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Restricted IPCW Mean for Censored Survival Data

Source: R/restricted.mean.R
resmeanIPCW.Rd

Provides a fast implementation of Inverse Probability of Censoring Weighting (IPCW) regression for a single time point. It fits the model: $$ E( \min(T, t) | X ) = \exp( X^T \beta) $$ or, in the case of competing risks data: $$ E( I(\epsilon=1) (t - \min(T, t)) | X ) = \exp( X^T \beta) $$ which represents the "Years Lost Due to Cause" (RMTL).

Usage

resmeanIPCW(formula, data, outcome = c("rmst", "rmtl"), ...)

Arguments

formula

Formula with an Event outcome (e.g., Event(time, cause)).

data

Data frame containing the variables.

outcome

Outcome type: "rmst" (Restricted Mean Survival Time) or "rmtl" (Restricted Mean Time Lost).

...

Additional arguments passed to binreg, such as time, cause, cens.model, model, type, etc.

Value

An object of class "binreg" containing:

coef

Coefficient estimates.

se

Standard errors.

var

Variance-covariance matrix.

iid

Influence function decomposition.

naive.var

Variance under known censoring model (if applicable).

time

Time point used.

outcome

Type of outcome analyzed.

Details

The method solves the binomial regression IPCW response estimating equation: $$ X \left( \frac{\Delta(\min(T,t)) Y}{G_c(\min(T,t))} - \exp( X^T \beta) \right) = 0 $$ where \(\Delta(\min(T,t)) = I(\min(T,t) \leq C)\) is the indicator of being uncensored at the time of interest.

When the status variable is binary, the outcome is assumed to be \(Y = \min(T,t)\) (RMST). If the status has more than two levels (competing risks), the outcome is \(Y = (t - \min(T,t)) I(\text{status}=\text{cause})\) (RMTL for a specific cause).

The function supports:

  • IPCW Adjustment: Weights by the inverse of the censoring survival probability.

  • Augmentation: Can include an augmentation term (type="II" or "III") to improve efficiency and robustness (Double Robust estimation).

  • Variance Estimation: Based on the influence function, including adjustments for the estimation of the censoring model.

References

Scheike, T. and Holst, K. K. (2024). Restricted mean time lost for survival and competing risks data using mets in R. WIP.

See also

binreg, resmeanATE, rmstIPCW

Author

Thomas Scheike

Examples

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

# E( min(T;t) | X ) = exp( a+b X) with IPCW estimation 
out <- resmeanIPCW(Event(time,cause!=0)~tcell+platelet+age, bmt,
                time=50, cens.model=~strata(platelet), model="exp")
summary(out)
#>    n events
#>  408    245
#> 
#>  408 clusters
#> coeffients:
#>              Estimate   Std.Err      2.5%     97.5% P-value
#> (Intercept)  3.014368  0.065112  2.886750  3.141986  0.0000
#> tcell        0.106635  0.138266 -0.164362  0.377631  0.4406
#> platelet     0.247037  0.097339  0.056256  0.437819  0.0112
#> age         -0.185916  0.043567 -0.271305 -0.100527  0.0000
#> 
#> exp(coeffients):
#>             Estimate     2.5%   97.5%
#> (Intercept) 20.37621 17.93493 23.1498
#> tcell        1.11253  0.84844  1.4588
#> platelet     1.28023  1.05787  1.5493
#> age          0.83034  0.76238  0.9044
#> 
#> 

 ## Reduce Ex.Timings
## Weighted GLM version (RMST)
out2 <- logitIPCW(Event(time,cause!=0)~tcell+platelet+age, bmt,
            time=50, cens.model=~strata(platelet), model="exp", outcome="rmst")
summary(out2)
#>    n   events
#>  408 7467.644
#> 
#>  408 clusters
#> coeffients:
#>               Estimate    Std.Err       2.5%      97.5% P-value
#> (Intercept)  3.0201548  0.0748731  2.8734062  3.1669033  0.0000
#> tcell        0.0248183  0.1868530 -0.3414069  0.3910434  0.8943
#> platelet     0.2531265  0.1262746  0.0056329  0.5006201  0.0450
#> age         -0.1803174  0.0526445 -0.2834988 -0.0771360  0.0006
#> 
#> exp(coeffients):
#>             Estimate     2.5%   97.5%
#> (Intercept) 20.49446 17.69720 23.7339
#> tcell        1.02513  0.71077  1.4785
#> platelet     1.28805  1.00565  1.6497
#> age          0.83501  0.75314  0.9258
#> 
#> 

### Time-lost (RMTL)
outtl <- resmeanIPCW(Event(time,cause!=0)~tcell+platelet+age, bmt,
                time=50, cens.model=~strata(platelet), model="exp", outcome="rmtl")
summary(outtl)
#>    n events
#>  408    245
#> 
#>  408 clusters
#> coeffients:
#>              Estimate   Std.Err      2.5%     97.5% P-value
#> (Intercept)  3.361796  0.047702  3.268301  3.455291  0.0000
#> tcell       -0.085197  0.127470 -0.335034  0.164641  0.5039
#> platelet    -0.239899  0.100767 -0.437399 -0.042399  0.0173
#> age          0.175625  0.044854  0.087713  0.263537  0.0001
#> 
#> exp(coeffients):
#>             Estimate     2.5%   97.5%
#> (Intercept) 28.84093 26.26666 31.6675
#> tcell        0.91833  0.71531  1.1790
#> platelet     0.78671  0.64571  0.9585
#> age          1.19199  1.09167  1.3015
#> 
#> 

### Same as Kaplan-Meier for full censoring model 
bmt$int <- with(bmt, strata(tcell, platelet))
out <- resmeanIPCW(Event(time,cause!=0)~-1+int, bmt, time=30,
                             cens.model=~strata(platelet, tcell), model="lin")
estimate(out)
#>                        Estimate Std.Err  2.5% 97.5%   P-value
#> inttcell=0, platelet=0    13.60  0.8316 11.97 15.23 3.830e-60
#> inttcell=0, platelet=1    18.90  1.2696 16.41 21.39 4.003e-50
#> inttcell=1, platelet=0    16.19  2.4061 11.48 20.91 1.704e-11
#> inttcell=1, platelet=1    17.77  2.4536 12.96 22.58 4.464e-13
out1 <- phreg(Surv(time,cause!=0)~strata(tcell,platelet), data=bmt)
rm1 <- resmean_phreg(out1, times=30)
summary(rm1)
#>                     strata times    rmean  se.rmean    lower    upper
#> tcell=0, platelet=0      0    30 13.60291 0.8315434 12.06697 15.33436
#> tcell=0, platelet=1      1    30 18.90123 1.2693318 16.57016 21.56023
#> tcell=1, platelet=0      2    30 16.19125 2.4006087 12.10811 21.65132
#> tcell=1, platelet=1      3    30 17.76607 2.4422072 13.57004 23.25956
#>                     years.lost
#> tcell=0, platelet=0   16.39709
#> tcell=0, platelet=1   11.09877
#> tcell=1, platelet=0   13.80875
#> tcell=1, platelet=1   12.23393

### Years lost regression
outl <- resmeanIPCW(Event(time,cause!=0)~-1+int, bmt, time=30, outcome="years-lost",
                             cens.model=~strata(platelet, tcell), model="lin")
estimate(outl)
#>                        Estimate Std.Err   2.5% 97.5%   P-value
#> inttcell=0, platelet=0    16.40  0.8315 14.767 18.03 1.486e-86
#> inttcell=0, platelet=1    11.10  1.2693  8.611 13.59 2.254e-18
#> inttcell=1, platelet=0    13.81  2.4006  9.104 18.51 8.810e-09
#> inttcell=1, platelet=1    12.23  2.4423  7.447 17.02 5.467e-07

## Competing risks years-lost for cause 1  
out <- resmeanIPCW(Event(time,cause)~-1+int, bmt, time=30, cause=1,
                            cens.model=~strata(platelet, tcell), model="lin")
estimate(out)
#>                        Estimate Std.Err   2.5%  97.5%   P-value
#> inttcell=0, platelet=0   12.105  0.8508 10.438 13.773 6.162e-46
#> inttcell=0, platelet=1    6.884  1.1741  4.583  9.185 4.536e-09
#> inttcell=1, platelet=0    7.261  2.3533  2.648 11.873 2.033e-03
#> inttcell=1, platelet=1    5.780  2.0925  1.679  9.882 5.737e-03
## Same as integrated cumulative incidence 
rmc1 <- cif_yearslost(Event(time,cause)~strata(tcell,platelet), data=bmt, times=30)
summary(rmc1)
#> $estimate
#> $estimate$intF_1
#>                     strata times    intF_1 se.intF_1 lower_intF_1 upper_intF_1
#> tcell=0, platelet=0      0    30 12.105150 0.8508117    10.547351    13.893030
#> tcell=0, platelet=1      1    30  6.884207 1.1741044     4.928119     9.616714
#> tcell=1, platelet=0      2    30  7.260710 2.3532715     3.846767    13.704473
#> tcell=1, platelet=1      3    30  5.780407 2.0925106     2.843302    11.751515
#> 
#> $estimate$intF_2
#>                     strata times   intF_2 se.intF_2 lower_intF_2 upper_intF_2
#> tcell=0, platelet=0      0    30 4.291939 0.6161454     3.239337     5.686578
#> tcell=0, platelet=1      1    30 4.214566 0.9057057     2.765862     6.422072
#> tcell=1, platelet=0      2    30 6.548043 1.9703358     3.630623    11.809783
#> tcell=1, platelet=1      3    30 6.453525 2.0815194     3.429656    12.143489
#> 
#> 
#> $total.years.lost
#> [1] 16.39709 11.09877 13.80875 12.23393
#>