GoodPretreatContCont: Examine the plausibility of finding a good pretreatment...
In EffectTreat: Prediction of Therapeutic Success

Description Usage Arguments Value Author(s) References See Also Examples

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

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

`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.

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}}).

Wim Van der Elst, Ariel Alonso, & Geert Molenberghs

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

PCA.ContCont

# 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)