R/DerivEffect.R

In npDoseResponse: Nonparametric Estimation and Inference on Dose-Response Curves

#' The proposed localized derivative estimator.
#'
#' This function implements our proposed estimator for estimating the derivative
#' of a dose-response curve via Nadaraya-Watson conditional CDF estimator.
#'
#' @param Y The input n-dimensional outcome variable vector.
#' @param 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.
#' @param t_eval The m-dimensional vector for evaluating the derivative. (Default:
#' t_eval = NULL. Then, t_eval = \code{X[,1]}, which consists of the observed treatment variables.)
#' @param 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.)
#' @param kernT_bar The name of the kernel function for the Nadaraya-Watson conditional
#' CDF estimator. (Default: "gaussian".)
#' @param 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.)
#' @param C_h,C_b The scaling factors for the rule-of-thumb bandwidth parameters.
#' @param print_bw The indicator of whether the current bandwidth parameters
#' should be printed to the console. (Default: print_bw = TRUE.)
#' @param degree Degree of local polynomials. (Default: degree = 2.)
#' @param 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.)
#' @param kernT,kernS The names of kernel functions for the treatment/exposure
#' variable and confounding variables. (Default: kernT = "epanechnikov",
#' kernS = "epanechnikov".)
#' @param parallel The indicator of whether the function should be parallel
#' executed. (Default: parallel = TRUE.)
#' @param cores The number of cores for parallel execution. (Default: cores = 6.)
#'
#' @return The estimated derivative of the dose-response curve evaluated at
#' points \code{t_eval}.
#'
#' @author Yikun Zhang, \email{yikunzhang@@foxmail.com}
#' @references Zhang, Y., Chen, Y.-C., and Giessing, A. (2024)
#' \emph{Nonparametric Inference on Dose-Response Curves Without the Positivity Condition.}
#' \url{https://arxiv.org/abs/2405.09003}.
#'
#' Hall, P., Wolff, R. C., and Yao, Q. (1999) \emph{Methods for Estimating A
#' Conditional Distribution Function. Journal of the American Statistical Association,
#' 94 (445): 154-163}.
#' @keywords curve dose-response a of derivative the of estimator localized
#'
#' @examples
#' \donttest{
#'   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"))
#' }
#'
#' @export
#' @importFrom parallel mclapply
#' @importFrom stats sd
#'

DerivEffect <- function(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) {
  if (is.null(t_eval)) {
    t_eval <- X[,1]
  }

  n <- nrow(X)
  d <- 1
  if (is.null(h_bar)) {
    h_bar <- (4 / (d + 2))^(1 / (d + 4)) * (n^(-1 / (d + 4))) * sd(X[,1]) * sqrt((n-1)/n)
  }

  if (print_bw) {
    cat("The current bandwidth for the conditional CDF estimator is", h_bar, ".\n")
  }

  kernel_result <- KernelRetrieval(kernT_bar)
  kernT_bar <- kernel_result$KernFunc

  weight_mat <- kernT_bar((outer(t_eval, X[,1], "-")) / h_bar)
  weight_mat <- t(weight_mat / rowSums(weight_mat))
  weight_mat[is.nan(weight_mat)] <- 0

  if (parallel) {
    # Use parallel computing
    beta_mat <- mclapply(t_eval, function(t) {
      X_mat <- as.matrix(cbind(rep(t, n), X[, -1]))
      return(LocalPolyReg(Y, X, x_eval = X_mat, degree = degree, deriv_ord = deriv_ord,
                          h = h, b = b, C_h = C_h, C_b = C_b, print_bw = print_bw,
                          kernT = kernT, kernS = kernS))
    }, mc.cores = cores)
    beta_mat <- do.call(cbind, beta_mat)
  } else {
    beta_mat <- matrix(0, nrow = n, ncol = length(t_eval))
    for (i in 1:length(t_eval)) {
      X_mat <- as.matrix(cbind(rep(t_eval[i], n), X[, -1]))
      beta_mat[, i] <- LocalPolyReg(Y, X, x_eval = X_mat, degree = degree,
                                    deriv_ord = deriv_ord, h = h, b = b,
                                    C_h = C_h, C_b = C_b, print_bw = print_bw,
                                    kernT = kernT, kernS = kernS)
    }
  }

  theta_C <- colSums(weight_mat * beta_mat)
  return(theta_C)
}