est_funct_expr {CIEE}

Estimating functions.

Description

Function to compute logL1 and logL2 under the GLM and AFT setting for the analysis of a normally-distributed and of a censored time-to-event primary outcome. logL1 and logL2 are functions which underlie the estimating functions of CIEE for the derivation of point estimates and standard error estimates. est_funct_expr computes their expression, which is then further used in the functions deriv_obj, ciee and ciee_loop.

Usage

est_funct_expr(setting = "GLM")

Arguments

setting

String with value "GLM" or "AFT" indicating whether the expression of logL1 and logL2 is computed under the GLM or AFT setting.

Details

Under the GLM setting for the analysis of a normally-distributed primary outcome Y, the goal is to obtain estimates for the pararameters \alpha_0, \alpha_1, \alpha_2, \alpha_3, \sigma_1^2, \alpha_4, \alpha_{XY}, \sigma_2^2 under the model

Y = \alpha_0 + \alpha_1 \cdot K + \alpha_2 \cdot X + \alpha_3 \cdot L + \epsilon_1, \epsilon_1 \sim N(0,\sigma_1^2)

Y^* = Y - \overline{Y} - \alpha_1 \cdot (K-\overline{K})

Y^* = \alpha_0 + \alpha_{XY} \cdot X + \epsilon_2, \epsilon_2 \sim N(0,\sigma_2^2)

logL1 underlies the estimating functions for the derivation of the first 5 parameters \alpha_0, \alpha_1, \alpha_2, \alpha_3, \sigma_1^2 and logL2 underlies the estimating functions for the derivation of the last 3 parameters \alpha_4, \alpha_{XY}, \sigma_2^2.

Under the AFT setting for the analysis of a censored time-to-event primary outcome Y, the goal is to obtain estimates of the parameters \alpha_0, \alpha_1, \alpha_2, \alpha_3, \sigma_1, \alpha_4, \alpha_{XY}, \sigma_2^2. Here, logL1 similarly underlies the estimating functions for the derivation of the first 5 parameters and logL2 underlies the estimating functions for the derivation of the last 3 parameters.

logL1, logL2 equal the log-likelihood functions (logL2 given that \alpha_1 is known). For more details and the underlying model, see the vignette.

Value

Returns a list containing the expression of the functions logL1 and logL2.

Examples

est_funct_expr(setting = "GLM")
est_funct_expr(setting = "AFT")