AUC_Lagrange_Cjp_coefficients: Time Dependent Coefficients Cjp for AUC Lagrange...

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

Description

\loadmathjax

This function calculate the time-dependent coefficients Cjp involved in the calculation of the are under the curve when the Lagrange interpolation method is used.

Usage

AUC_Lagrange_Cjp_coefficients(ind_j,ind_p,t)

Arguments

ind_j	a numerical scalar indicating the value of the index j.
ind_p	a numerical scalar indicating the value of the index p
t	a numerical vector of time points (x-axis coordinates) to consider for the AUC calculation.

Details

The coefficients \mjteqnC_jpC_jpC_jp involved in the calculation of the AUC are defined as \mjtdeqnC_2p = (t_2-t_1)\prod_l=0 ;\ l\neq p^P=2 t_1+l - \frac(t_2^2-t_1^2)2\sum_l=0 ;\ l\neq p^P=2 t_1+l + \frac(t_2^3-t_1^3)3 C_2p = (t_2-t_1)\prod_l=0 ;\ l\neq p^P=2 t_1+l - \frac(t_2^2-t_1^2)2\sum_l=0 ;\ l\neq p^P=2 t_1+l + \frac(t_2^3-t_1^3)3 C_2p = (t_2-t_1)\prod_l=0 ;\ l\neq p^P=2 t_1+l - \frac(t_2^2-t_1^2)2\sum_l=0 ;\ l\neq p^P=2 t_1+l + \frac(t_2^3-t_1^3)3 \mjtdeqnC_mp = (t_m-t_m-1)\prod_l=0 ;\ l\neq p^P=2 t_m-2+l - \frac(t_m^2-t_m-1^2)2\sum_l=0 ;\ l\neq p^P=2 t_m-2+l + \frac(t_m^3-t_m-1^3)3 C_mp = (t_m-t_m-1)\prod_l=0 ;\ l\neq p^P=2 t_m-2+l - \frac(t_m^2-t_m-1^2)2\sum_l=0 ;\ l\neq p^P=2 t_m-2+l + \frac(t_m^3-t_m-1^3)3 C_mp = (t_m-t_m-1)\prod_l=0 ;\ l\neq p^P=2 t_m-2+l - \frac(t_m^2-t_m-1^2)2\sum_l=0 ;\ l\neq p^P=2 t_m-2+l + \frac(t_m^3-t_m-1^3)3 \mjtdeqnC_jp = -(t_j-t_j-1)\prod_l=0 ;\ l\neq p^P=3 t_j-2+l + \frac(t_j^2-t_j-1^2)2\sum_l_1=0 ;\ l_1\neq p^P-1=2\sum_l_2=l_1+1 ;\ l_2\neq p^P=3t_j-2+l_1\cdot t_j-2+l_2 - C_jp = -(t_j-t_j-1)\prod_l=0 ;\ l\neq p^P=3 t_j-2+l + \frac(t_j^2-t_j-1^2)2\sum_l_1=0 ;\ l_1\neq p^P-1=2\sum_l_2=l_1+1 ;\ l_2\neq p^P=3t_j-2+l_1\cdot t_j-2+l_2 - C_jp = -(t_j-t_j-1)\prod_l=0 ;\ l\neq p^P=3 t_j-2+l + \frac(t_j^2-t_j-1^2)2\sum_l_1=0 ;\ l_1\neq p^P-1=2\sum_l_2=l_1+1 ;\ l_2\neq p^P=3t_j-2+l_1\cdot t_j-2+l_2 - \mjtdeqn\frac(t_j^3-t_j-1^3)3 \sum_l=0 ;\ l\neq p^P=3 t_j-2+l + \frac(t_j^4-t_j-1^4)4\frac(t_j^3-t_j-1^3)3 \sum_l=0 ;\ l\neq p^P=3 t_j-2+l + \frac(t_j^4-t_j-1^4)4\frac(t_j^3-t_j-1^3)3 \sum_l=0 ;\ l\neq p^P=3 t_j-2+l + \frac(t_j^4-t_j-1^4)4 where \mjteqnmmm is the number of time points in the vector t.

Value

a numerical scalar corresponding to the coefficient \mjteqnC_jpC_jpC_jp evaluated for j = ind_j and p = ind_p.

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