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

Arguments

Details

Under the GLM setting for the analysis of a normally-distributed primary outcome Y, the goal is to obtain estimates for the pararameters α0, α1, α2, α3, σ1^2, α4, αXY, σ2^2 under the model

Y = α0 + α1*K + α2*X + α3*L + ε1, ε1 ~ N(0,σ1^2)

Y* = Y - mean(Y) - α1*(K-mean(K))

Y* = α0 + αXY*X + ε2, ε2 ~ N(0,σ2^2).

logL1 underlies the estimating functions for the derivation of the first 5 parameters α0, α1, α2, α3, σ1^2 and logL2 underlies the estimating functions for the derivation of the last 3 parameters α4, αXY, σ2^2.

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 α0, α1, α2, α3, σ1, α4, αXY, σ2^2. 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 α1 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