binregRatio: Percentage of Years Lost Due to a Cause Regression

Description

Estimates the percentage of the restricted mean time lost (RMTL) that is attributable to a specific cause and models how covariates affect this percentage using IPCW regression.

Usage

binregRatio(
  formula,
  data,
  cause = 1,
  time = NULL,
  beta = NULL,
  type = c("III", "II", "I"),
  offset = NULL,
  weights = NULL,
  cens.weights = NULL,
  cens.model = ~+1,
  se = TRUE,
  relative.to.causes = NULL,
  kaplan.meier = TRUE,
  cens.code = 0,
  no.opt = FALSE,
  method = "nr",
  augmentation = NULL,
  outcome = c("rmtl", "cif"),
  model = c("logit", "exp", "lin"),
  Ydirect = NULL,
  ...
)

Value

An object of class "binreg" and "ratio" containing:

coef: Coefficient estimates.
se.coef: Standard errors.
var: Variance-covariance matrix.
iid: Influence function decomposition (with censoring adjustment).
iidI: Influence function without censoring adjustment.
naive.var: Variance assuming known censoring.
time: Time point used.
cause: Cause of interest.
Causes: Set of causes considered in the denominator.
Yipcw: IPCW-adjusted response matrix.
coefI, varI: Results from the initial (type "I") fit.
augmentation: Final augmentation term used.

Arguments

formula: Formula with an outcome (see coxph). The first covariate on the RHS is typically the treatment or group indicator. Can include cluster(id).
data: Data frame containing the variables.
cause: Numeric code of the cause of interest.
time: Time point $t$ for the analysis. Required.
beta: Starting values for optimization (default NULL, uses zeros).
type: Type of estimator: "I" (IPCW only), "II" (IPCW + augmentation), or "III" (IPCW + complex augmentation). Default is "III".
offset: Offsets for the partial likelihood.
weights: Weights for the score equations.
cens.weights: External censoring weights (if provided, cens.model is ignored).
cens.model: Formula for the censoring model (default ~+1, stratified KM). Can include strata() for stratified censoring.
se: Logical; if TRUE, computes standard errors based on IPCW (default TRUE).
relative.to.causes: If not NULL, compares the RMTL of the specified cause to the RMTL of the causes in this vector (the denominator becomes the sum of these causes).
kaplan.meier: Logical; if TRUE, uses Kaplan-Meier for IPCW weights; if FALSE, uses $\exp(-\text{cumulative hazard})$.
cens.code: Censoring code (default 0).
no.opt: Logical; if TRUE, skips optimization and uses beta directly.
method: Optimization method: "nr" (Newton-Raphson) or "nlm".
augmentation: Initial augmentation term (used for type "II" and "III").
outcome: Outcome type: "rmtl" (years lost) or "cif" (cumulative incidence).
model: Link function: "logit" (default), "exp", or "lin".
Ydirect: Matrix with two columns (numerator, denominator) to use directly as the response.
...: Additional arguments passed to lower-level functions.

Author

Thomas Scheike

Details

Let the total years lost be $Y = t - \min(T, t)$ and the years lost due to cause 1 be $Y_1 = I(\epsilon=1) (t - \min(T, t))$. The function models the ratio: $$ \text{logit}\left( \frac{E(Y_1 | X)}{E(Y | X)} \right) = X^T \beta $$

Estimation is based on a binomial regression IPCW response estimating equation: $$ X \left( \Delta^{\text{ipcw}}(t) \left( Y \cdot \text{expit}(X^T \beta) - Y_1 \right) \right) = 0 $$ where $\Delta^{\text{ipcw}}(t) = I(\min(t,T) < C) / G_c(\min(t,T))$ is the IPCW adjustment.

The function supports three types of estimators:

"I": Classical outcome IPCW regression (no augmentation).
"II": Adds a censoring augmentation term $X \int E(Z(t)| T>s)/G_c(s) d \hat M_c$ to improve efficiency (requires an initial estimate of $\beta$).
"III": Adds a more complex augmentation term separating the expectations of $Y$ and $Y_1$ for further efficiency gains.

The variance is based on the squared influence functions (IID). A "naive" variance (assuming known censoring) is also provided for comparison.

References

Scheike, T. & Tanaka, S. (2025). Restricted mean time lost ratio regression: Percentage of restricted mean time lost due to specific cause. WIP.

Examples

Run this code

data(bmt); bmt$time <- bmt$time+runif(408)*0.001

rmtl30 <- rmstIPCW(Event(time,cause!=0)~platelet+tcell+age, bmt, time=30, cause=1, outcome="rmtl")
rmtl301 <- rmstIPCW(Event(time,cause)~platelet+tcell+age, bmt, time=30, cause=1)
rmtl302 <- rmstIPCW(Event(time,cause)~platelet+tcell+age, bmt, time=30, cause=2)

estimate(rmtl30)
estimate(rmtl301)
estimate(rmtl302)

## Percentage of total RMTL due to cause 1
rmtlratioI <- rmtlRatio(Event(time,cause)~platelet+tcell+age, bmt, time=30, cause=1)
summary(rmtlratioI)

newdata <- data.frame(platelet=1, tcell=1, age=1)
pp <- predict(rmtlratioI, newdata)
pp

## Percentage of total cumulative incidence due to cause 1
cifratio <- binregRatio(Event(time,cause)~platelet+tcell+age, bmt, time=30, cause=1, model="cif")
summary(cifratio)
pp <- predict(cifratio, newdata)
pp

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