Effective Information for Continuous Outcomes (Gaussian)

Computes \(d_{\text{eff}} = n_H / \sigma_Y^2\) from the Fisher information of the Gaussian linear model treatment coefficient.

Usage

d_eff_continuous(n_sg, sigma_y)

Arguments

n_sg

Integer. Subgroup sample size.

sigma_y

Numeric. Residual standard deviation of the outcome.

Value

Numeric. Effective information.

Details

For the model \(Y_i = \beta_0 + \beta V_i + \epsilon_i\), \(\epsilon_i \sim N(0, \sigma^2)\), with balanced arms: $$\text{Var}(\hat\beta) = \frac{4\sigma^2}{n_H}$$

Examples

d_eff_continuous(n_sg = 100, sigma_y = 1.5)
#> [1] 44.44444
# 44.4