GoodPretreatContCont function

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

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

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

Returns

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., $\rho(_{T_{0},T_{1}})$).

• 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 $\rho(_{T_{0},T_{1})}$.

• Rho2.Min: A scalar or vector that contains the $\rho_{min}^{2}$ values as a function of $\rho(_{T_{0},T_{1}})$.

References

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

Author(s)

Wim Van der Elst, Ariel Alonso, & Geert Molenberghs

See Also

PCA.ContCont

Examples

# 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)