AUC_Spline_matrix_B: Spline Interpolation Method - Matrix of the zero order...

In marie-alexandre/AUCcomparison: Statistical test - Between group comparison of AUC

Description

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In the area under the curve calculation using the spline interpolation method, the vector of the second derivative of the outcome of interest \mjseqnY is expressed as \mjseqnA Y^” = B Y + F. This function calculate calculate the matrix B.

Usage

AUC_Spline_matrix_B(time)

Arguments

time	a numerical vector of time points of length m (x-axis coordinates).

Details

The tridiagonal matrix \mjteqnBBB is defined as (for the "not-a-knot boundary conditions): The \mjteqnjjjth line of the matrix, \mjteqnB_[j,\ :]B_[j,\ :]B_[j,\ :] is given by \mjtdeqnB_[j,\ :] = \left(0, \cdots, 0\right) \ if \ j=1B_[j,\ :] = \left(0, \cdots, 0\right) \ if \ j=1B_[j,\ :] = \left(0, \cdots, 0\right) \ if \ j=1 \mjtdeqnB_[j,\ :] = \left(0, \cdots, 0\right) \ if \ j=mB_[j,\ :] = \left(0, \cdots, 0\right) \ if \ j=mB_[j,\ :] = \left(0, \cdots, 0\right) \ if \ j=m \mjtdeqnB_[j,\ :] = \left(0_1, \cdots, 0_j-2, \frac1h_j,-\left[\frac1h_j + \frac1h_j+1\right], \frac1h_j+1, 0_j+2, \cdots, 0_m \right) \ otherwise B_[j,\ :] = \left(0_1, \cdots, 0_j-2, \frac1h_j,-\left[\frac1h_j + \frac1h_j+1\right], \frac1h_j+1, 0_j+2, \cdots, 0_m \right) \ otherwise B_[j,\ :] = \left(0_1, \cdots, 0_j-2, \frac1h_j,-\left[\frac1h_j + \frac1h_j+1\right], \frac1h_j+1, 0_j+2, \cdots, 0_m \right) \ otherwise

Value

a tridiagonal matrix corresponding to the weights of the variable of interest in the spline interpolation method. In this version, the matrix is build considering the "not-a-knot" spline boundary conditions.

marie-alexandre/AUCcomparison documentation built on Dec. 21, 2021, 1:52 p.m.