# Multivar.PCAContCont: Compute the multivariate predictive causal association (PCA)... In EffectTreat: Prediction of Therapeutic Success

## Description

The function Multivar.PCA.ContCont computes the predictive causal association (PCA) when S = the vector of pretreatment predictors and T = the True endpoint. All S and T should be continuous normally distributed endpoints. See Details below.

## Usage

 1 Multivar.PCA.ContCont(Sigma_TT, Sigma_TS, Sigma_SS, T0T1=seq(-1, 1, by=.01), M=NA) 

## Arguments

 Sigma_TT The variance-covariance matrix \bold{Σ}_{TT}=≤ft(\begin{array}{cc}σ_{T0T0} & σ_{T0T1} \\ σ_{T0T1} & σ_{T1T1}\end{array}\right). Sigma_TS The matrix that contains the covariances σ_{T0Sr}, σ_{T1Sr}. For example, when there are 2 pretreatment predictors \bold{Σ}_{TS}=≤ft(\begin{array}{cc}σ_{T0S1} & σ_{T0S2} \\ σ_{T1S1} & σ_{T1S2}\end{array}\right). Sigma_SS The variance-covariance matrix of the pretreatment predictors. For example, when there are 2 pretreatment predictors \bold{Σ}_{SS}=≤ft(\begin{array}{cc}σ_{S1S1} & σ_{S1S2} \\ σ_{S1S2} & σ_{S2S2}\end{array}\right). T0T1 A scalar or vector that contains the correlation(s) between the counterfactuals T_0 and T_1 that should be considered in the computation of R^2_{ψ}. Default seq(-1, 1, by=.01), i.e., the values -1, -0.99, -0.98, ..., 1. M If M=NA, all correlation(s) between the counterfactuals T_0 and T_1 specified in the argument T0T1 are used to compute R^2_{ψ}. If M=m, random draws are taken from T0T1 until m R^2_{ψ} are found. Default M=NA.

## Value

An object of class Multivar.PCA.ContCont with components,

 Total.Num.Matrices An object of class numeric that contains the total number of matrices that can be formed as based on the user-specified correlations in the function call. Pos.Def A data.frame that contains the positive definite matrices that can be formed based on the user-specified correlations. These matrices are used to compute the vector of the R^2_{ψ} values. PCA A scalar or vector that contains the PCA (R^2_{ψ}) value(s). R2_psi_g A Data.frame that contains R^2_{ψ g}.

## Author(s)

Wim Van der Elst, Ariel Alonso, & Geert Molenberghs

## References

Alonso, A., & Van der Elst, W. (submitted). Evaluating multivariate predictors of therapeutic success: a causal inference approach.

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 # First specify the covariance matrices to be used Sigma_TT = matrix(c(177.870, NA, NA, 162.374), byrow=TRUE, nrow=2) Sigma_TS = matrix(data = c(-45.140, -109.599, 11.290, -56.542, -106.897, 20.490), byrow = TRUE, nrow = 2) Sigma_SS = matrix(data=c(840.564, 73.936, -3.333, 73.936, 357.719, -30.564, -3.333, -30.564, 95.063), byrow = TRUE, nrow = 3) # Compute PCA Results <- Multivar.PCA.ContCont(Sigma_TT = Sigma_TT, Sigma_TS = Sigma_TS, Sigma_SS = Sigma_SS) # Evaluate results summary(Results) plot(Results) 

EffectTreat documentation built on July 8, 2020, 7:17 p.m.