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

Description

This function computes the predicted Δ T_j of a patient based on the pretreatment value S_j of a patient in the continuous-continuous setting.

Usage

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Predict.Treat.ContCont(x, S, Beta, SS, mu_S)

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 pretreatment predictor (in the validation sample).

Value

An object of class PCA.Predict.Treat.ContCont with components,

Pred_T

The predicted Δ T_j.

Var_Delta.T

The variance σ_{Δ_{T}}.

T0T1

The correlation between the counterfactuals T_{0}, T_{1}.

PCA

The vector of ρ_{ψ} values.

Var_Delta.T_S

The variance σ_{Δ_{T}}|S_j.

Author(s)

Wim Van der Elst, Ariel Alonso, & Geert Molenberghs

References

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

See Also

PCA.ContCont

Examples

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# 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
Predict <- Predict.Treat.ContCont(x=PCA, S=10, Beta=5, SS=2, mu_S=4)

# examine the results
summary(Predict)

# plot Delta_T_j given S_T, for the mean value of the valid rho_T0T1  
plot(Predict, Mean.T0T1=TRUE, Median.T0T1=FALSE)