Type:	Package
Title:	Nonparametric Estimation and Inference on Dose-Response Curves
Version:	0.1
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>.
URL:	https://github.com/zhangyk8/npDoseResponse/
BugReports:	https://github.com/zhangyk8/npDoseResponse/issues
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.2.3
Imports:	parallel, stats
Suggests:	locpol
Maintainer:	Yikun Zhang <yikunzhang@foxmail.com>
NeedsCompilation:	no
Packaged:	2024-05-27 15:59:29 UTC; yikun
Author:	Yikun Zhang [aut, cre], Yen-Chi Chen [aut]
Repository:	CRAN
Date/Publication:	2024-05-28 11:30:02 UTC

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
)

Arguments

Value

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

Author(s)

Yikun Zhang, yikunzhang@foxmail.com

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"))

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
)

Arguments

Value

A list that contains four elements.

Author(s)

Yikun Zhang, yikunzhang@foxmail.com

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)

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
)

Arguments

Value

The estimated dose-response curve evaluated at points t_eval.

Author(s)

Yikun Zhang, yikunzhang@foxmail.com

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"))

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
)

Arguments

Value

A list that contains four elements.

Author(s)

Yikun Zhang, yikunzhang@foxmail.com

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)

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)

Arguments

Value

A list that contains three elements.

Author(s)

Yikun Zhang, yikunzhang@foxmail.com

Examples

  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"
)

Arguments

Value

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

Author(s)

Yikun Zhang, yikunzhang@foxmail.com

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")

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"
)

Arguments

Value

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

Author(s)

Yikun Zhang, yikunzhang@foxmail.com

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
)

Arguments

Value

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

Author(s)

Yikun Zhang, yikunzhang@foxmail.com

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)

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
)

Arguments

Value

A list that contains two elements.

Author(s)

Yikun Zhang, yikunzhang@foxmail.com

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.