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Percentage of Years Lost Due to a Cause Regression

Source: R/ratio.regression.R
binregRatio.Rd

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,
  ...
)

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.

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.

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.

See also

resmeanIPCW, binreg

Author

Thomas Scheike

Examples

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 Std.Err    2.5%   97.5%   P-value
#> (Intercept)   2.7657 0.05104  2.6657  2.8658 0.000e+00
#> platelet     -0.3004 0.11176 -0.5194 -0.0813 7.201e-03
#> tcell        -0.1455 0.14445 -0.4286  0.1377 3.139e-01
#> age           0.2015 0.04824  0.1069  0.2960 2.961e-05
estimate(rmtl301)
#>             Estimate Std.Err    2.5%      97.5%    P-value
#> (Intercept)   2.4449 0.07291  2.3020  2.5878254 1.618e-246
#> platelet     -0.4519 0.16739 -0.7800 -0.1238266  6.940e-03
#> tcell        -0.4937 0.25146 -0.9866 -0.0008656  4.960e-02
#> age           0.2747 0.06538  0.1466  0.4028542  2.648e-05
estimate(rmtl302)
#>             Estimate Std.Err    2.5%  97.5%   P-value
#> (Intercept)  1.45849  0.1362  1.1915 1.7255 9.621e-27
#> platelet    -0.01890  0.2224 -0.4548 0.4170 9.323e-01
#> tcell        0.40759  0.2648 -0.1113 0.9265 1.237e-01
#> age          0.04576  0.1191 -0.1877 0.2792 7.008e-01

## Percentage of total RMTL due to cause 1
rmtlratioI <- rmtlRatio(Event(time,cause)~platelet+tcell+age, bmt, time=30, cause=1)
summary(rmtlratioI)
#>    n events
#>  408    154
#> 
#>  408 clusters
#> coeffients:
#>              Estimate   Std.Err      2.5%     97.5% P-value
#> (Intercept)  0.973135  0.177855  0.624545  1.321725  0.0000
#> platelet    -0.402875  0.323413 -1.036753  0.231002  0.2129
#> tcell       -0.845357  0.419214 -1.667002 -0.023712  0.0437
#> age          0.214462  0.168387 -0.115571  0.544495  0.2028
#> 
#> exp(coeffients):
#>             Estimate    2.5%  97.5%
#> (Intercept)  2.64623 1.86740 3.7499
#> platelet     0.66840 0.35460 1.2599
#> tcell        0.42940 0.18881 0.9766
#> age          1.23920 0.89086 1.7237
#> 
#> 

newdata <- data.frame(platelet=1, tcell=1, age=1)
pp <- predict(rmtlratioI, newdata)
pp
#>        pred        se    lower     upper
#> 1 0.4848458 0.1092229 0.270769 0.6989226

## 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)
#>    n events
#>  408    154
#> 
#>  408 clusters
#> coeffients:
#>               Estimate    Std.Err       2.5%      97.5% P-value
#> (Intercept)  0.7239521  0.0355963  0.6541846  0.7937196  0.0000
#> platelet    -0.0889619  0.0730427 -0.2321228  0.0541991  0.2232
#> tcell       -0.1951701  0.1005726 -0.3922888  0.0019486  0.0523
#> age          0.0452930  0.0358278 -0.0249281  0.1155142  0.2062
#> 
#> 
#> 
pp <- predict(cifratio, newdata)
pp
#>        pred        se     lower     upper
#> 1 0.4851132 0.1050915 0.2791377 0.6910887