DerivEffect {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
)

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, [e-mail]

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"))