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

## 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

 `1` ```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.

`PCA.ContCont`
 ```1 2 3 4 5``` ```# 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) ```