Predict.Treat.Multivar.ContCont function

Compute the predicted treatment effect on the true endpoint of a patient based on his or her observed vector of pretreatment predictor values in the continuous-continuous setting

This function computes the predicted $\Delta T_j$ of a patient based on the vector of pretreatment values $\bold{S}_j$ of a patient in the continuous-continuous setting.

Predict.Treat.Multivar.ContCont(Sigma_TT, Sigma_TS, Sigma_SS, Beta, 
S, mu_S, T0T1=seq(-1, 1, by=.01))

Arguments

• Sigma_TT: The variance-covariance matrix $\bold{\Sigma}_{TT}=\left(\begin{array}{cc}\sigma_{T0T0} & \sigma_{T0T1} \\ \sigma_{T0T1} & \sigma_{T1T1}\end{array}\right)$.
• Sigma_TS: The matrix that contains the covariances $\sigma_{T0Sr}$, $\sigma_{T1Sr}$. For example, when there are $2$ pretreatment predictors $\bold{\Sigma}_{TS}=\left(\begin{array}{cc}\sigma_{T0S1} & \sigma_{T0S2} \\ \sigma_{T1S1} & \sigma_{T1S2}\end{array}\right)$.
• Sigma_SS: The variance-covariance matrix of the pretreatment predictors. For example, when there are $2$ pretreatment predictors $\bold{\Sigma}_{SS}=\left(\begin{array}{cc}\sigma_{S1S1} & \sigma_{S1S2} \\ \sigma_{S1S2} & \sigma_{S2S2}\end{array}\right)$.
• Beta: The estimated treatment effect on the true endpoint (in the validation sample).
• S: The vector of observed pretreatment values $\bold{S}_j$ for a patient.
• mu_S: The vector of estimated means of the pretreatment predictor (in the validation sample).
• 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 $\rho_{\psi}$. Default seq(-1, 1, by=.01), i.e., the values $-1$, $-0.99$, $-0.98$, ..., $1$.

Returns

An object of class PCA.Predict.Treat.Multivar.ContCont with components, - Pred_T: The predicted $\Delta T_j$.

• Var_Delta.T_S: The variance $\sigma_{\Delta_{T}}$|$S_j$.

• T0T1: The correlation between the counterfactuals $T_{0}$, $T_{1}$.

References

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

Author(s)

Wim Van der Elst, Ariel Alonso, & Geert Molenberghs

See Also

PCA.ContCont , Multivar.PCA.ContCont

Examples

# 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)

# Specify treatment effect (Beta), means of vector S (mu_s), and 
# observed pretreatment variable values for patient (S)
Beta <- -0.9581 # treatment effect
mu_S = matrix(c(66.8149, 84.8393, 25.1939), nrow=3) #means S_1--S_3
S = matrix(c(90, 180, 30), nrow=3) # S_1--S_3 values for a patient

# predict Delta_T based on S
Pred_S <- Predict.Treat.Multivar.ContCont(Sigma_TT=Sigma_TT, Sigma_TS=Sigma_TS,
Sigma_SS=Sigma_SS, Beta=Beta, S=S, mu_S=mu_S, T0T1=seq(-1, 1, by=.01))

# Explore results
summary(Pred_S)
plot(Pred_S)