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Likelihood-based estimator via optimx for general AW + Z model

estimate_beta_mle.Rd

Fits a parametric likelihood model for the outcome and the right-censored covariate using direct maximization of the log-likelihood with optimx. The outcome model is specified by model, typically of the form y ~ AW + Z1 + ... + Zp, where AW = A - X. The distribution of X | Z is modeled via a Weibull AFT model, whose covariate structure can be specified by model_xz or, by default, derived from the right-hand side of model by excluding AW.

Usage

estimate_beta_mle(
  data_yXZ,
  model,
  aw_var = "AW",
  model_weights,
  model_xz = NULL,
  trace = 0
)

Arguments

data_yXZ

A data frame containing at least the outcome y, the auxiliary covariate A, the observed covariate W, the event indicator D, the exposure covariate AW (or another name specified by aw_var), and any additional covariates appearing in model and optionally model_xz.

model

A formula specifying the outcome regression model, e.g. y ~ AW + Z1 + Z2.

aw_var

Character string giving the name of the exposure covariate that is defined as A - X (default is "AW"). This variable must appear on the right-hand side of model and as a column in data_yXZ.

model_weights

A right-hand-side formula specifying the variables in the censoring model, e.g. ~ y + Z. This will be expanded to Surv(W, 1 - D) ~ y + Z internally. This is needed so that we can compute an initial “good" estimate for our regression parameters using the IPW estimator.

model_xz

Optional formula specifying the AFT model for X | Z. If NULL (default), the model for X | Z is taken to be Weibull with log-mean linear in (1, Z1, ..., Zp), where Z1, ..., Zp are all covariates on the right-hand side of model except aw_var. If provided, model_xz can be either a full Surv formula such as Surv(W, D) ~ Z1 + Z2 or a right-hand-side formula such as ~ Z1 + Z2, in which case the left-hand side Surv(W, D) is filled in automatically. ' @param trace Optional, set equal to 1 if you want the trace of the optimx model. Leave at 0 if you do not want a trace

Value

A list with component

beta_est

A numeric vector containing the parameter vector \(\theta = (\beta, \psi, \gamma_x, \text{shape}_x)\), where \(\beta\) are the outcome regression coefficients (dimension determined by model), \(\psi\) is the residual standard deviation on the original scale, \(\gamma_x\) indexes the mean of \(X | Z\), and \(\text{shape}_x\) is the Weibull shape parameter for \(X | Z\).