R/gridpts_h1_hupdate_rcpp_interface.R

In keaven/gsDesign2: Group Sequential Design with Non-Constant Effect

#  Copyright (c) 2022 Merck Sharp & Dohme Corp. a subsidiary of Merck & Co., Inc., Rahway, NJ, USA.
#
#  This file is part of the gsDesign2 program.
#
#  gsDesign2 is free software: you can redistribute it and/or modify
#  it under the terms of the GNU General Public License as published by
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#  GNU General Public License for more details.
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#  You should have received a copy of the GNU General Public License
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#' @import Rcpp
NULL

#' Grid points for group sequential design numerical integration
#'
#' Points and weights for Simpson's rule numerical integration from
#' p 349 - 350 of Jennison and Turnbull book.
#' This is not used for arbitrary integration, but for the canonical form of Jennison and Turnbull.
#' mu is computed elsewhere as drift parameter times sqrt of information.
#' Since this is a lower-level routine, no checking of input is done; calling routines should
#' ensure that input is correct.
#' Lower limit of integration can be \code{-Inf} and upper limit of integration can be \code{Inf}
#'
#' @details
#' Jennison and Turnbull (p 350) claim accuracy of \code{10E-6} with \code{r=16}.
#' The numerical integration grid spreads out at the tail to enable accurate tail probability calcuations.
#'
#'
#' @param r Integer, at least 2; default of 18 recommended by Jennison and Turnbull
#' @param mu Mean of normal distribution (scalar) under consideration
#' @param a lower limit of integration (scalar)
#' @param b upper limit of integration (scalar \code{> a})
#' @section Specification:
#' \if{latex}{
#'  \itemize{
#'    \item Define odd numbered grid points for real line.
#'    \item Trim points outside of [a, b] and include those points.
#'    \item If extreme, include only 1 point where density will be essentially 0.
#'    \item Define even numbered grid points between the odd ones.
#'    \item Compute weights for odd numbered grid points.
#'    \item Combine odd- and even-numbered grid points with their corresponding weights.
#'    \item Return a tibble of with grid points in z and numerical integration weights in z.
#'   }
#' }
#' \if{html}{The contents of this section are shown in PDF user manual only.}
#'
#' @return A \code{list} with grid points in \code{z} and numerical integration weights in \code{w}
#' 
#' @examples
#'
#' # approximate variance of standard normal (i.e., 1)
#' g <- gridpts()
#' sum((g$z)^2 * g$w * dnorm(g$z))
#'
#' # approximate probability above .95 quantile (i.e., .05)
#' g <- gridpts(a = qnorm(.95), b = Inf)
#' sum(g$w * dnorm(g$z))
#' @noRd
gridpts <- function(r = 18, mu = 0, a = -Inf, b = Inf) {
  .gridptsRcpp(r = r, mu = mu, a = a, b = b)
}

#' Initialize numerical integration for group sequential design
#'
#' Compute grid points for first interim analysis in a group sequential design
#'
#' @param r Integer, at least 2; default of 18 recommended by Jennison and Turnbull
#' @param theta Drift parameter for first analysis
#' @param I Information at first analysis
#' @param a lower limit of integration (scalar)
#' @param b upper limit of integration (scalar \code{> a})
#'
#' @details Mean for standard normal distribution under consideration is \code{mu = theta * sqrt(I)}
#' @section Specification:
#' \if{latex}{
#'  \itemize{
#'    \item Compute drift at analysis 1.
#'    \item Compute deviation from drift.
#'    \item Compute standard normal density, multiply by grid weight.
#'    \item Return a tibble of z, w, and h.
#'   }
#' }
#' \if{html}{The contents of this section are shown in PDF user manual only.}
#'
#' @return A \code{list} with grid points in \code{z}, numerical integration weights in \code{w},
#' and a normal density with mean \code{mu = theta * sqrt{I}} and variance 1 times the weight in \code{w}.
#'
#' @examples
#' 
#' # Replicate variance of 1, mean of 35
#' g <- h1(theta = 5, I = 49)
#' mu <- sum(g$z * g$h)
#' var <- sum((g$z - mu)^2 * g$h)
#'
#' # Replicate p-value of .0001 by numerical integration of tail
#' g <- h1(a = qnorm(.9999))
#' sum(g$h)
#' @noRd
h1 <- function(r = 18, theta = 0, I = 1, a = -Inf, b = Inf){
  .h1Rcpp(r = r, theta = theta, I = I, a = a, b = b)
}

#' Update numerical integration for group sequential design
#'
#' Update grid points for numerical integration from one analysis to the next
#'
#' @param r Integer, at least 2; default of 18 recommended by Jennison and Turnbull
#' @param theta Drift parameter for current analysis
#' @param I Information at current analysis
#' @param a lower limit of integration (scalar)
#' @param b upper limit of integration (scalar \code{> a})
#' @param thetam1  Drift parameter for previous analysis
#' @param Im1 Information at previous analysis
#' @param gm1 numerical integration grid from \code{h1()} or previous run of \code{hupdate()}
#' @section Specification:
#' \if{latex}{
#'  \itemize{
#'    \item Compute the square root of the change in information.
#'    \item Compute the grid points for group sequential design numerical integration.
#'    \item Update the integration.
#'    \item Return a tibble of z, w, and h.
#'   }
#' }
#' \if{html}{The contents of this section are shown in PDF user manual only.}
#'
#' @return A \code{list} with grid points in \code{z}, numerical integration weights in \code{w},
#' and a normal density with mean \code{mu = theta * sqrt{I}} and variance 1 times the weight in \code{w}.
#'
#' @examples
#' 
#' # 2nd analysis with no interim bound and drift 0 should have mean 0, variance 1
#' g <- hupdate()
#' mu <- sum(g$z * g$h)
#' var <- sum((g$z - mu)^2 * g$h)
#' @noRd
hupdate <- function(r = 18, theta = 0, I = 2, a = -Inf, b = Inf, thetam1 = 0, Im1 = 1, gm1 = h1()){
  .hupdateRcpp(r = r, theta = theta, I = I, a = a, b = b, thetam1 = thetam1, Im1 = Im1, gm1 = gm1)
}