binregATE: Average Treatment Effect for Censored Competing Risks Data using Binomial Regression

Description

Estimates the average treatment effect (ATE) $E(Y(1) - Y(0))$ for censored competing risks data using binomial regression with Inverse Probability of Censoring Weighting (IPCW).

Usage

binregATE(
  formula,
  data,
  cause = 1,
  time = NULL,
  beta = NULL,
  treat.model = ~+1,
  cens.model = ~+1,
  offset = NULL,
  weights = NULL,
  cens.weights = NULL,
  se = TRUE,
  type = c("II", "I"),
  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,
  typeATE = "II",
  ...
)

Value

An object of class c("binreg", "ATE") containing:

coef: Estimated coefficients from the outcome model.
riskDR: Double-robust marginal risk estimates for each treatment level.
riskG: G-formula marginal risk estimates for each treatment level.
difriskDR: Difference in risks (ATE) using double-robust estimator.
difriskG: Difference in risks (ATE) using G-formula estimator.
riskDR.iid, riskG.iid: Influence functions for marginal risk estimates.
var, var.riskDR, var.riskG: Variance-covariance matrices.
se.coef, se.riskDR, se.riskG: Standard errors.

Arguments

formula: A formula object specifying the outcome and covariates (see coxph). The first covariate should be the treatment variable coded as a factor.
data: A data frame containing the variables in the formula.
cause: Numeric scalar indicating the cause of interest for competing risks.
time: Numeric scalar indicating the time point of interest.
beta: Optional numeric vector of starting values for the coefficients.
treat.model: A formula specifying the logistic treatment model given covariates (e.g., treatment ~ covariate1 + covariate2).
cens.model: A formula specifying the censoring model. Only stratified Cox models without covariates are supported (e.g., ~ strata(group)).
offset: Optional numeric vector of offsets for the partial likelihood.
weights: Optional numeric vector of weights for the score equations.
cens.weights: Optional numeric vector of pre-calculated censoring weights. If NULL, weights are estimated internally.
se: Logical. If TRUE, computes standard errors with IPCW adjustment. If FALSE, assumes IPCW weights are known.
type: Character string. Either "I" (classic binomial regression) or "II" (adds augmentation term for efficiency).
kaplan.meier: Logical. If TRUE, uses Kaplan-Meier for IPCW weights; otherwise uses $\exp(-\text{Baseline})$.
cens.code: Numeric code representing censored observations in the status variable.
no.opt: Logical. If TRUE, optimization is skipped and starting values are used.
method: Character string. Optimization method: "nr" (Newton-Raphson) or "nlm".
augmentation: Optional numeric vector for augmenting binomial regression.
outcome: Character string. Outcome type: "cif" (Cumulative Incidence Function, $F(t|X)$), "rmst" (Restricted Mean Survival Time, $E(\min(T, t) | X)$), or "rmtl" (Restricted Mean Time Lost, $E(I(\epsilon=\text{cause})(t - \min(T,t)) | X)$).
model: Character string. Link function for the outcome model: "exp" or "lin" (identity). For "cif", "logit" is typically used.
Ydirect: Optional numeric vector. Use this outcome Y with IPCW version instead of constructing one from outcome.
typeATE: Character string. Either "II" (censoring augmentation of the estimating equation) or "I" (standard).
...: Additional arguments passed to lower-level functions (e.g., binreg that fits the outcome model).

Author

Thomas Scheike

Details

Under standard causal assumptions, the ATE can be estimated. These assumptions include:

Consistency: The observed outcome equals the potential outcome under the observed treatment.
Ignorability: $(Y(1), Y(0)) \perp A | X$ (treatment assignment is independent of potential outcomes given covariates).
Positivity: All treatment levels have non-zero probability given covariates.

The first covariate in the competing risks regression model must be the treatment variable, which should be coded as a factor. If the factor has more than two levels, multinomial logistic regression (mlogit) is used for propensity score modeling. In the absence of censoring, this reduces to ordinary logistic regression.

The ATE is estimated using standard doubly robust estimating equations that are IPCW-censoring adjusted. As an alternative to binomial regression, logitIPCWATE provides an IPCW-weighted version of standard logistic regression.

When typeATE = "II", the estimating equation is augmented with: $$ (A/\pi(X)) \int E( O(t) | T \geq t, S(X))/ G_c(t,S(X)) d \hat M_c(s) $$ when estimating the mean outcome for the treated group.

References

Blanche PF, Holt A, Scheike T (2022). "On logistic regression with right censored data, with or without competing risks, and its use for estimating treatment effects." Lifetime Data Analysis, 29, 441–482.

Examples

Run this code

data(bmt)
dfactor(bmt)  <-  ~.

brs <- binregATE(Event(time,cause)~tcell.f+platelet+age,bmt,time=50,cause=1,
  treat.model=tcell.f~platelet+age)
summary(brs)
head(brs$riskDR.iid)
head(brs$riskG.iid)

brsi <- binregATE(Event(time,cause)~tcell.f+tcell.f*platelet+tcell.f*age,bmt,time=50,cause=1,
  treat.model=tcell.f~platelet+age)
summary(brsi)
head(brs$riskDR.iid)
head(brs$riskG.iid)

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