ICA_alpha_ContCont: Assess surrogacy using a Rényi divergence based family of metrics in the causal-inference single-trial setting in normal case

Description

The function ICA_alpha_ContCont() is a set of metrics to evaluate surrogacy. ICA_alpha have the similar mathematical properties with ICA.ContCont().

Usage

ICA_alpha_ContCont(
  alpha = numeric(),
  T0S0,
  T1S1,
  T0T0 = 1,
  T1T1 = 1,
  S0S0 = 1,
  S1S1 = 1,
  T0T1 = seq(-1, 1, by = 0.1),
  T0S1 = seq(-1, 1, by = 0.1),
  T1S0 = seq(-1, 1, by = 0.1),
  S0S1 = seq(-1, 1, by = 0.1)
)

Value

Total.Num.Matrices: An object of class numeric that contains the total number of matrices that can be formed as based on the user-specified correlations in the function call.
Pos.Def: A data.frame that contains the positive definite matrices that can be formed based on the user-specified correlations. These matrices are used to compute the vector of the \(\rho_{\Delta}\) values.
rho: A scalar or vector that contains the individual causal association \(\rho_{\Delta}\)
ICA: A scalar or vector that contains the individual causal association \(\rho_{\Delta}^2=ICA\)
ICA_alpha: A scalar or vector that contains the individual causal association \(ICA_{\alpha}\)
Sigmas: A data.frame that contains the \(\sigma_{\Delta T}\) and \(\sigma_{\Delta S}\)

Arguments

alpha: (numeric) is order alpha in [0, infinity]
T0S0: A scalar or vector that specifies the correlation(s) between the surrogate and the true endpoint in the control treatment condition
T1S1: A scalar or vector that specifies the correlation(s) between the surrogate and the true endpoint in the control treatment condition
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 control treatment condition
S0S0: A scalar that specifies the variance of the true endpoint in the control treatment condition
S1S1: A scalar that specifies the variance of the true endpoint in the control treatment condition
T0T1: A scalar or vector that contains the correlation(s) between the counterfactuals T0 and T1
T0S1: A scalar or vector that contains the correlation(s) between the counterfactuals T0 and S1
T1S0: A scalar or vector that contains the correlation(s) between the counterfactuals T1 and S0
S0S1: A scalar or vector that contains the correlation(s) between the counterfactuals S0 and S1