpha`	The width of the uniform confidence band.
`m_alpha_var`	The widths of the pointwise confidence bands at evaluation points `t_eval`.

Author(s)

Yikun Zhang, [email protected]

References

Zhang, Y., Chen, Y.-C., and Giessing, A. (2024) Nonparametric Inference on Dose-Response Curves Without the Positivity Condition. https://arxiv.org/abs/2405.09003.

Examples


  set.seed(123)
  n <- 300

  S2 <- cbind(2 * runif(n) - 1, 2 * runif(n) - 1)
  Z2 <- 4 * S2[, 1] + S2[, 2]
  E2 <- 0.2 * runif(n) - 0.1
  T2 <- cos(pi * Z2^3) + Z2 / 4 + E2
  Y2 <- T2^2 + T2 + 10 * Z2 + rnorm(n, mean = 0, sd = 1)
  X2 <- cbind(T2, S2)

  t_qry2 = seq(min(T2) + 0.01, max(T2) - 0.01, length.out = 100)
  chk <- Sys.getenv("_R_CHECK_LIMIT_CORES_", "")
  if (nzchar(chk) && chk == "TRUE") {
    # use 2 cores in CRAN/Travis/AppVeyor
    num_workers <- 2L
  } else {
    # use all cores in devtools::test()
    num_workers <- parallel::detectCores()
  }

  # Increase bootstrap times "boot_num" to a larger integer in practice
  m_boot2 = IntegEstBoot(Y2, X2, t_eval = t_qry2, boot_num = 3, alpha=0.95,
                        h_bar = NULL, kernT_bar = "gaussian", h = NULL, b = NULL,
                        C_h = 7, C_b = 3, print_bw = FALSE, degree = 2,
                        deriv_ord = 1, kernT = "epanechnikov", kernS = "epanechnikov",
                        parallel = TRUE, cores = num_workers)


set.seed(123)
  n <- 300

  S2 <- cbind(2 * runif(n) - 1, 2 * runif(n) - 1)
  Z2 <- 4 * S2[, 1] + S2[, 2]
  E2 <- 0.2 * runif(n) - 0.1
  T2 <- cos(pi * Z2^3) + Z2 / 4 + E2
  Y2 <- T2^2 + T2 + 10 * Z2 + rnorm(n, mean = 0, sd = 1)
  X2 <- cbind(T2, S2)

  t_qry2 = seq(min(T2) + 0.01, max(T2) - 0.01, length.out = 100)
  chk <- Sys.getenv("_R_CHECK_LIMIT_CORES_", "")
  if (nzchar(chk) && chk == "TRUE") {
    # use 2 cores in CRAN/Travis/AppVeyor
    num_workers <- 2L
  } else {
    # use all cores in devtools::test()
    num_workers <- parallel::detectCores()
  }

  # Increase bootstrap times "boot_num" to a larger integer in practice
  m_boot2 = IntegEstBoot(Y2, X2, t_eval = t_qry2, boot_num = 3, alpha=0.95,
                        h_bar = NULL, kernT_bar = "gaussian", h = NULL, b = NULL,
                        C_h = 7, C_b = 3, print_bw = FALSE, degree = 2,
                        deriv_ord = 1, kernT = "epanechnikov", kernS = "epanechnikov",
                        parallel = TRUE, cores = num_workers)

The helper function for retrieving a kernel function and its associated statistics.

Description

This function helps retrieve the commonly used kernel function, its second moment, and its variance based on the name.

Usage

KernelRetrieval(name)
KernelRetrieval(name)

Arguments

name

The lower-case full name of the kernel function.

Value

A list that contains three elements.

`KernFunc`	The interested kernel function.
`sigmaK_sq`	The second moment of the kernel function.
`K_sq`	The variance of the kernel function.

Author(s)

Yikun Zhang, [email protected]

Examples


  kernel_result <- KernelRetrieval("epanechnikov")
  kernT <- kernel_result$KernFunc
  sigmaK_sq <- kernel_result$sigmaK_sq
  K_sq <- kernel_result$K_sq


kernel_result <- KernelRetrieval("epanechnikov")
  kernT <- kernel_result$KernFunc
  sigmaK_sq <- kernel_result$sigmaK_sq
  K_sq <- kernel_result$K_sq

The (partial) local polynomial regression.

Description

This function implements the (partial) local polynomial regression for estimating the conditional mean outcome function and its partial derivatives. We use higher-order local monomials for the treatment variable and first-order local monomials for the confounding variables.

Usage

LocalPolyReg(
  Y,
  X,
  x_eval = NULL,
  degree = 2,
  deriv_ord = 1,
  h = NULL,
  b = NULL,
  C_h = 7,
  C_b = 3,
  print_bw = TRUE,
  kernT = "epanechnikov",
  kernS = "epanechnikov"
)
LocalPolyReg(
  Y,
  X,
  x_eval = NULL,
  degree = 2,
  deriv_ord = 1,
  h = NULL,
  b = NULL,
  C_h = 7,
  C_b = 3,
  print_bw = TRUE,
  kernT = "epanechnikov",
  kernS = "epanechnikov"
)

Arguments

`Y`	The input n-dimensional outcome variable vector.
`X`	The input n*(d+1) matrix. The first column of X stores the treatment/exposure variables, while the other d columns are confounding variables.
`x_eval`	The n*(d+1) matrix for evaluating the local polynomial regression estimates. (Default: x_eval = NULL. Then, x_eval = `X`.)
`degree`	Degree of local polynomials. (Default: degree = 2.)
`deriv_ord`	The order of the estimated derivative of the conditional mean outcome function. (Default: deriv_ord = 1.)
`h`	The bandwidth parameter for the treatment/exposure variable. (Default: h = NULL. Then, the rule-of-thumb bandwidth selector in Eq. (A1) of Yang and Tschernig (1999) is used with additional scaling factors C_h.)
`b`	The bandwidth vector for the confounding variables. (Default: b = NULL. Then, the rule-of-thumb bandwidth selector in Eq. (A1) of Yang and Tschernig (1999) is used with additional scaling factors C_b.)
`C_h`	The scaling factor for the rule-of-thumb bandwidth parameter `h`.
`C_b`	The scaling factor for the rule-of-thumb bandwidth vector `b`.
`print_bw`	The indicator of whether the current bandwidth parameters should be printed to the console. (Default: print_bw = TRUE.)
`kernT`, `kernS`	The names of kernel functions for the treatment/exposure variable and confounding variables. (Default: kernT = "epanechnikov", kernS = "epanechnikov".)

Value

The estimated conditional mean outcome function or its partial derivatives evaluated at points x_eval.

Author(s)

Yikun Zhang, [email protected]

References

Zhang, Y., Chen, Y.-C., and Giessing, A. (2024) Nonparametric Inference on Dose-Response Curves Without the Positivity Condition. https://arxiv.org/abs/2405.09003.

Fan, J. and Gijbels, I. (1996) Local Polynomial Modelling and its Applications. Chapman & Hall/CRC.

Examples

library(parallel)
set.seed(123)
n <- 300
S2 <- cbind(2 * runif(n) - 1, 2 * runif(n) - 1)
Z2 <- 4 * S2[, 1] + S2[, 2]
E2 <- 0.2 * runif(n) - 0.1
T2 <- cos(pi * Z2^3) + Z2 / 4 + E2
Y2 <- T2^2 + T2 + 10 * Z2 + rnorm(n, mean = 0, sd = 1)
X2 <- cbind(T2, S2)
t_qry2 = seq(min(T2) + 0.01, max(T2) - 0.01, length.out = 100)
chk <- Sys.getenv("_R_CHECK_LIMIT_CORES_", "")
if (nzchar(chk) && chk == "TRUE") {
  # use 2 cores in CRAN/Travis/AppVeyor
  num_workers <- 2L
} else {
  # use all cores in devtools::test()
  num_workers <- parallel::detectCores()
}
Y_est2 = LocalPolyReg(Y2, X2, x_eval = NULL, degree = 2, deriv_ord = 0,
                      h = NULL, b = NULL, C_h = 7, C_b = 3, print_bw = TRUE,
                      kernT = "epanechnikov", kernS = "epanechnikov")

library(parallel)
set.seed(123)
n <- 300
S2 <- cbind(2 * runif(n) - 1, 2 * runif(n) - 1)
Z2 <- 4 * S2[, 1] + S2[, 2]
E2 <- 0.2 * runif(n) - 0.1
T2 <- cos(pi * Z2^3) + Z2 / 4 + E2
Y2 <- T2^2 + T2 + 10 * Z2 + rnorm(n, mean = 0, sd = 1)
X2 <- cbind(T2, S2)
t_qry2 = seq(min(T2) + 0.01, max(T2) - 0.01, length.out = 100)
chk <- Sys.getenv("_R_CHECK_LIMIT_CORES_", "")
if (nzchar(chk) && chk == "TRUE") {
  # use 2 cores in CRAN/Travis/AppVeyor
  num_workers <- 2L
} else {
  # use all cores in devtools::test()
  num_workers <- parallel::detectCores()
}
Y_est2 = LocalPolyReg(Y2, X2, x_eval = NULL, degree = 2, deriv_ord = 0,
                      h = NULL, b = NULL, C_h = 7, C_b = 3, print_bw = TRUE,
                      kernT = "epanechnikov", kernS = "epanechnikov")

The main function of the (partial) local polynomial regression.

Description

This function implements the main part of the (partial) local polynomial regression for estimating the conditional mean outcome function and its partial derivatives.

Usage

LocalPolyRegMain(
  Y,
  X,
  x_eval = NULL,
  degree = 2,
  deriv_ord = 1,
  h = NULL,
  b = NULL,
  kernT = "epanechnikov",
  kernS = "epanechnikov"
)
LocalPolyRegMain(
  Y,
  X,
  x_eval = NULL,
  degree = 2,
  deriv_ord = 1,
  h = NULL,
  b = NULL,
  kernT = "epanechnikov",
  kernS = "epanechnikov"
)

Arguments

`Y`	The input n-dimensional outcome variable vector.
`X`	The input n*(d+1) matrix. The first column of X stores the treatment/exposure variables, while the other d columns are confounding variables.
`x_eval`	The n*(d+1) matrix for evaluating the local polynomial regression estimates. (Default: x_eval = NULL. Then, x_eval = `X`.)
`degree`	Degree of local polynomials. (Default: degree = 2.)
`deriv_ord`	The order of the estimated derivative of the conditional mean outcome function. (Default: deriv_ord = 1.)
`h`, `b`	The bandwidth parameters for the treatment/exposure variable and confounding variables (Default: h = NULL, b = NULL. Then, the rule-of-thumb bandwidth selector in Eq. (A1) of Yang and Tschernig (1999) is used with additional scaling factors C_h and C_b, respectively.)
`kernT`, `kernS`	The names of kernel functions for the treatment/exposure variable and confounding variables. (Default: kernT = "epanechnikov", kernS = "epanechnikov".)

Value

The estimated conditional mean outcome function or its partial derivatives evaluated at points x_eval.

Author(s)

Yikun Zhang, [email protected]

References

Zhang, Y., Chen, Y.-C., and Giessing, A. (2024) Nonparametric Inference on Dose-Response Curves Without the Positivity Condition. https://arxiv.org/abs/2405.09003.

Fan, J. and Gijbels, I. (1996) Local Polynomial Modelling and its Applications. Chapman & Hall/CRC.

The regression adjustment estimator of the dose-response curve.

Description

This function implements the standard regression adjustment or G-computation estimator of the dose-response curve or its derivative via (partial) local polynomial regression.

Usage

RegAdjust(
  Y,
  X,
  t_eval = NULL,
  h = NULL,
  b = NULL,
  C_h = 7,
  C_b = 3,
  print_bw = TRUE,
  degree = 2,
  deriv_ord = 0,
  kernT = "epanechnikov",
  kernS = "epanechnikov",
  parallel = TRUE,
  cores = 6
)
RegAdjust(
  Y,
  X,
  t_eval = NULL,
  h = NULL,
  b = NULL,
  C_h = 7,
  C_b = 3,
  print_bw = TRUE,
  degree = 2,
  deriv_ord = 0,
  kernT = "epanechnikov",
  kernS = "epanechnikov",
  parallel = TRUE,
  cores = 6
)

Arguments

`Y`	The input n-dimensional outcome variable vector.
`X`	The input n*(d+1) matrix. The first column of X stores the treatment/exposure variables, while the other d columns are confounding variables.
`t_eval`	The m-dimensional vector for evaluating the dose-response curve. (Default: t_eval = NULL. Then, t_eval = `X[,1]`, which consists of the observed treatment variables.)
`h`, `b`	The bandwidth parameters for the treatment/exposure variable and confounding variables (Default: h = NULL, b = NULL. Then, the rule-of-thumb bandwidth selector in Eq. (A1) of Yang and Tschernig (1999) is used with additional scaling factors C_h and C_b, respectively.)
`C_h`, `C_b`	The scaling factors for the rule-of-thumb bandwidth parameters.
`print_bw`	The indicator of whether the current bandwidth parameters should be printed to the console. (Default: print_bw = TRUE.)
`degree`	Degree of local polynomials. (Default: degree = 2.)
`deriv_ord`	The order of the estimated derivative of the conditional mean outcome function. (Default: deriv_ord = 1.)
`kernT`, `kernS`	The names of kernel functions for the treatment/exposure variable and confounding variables. (Default: kernT = "epanechnikov", kernS = "epanechnikov".)
`parallel`	The indicator of whether the function should be parallel executed. (Default: parallel = TRUE.)
`cores`	The number of cores for parallel execution. (Default: cores = 6.)

Value

The estimated dose-response curves or its derivatives evaluated at points t_eval.

Author(s)

Yikun Zhang, [email protected]

References

Zhang, Y., Chen, Y.-C., and Giessing, A. (2024) Nonparametric Inference on Dose-Response Curves Without the Positivity Condition. https://arxiv.org/abs/2405.09003.

Fan, J. and Gijbels, I. (1996) Local Polynomial Modelling and its Applications. Chapman & Hall/CRC.

Examples


  library(parallel)
  set.seed(123)
  n <- 300

  S2 <- cbind(2 * runif(n) - 1, 2 * runif(n) - 1)
  Z2 <- 4 * S2[, 1] + S2[, 2]
  E2 <- 0.2 * runif(n) - 0.1
  T2 <- cos(pi * Z2^3) + Z2 / 4 + E2
  Y2 <- T2^2 + T2 + 10 * Z2 + rnorm(n, mean = 0, sd = 1)
  X2 <- cbind(T2, S2)

  t_qry2 = seq(min(T2) + 0.01, max(T2) - 0.01, length.out = 100)
  chk <- Sys.getenv("_R_CHECK_LIMIT_CORES_", "")
  if (nzchar(chk) && chk == "TRUE") {
    # use 2 cores in CRAN/Travis/AppVeyor
    num_workers <- 2L
  } else {
    # use all cores in devtools::test()
    num_workers <- parallel::detectCores()
  }
  Y_RA2 = RegAdjust(Y2, X2, t_eval = t_qry2, h = NULL, b = NULL, C_h = 7, C_b = 3,
                    print_bw = FALSE, degree = 2, deriv_ord = 0,
                    kernT = "epanechnikov", kernS = "epanechnikov",
                    parallel = TRUE, cores = num_workers)


library(parallel)
  set.seed(123)
  n <- 300

  S2 <- cbind(2 * runif(n) - 1, 2 * runif(n) - 1)
  Z2 <- 4 * S2[, 1] + S2[, 2]
  E2 <- 0.2 * runif(n) - 0.1
  T2 <- cos(pi * Z2^3) + Z2 / 4 + E2
  Y2 <- T2^2 + T2 + 10 * Z2 + rnorm(n, mean = 0, sd = 1)
  X2 <- cbind(T2, S2)

  t_qry2 = seq(min(T2) + 0.01, max(T2) - 0.01, length.out = 100)
  chk <- Sys.getenv("_R_CHECK_LIMIT_CORES_", "")
  if (nzchar(chk) && chk == "TRUE") {
    # use 2 cores in CRAN/Travis/AppVeyor
    num_workers <- 2L
  } else {
    # use all cores in devtools::test()
    num_workers <- parallel::detectCores()
  }
  Y_RA2 = RegAdjust(Y2, X2, t_eval = t_qry2, h = NULL, b = NULL, C_h = 7, C_b = 3,
                    print_bw = FALSE, degree = 2, deriv_ord = 0,
                    kernT = "epanechnikov", kernS = "epanechnikov",
                    parallel = TRUE, cores = num_workers)

The rule-of-thumb bandwidth selector for the (partial) local polynomial regression.

Description

This function implements the rule-of-thumb bandwidth selector for the (partial) local polynomial regression.

Usage

RoTBWLocalPoly(
  Y,
  X,
  kernT = "epanechnikov",
  kernS = "epanechnikov",
  C_h = 7,
  C_b = 3
)
RoTBWLocalPoly(
  Y,
  X,
  kernT = "epanechnikov",
  kernS = "epanechnikov",
  C_h = 7,
  C_b = 3
)

Arguments

`Y`	The input n-dimensional outcome variable vector.
`X`	The input n*(d+1) matrix. The first column of X stores the treatment/exposure variables, while the other d columns are confounding variables.
`kernT`, `kernS`	The names of kernel functions for the treatment/exposure variable and confounding variables. (Default: kernT = "epanechnikov", kernS = "epanechnikov".)
`C_h`, `C_b`	The scaling factors for the rule-of-thumb bandwidth parameters.

Value

A list that contains two elements.

`h`	The rule-of-thumb bandwidth parameter for the treatment/exposure variable.
`b`	The rule-of-thumb bandwidth vector for the confounding variables.

Author(s)

Yikun Zhang, [email protected]

References

Zhang, Y., Chen, Y.-C., and Giessing, A. (2024) Nonparametric Inference on Dose-Response Curves Without the Positivity Condition. https://arxiv.org/abs/2405.09003.

Yang, L. and Tschernig, R. (1999). Multivariate Bandwidth Selection for Local Linear Regression. Journal of the Royal Statistical Society Series B: Statistical Methodology, 61(4), 793-815.

Package 'npDoseResponse'

Help Index

The proposed localized derivative estimator.

Description

Usage

Arguments

Value

Author(s)

References

Examples

Nonparametric bootstrap inference on the derivative effect via our localized derivative estimator.

Description

Usage

Arguments

Value

Author(s)

References

Examples

The proposed integral estimator.

Description

Usage

Arguments

Value

Author(s)

References

Examples

Nonparametric bootstrap inference on the dose-response curve via our integral estimator.

Description

Usage

Arguments

Value

Author(s)

References

Examples

The helper function for retrieving a kernel function and its associated statistics.

Description

Usage

Arguments

Value

Author(s)

Examples

The (partial) local polynomial regression.

Description

Usage

Arguments

Value

Author(s)

References

Examples

The main function of the (partial) local polynomial regression.

Description

Usage

Arguments

Value

Author(s)

References

The regression adjustment estimator of the dose-response curve.

Description

Usage

Arguments

Value

Author(s)

References

Examples

The rule-of-thumb bandwidth selector for the (partial) local polynomial regression.

Description

Usage

Arguments

Value

Author(s)

References