Examine the plausibility of finding a good pretreatment predictor in the Continuous-continuous case

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Description

The function GoodPretreatContCont examines the plausibility of finding a good pretreatment predictor in the continuous-continuous setting. For details, see Alonso et al. (submitted).

Usage

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GoodPretreatContCont(T0T0, T1T1, Delta, T0T1=seq(from=0, to=1, by=.01))

Arguments

T0T0

A scalar that specifies the variance of the true endpoint in the control treatment condition.

T1T1

A scalar that specifies the variance of the true endpoint in the experimental treatment condition.

Delta

A scalar that specifies an upper bound for the prediction mean squared error when predicting the individual causal effect of the treatment on the true endpoint based on the pretreatment predictor.

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 ρ_{min}^{2}. Default seq(0, 1, by=.01), i.e., the values 0, 0.01, 0.02, ..., 1.

Value

An object of class GoodPretreatContCont with components,

T0T1

A scalar or vector that contains the correlation(s) between the counterfactuals T0 and T1 that were considered (i.e., ρ(_{T_{0},T_{1}})).

Sigma.Delta.T

A scalar or vector that contains the standard deviations of the individual causal treatment effects on the true endpoint as a function of ρ(_{T_{0},T_{1})}.

Rho2.Min

A scalar or vector that contains the ρ_{min}^{2} values as a function of ρ(_{T_{0},T_{1}}).

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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# Assess the plausibility of finding a good pretreatment predictor when
# sigma_T0T0 = sigma_T1T1 = 8 and Delta = 1
MinPred <- GoodPretreatContCont(T0T0 = 8, T1T1 = 8, Delta = 1)
summary(MinPred)
plot(MinPred)