EffectTreat (version 1.1)

Predict.Treat.T0T1.ContCont: 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 \(\rho_{T0T1}\).

Description

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.

Usage

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 \(0.05\).

Value

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.

See Also

PCA.ContCont

Examples

Run this code
# NOT RUN {
# 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)
# }

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