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")String with value "GLM" or "AFT" indicating whether
the expression of logL1 and logL2 is computed
under the GLM or AFT setting.
Returns a list containing the expression of the functions logL1
and logL2.
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.
# NOT RUN {
est_funct_expr(setting = "GLM")
est_funct_expr(setting = "AFT")
# }
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