Predict.Treat.T0T1ContCont function

Compute the predicted treatment effect on the true endpoint of a patient based on his or her observed pretreatment predictor value in the continuous-continuous setting for a particular (single) value of $\rho_{T0T1}$.

This function computes the predicted $\Delta T_j$ of a patient based on the pretreatment value $S_j$ of a patient in the continuous-continuous setting for a particular (single) value of rho_T0T1.

Predict.Treat.T0T1.ContCont(x, S, Beta, SS, mu_S, T0T1, alpha=0.05)

Arguments

• x: An object of class PCA.ContCont. See PCA.ContCont.
• S: The observed pretreatment value $S_j$ for a patient.
• Beta: The estimated treatment effect on the true endpoint (in the validation sample).
• SS: The estimated variance of the pretreatment predictor endpoint.
• mu_S: The estimated mean of the surrogate endpoint (in the validation sample).
• T0T1: The $\rho_{T0T1}$ value (used to compute the variance of $\Delta T_j$|$S_j$.
• alpha: The $\alpha$-level that is used to determine the confidence interval around $\Delta T_j$|$S_j$. Default $0.05$.

Returns

An object of class PCA.Predict.Treat.T0T1.ContCont with components, - Pred_T: The predicted $\Delta T_j$.

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

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

• CI_low: The lower border of the $1-\alpha$% confidence interval of $\Delta T_j$|$S_j$.

• CI_high: The upper border of the $1-\alpha$% confidence interval of $\Delta T_j$|$S_j$.

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

• alpha: The $\alpha$-level that is used to determine the confidence interval of $\Delta T_j$|$S_j$.

References

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

Author(s)

Wim Van der Elst, Ariel Alonso, & Geert Molenberghs

See Also

PCA.ContCont

Examples

# Generate the vector of PCA.ContCont values when rho_T0S=.3, rho_T1S=.9, 
# sigma_T0T0=2, sigma_T1T1=2,sigma_SS=2, and the grid of values {-1, -.99, 
# ..., 1} is considered for the correlations between T0 and T1:
PCA <- PCA.ContCont(T0S=.3, T1S=.9, T0T0=2, T1T1=2, SS=2, 
T0T1=seq(-1, 1, by=.01))

# Obtain the predicted value T for a patient who scores S = 10, using beta=5,
# SS=2, mu_S=4, assuming rho_T0T1=.6
indiv <- Predict.Treat.T0T1.ContCont(x=PCA, S=10, Beta=5, SS=2, mu_S=4, T0T1=.6)
summary(indiv)

# obtain a plot with the 95% CI around delta T_j | S_j (assuming rho_T0T1=.6)
plot(indiv)