Stratified Binomial Regression with cross-validation option

Fits a stratified binomial regression model for the cumulative incidence function (CIF), restricted mean survival time (RMST), or restricted mean time lost (RMTL), using inverse probability of censoring weighting (IPCW). Each stratum may either be fit on its own observations or, when cv.fold = TRUE, on the complement of its observations (i.e. a leave-one-stratum-out / cross-validation style fit). Standard errors are computed via an iid decomposition that accounts for the estimation of the censoring distribution.

Usage

binregStrata(
  formula,
  data,
  cause = 1,
  time = NULL,
  beta = NULL,
  type = c("II", "I"),
  offset = NULL,
  weights = NULL,
  cens.weights = NULL,
  cens.model = ~+1,
  se = TRUE,
  kaplan.meier = TRUE,
  cens.code = 0,
  no.opt = FALSE,
  method = "nr",
  augmentation = NULL,
  outcome = c("cif", "rmst", "rmtl"),
  model = c("default", "logit", "exp", "lin"),
  Ydirect = NULL,
  strata = NULL,
  cv.fold = FALSE,
  low.memory = FALSE,
  ...
)

Arguments

formula: A formula with a Surv or Event object on the left-hand side, and covariates, optional cluster(), strata(), offset(), and weights() terms on the right-hand side.
data: A data.frame containing the variables in formula.
cause: Value(s) of the status variable that identify the event of interest (cause 1 by default).
time: The fixed time-point at which the CIF, RMST, or RMTL is evaluated. Required.
beta: Optional starting values for the regression coefficients. Either a vector (recycled across strata) or a matrix with one row per stratum.
type: Character; either "II" (default) or "I". When "II", an additional augmentation term and an extra component of the censoring-related iid decomposition are computed.
offset: Optional offset term; can also be specified via the formula.
weights: Optional case weights; can also be specified via the formula.
cens.weights: Optional pre-computed inverse probability of censoring weights. If supplied, the internal censoring model fit is skipped and se is forced to FALSE.
cens.model: A formula for the censoring model (right-hand side only, fitted via phreg). Defaults to the Kaplan-Meier (~+1).
se: Logical. If TRUE (default), standard errors are computed, including the contribution from estimating the censoring distribution.
kaplan.meier: Logical. If TRUE (default), uses the Kaplan-Meier estimator for censoring weights when the censoring model has no covariates; otherwise a Cox-type estimator is used internally when covariates are present.
cens.code: The code in the status variable denoting censoring (default 0).
no.opt: Logical. If TRUE, no optimization is performed and the object is evaluated at the supplied beta.
method: Optimization method. Currently only "nr" (Newton-Raphson via lava::NR) is supported.
augmentation: Optional augmentation term(s) added to the score equations, either a vector (recycled across strata) or a matrix with one row per stratum.
outcome: Character; the outcome scale to model: "cif" (default), "rmst", or "rmtl".
model: Character; the link function: "default" (chooses "logit" for CIF and "exp" for RMST/RMTL), "logit", "exp", or "lin".
Ydirect: Optional, directly supplied response vector, overriding the response otherwise constructed from outcome.
strata: Optional numeric vector defining strata, used when strata are not specified via strata() in the formula.
cv.fold: Logical. If TRUE, for each stratum s the regression coefficients are estimated using all observations not in stratum s (a cross-validation-style fit), rather than the observations within stratum s (the default, FALSE).
low.memory: Logical. If TRUE only saves key quanties, coef, var, iid and some design structures.
...: Additional arguments, currently passed as optimizer control settings (e.g. tol, stepsize) to the Newton-Raphson routine.

Value

An object of class c("binregStrata","binreg"), a list with components including:

coef: Estimated regression coefficients (stacked across strata).
iid: Subject-level iid decomposition of the coefficients, adjusted for censoring estimation when se = TRUE.
var, robvar: Robust (sandwich) variance-covariance matrix.
se.coef, se.robust: Standard errors derived from var.
hessian, ihessian: Per-stratum Hessians and their (pseudo-)inverses.
coef_list: Per-stratum coefficient vectors.
time, cause, cens.code, model, outcome: Echoed arguments.
Y, Yipcw, IPCW: The constructed response, IPCW-weighted response, and IPCW weights.
cens.weights, formC, cens.strata, cens.nstrata: Censoring model weights and related information (when internally estimated).
nstrata, strata_orig, strata_call, cv.fold: Stratification information and whether the cross-validation fold scheme was used.
n, nevent, ncluster, nid, id, name.id: Sample size and identifier information.
call, design: The matched call and the design object.

Details

When cv.fold = FALSE (the standard case), the coefficients for stratum s are estimated using only observations with strata == s. When cv.fold = TRUE, the coefficients for stratum s are instead estimated using observations with strata != s, i.e. the complement; this also affects the construction of the censoring-related iid terms (MGCiid) and the per-stratum subject-level influence functions used for the robust variance.

Censoring weights are computed via a Cox model (phreg) on cens.model, evaluated at pmin(exit, time), unless cens.weights is supplied directly. When se = TRUE, the additional variability coming from the estimation of the censoring distribution is incorporated into the standard errors via a martingale-type iid decomposition (MGCiid).

Examples

if (FALSE) { # \dontrun{
library(mets)
data(bmt)
out <- binregStrata(Event(time, cause) ~ tcell + strata(platelet),
                     data = bmt, cause = 1, time = 50)
summary(out)
} # }