est_funct_expr function

Estimating functions.

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.

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.

Returns

Returns a list containing the expression of the functions logL1

and logL2.

Details

Under the GLM setting for the analysis of a normally-distributed primary outcome Y, the goal is to obtain estimates for the pararameters $\alpha0, \alpha1, \alpha2, \alpha3, \sigma1^2, \alpha4, \alphaXY, \sigma2^2$

under the model

logL1 underlies the estimating functions for the derivation of the first 5 parameters $\alpha0, \alpha1, \alpha2, \alpha3, \sigma1^2$

and logL2 underlies the estimating functions for the derivation of the last 3 parameters $\alpha4, \alphaXY, \sigma2^2$.

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 $\alpha0, \alpha1, \alpha2, \alpha3, \sigma1, \alpha4, \alphaXY, \sigma2^2$. 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 $\alpha1$ is known). For more details and the underlying model, see the vignette.

Examples

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