Augmentation for Fine-Gray model based on stratified NPMLE Cif (Aalen-Johansen)

Computes the augmentation term for each individual as well as the sum $$ A(\beta) = \int H(t,X,\beta) \frac{F_2^*(t,s)}{S^*(t,s)} \frac{1}{G_c(t)} dM_c $$ with $$ H(t,X,\beta) = \int_t^\infty (X - E(\beta,t) ) G_c(t) d\Lambda_1^*i(t,s) $$ using a KM for $$G_c(t)$$ and a working model for cumulative baseline related to $$F_1^*(t,s)$$ and $$s$$ is strata, $$S^*(t,s) = 1 - F_1^*(t,s) - F_2^*(t,s)$$, and $$E(\beta^p,t)$$ is given. Assumes that no strata for baseline of ine-Gay model that is augmented.

Usage

FG_AugmentCifstrata(
  formula,
  data = data,
  E = NULL,
  cause = NULL,
  cens.code = 0,
  km = TRUE,
  case.weights = NULL,
  weights = NULL,
  offset = NULL,
  ...
)

Arguments

formula

formula with 'Event', strata model for CIF given by strata, and strataC specifies censoring strata

data

data frame

E

from FG-model

cause

of interest

cens.code

code of censoring

km

to use Kaplan-Meier

case.weights

weights for FG score equations (that follow dN_1)

weights

weights for FG score equations

offset

offsets for FG model

...

Additional arguments to lower level funtions

Details

After a couple of iterations we end up with a solution of $$ \int (X - E(\beta) ) Y_1(t) w(t) dM_1 + A(\beta) $$ the augmented FG-score.

Standard errors computed under assumption of correct $$G_c$$ model.

Author

Thomas Scheike

Examples

library(mets)
set.seed(100)
rho1 <- 0.2; rho2 <- 10
n <- 100
beta=c(0.0,-0.1,-0.5,0.3)
dats <- simul.cifs(n,rho1,rho2,beta,rc=0.2)
dtable(dats,~status)
#> 
#> status
#>  0  1  2 
#>  6 13 81 
#> 
dsort(dats) <- ~time
fg <- cifreg(Event(time,status)~Z1+Z2,data=dats,cause=1,propodds=NULL)
summary(fg)
#> 
#>    n events
#>  100     13
#> 
#>  100 clusters
#> coeffients:
#>    Estimate     S.E.  dU^-1/2 P-value
#> Z1 -0.25559  0.27563  0.28698  0.3538
#> Z2  0.43883  0.55113  0.57407  0.4259
#> 
#> exp(coeffients):
#>    Estimate    2.5%  97.5%
#> Z1  0.77446 0.45121 1.3293
#> Z2  1.55089 0.52658 4.5677
#> 
plot(fg);  lines(attr(dats,"Lam1"),col=2)


fgaugS <- FG_AugmentCifstrata(Event(time,status)~Z1+Z2+strata(Z1,Z2),data=dats,cause=1,E=fg$E)
summary(fgaugS)
#> 
#>    n events
#>  100     13
#> 
#>  100 clusters
#> coeffients:
#>    Estimate     S.E.  dU^-1/2 P-value
#> Z1 -0.25559  0.27360  0.28698  0.3502
#> Z2  0.43883  0.54675  0.57407  0.4222
#> 
#> exp(coeffients):
#>    Estimate    2.5%  97.5%
#> Z1  0.77446 0.45301 1.3240
#> Z2  1.55089 0.53111 4.5287
#> 
fgaugS2 <- FG_AugmentCifstrata(Event(time,status)~Z1+Z2+strata(Z1,Z2),data=dats,cause=1,E=fgaugS$E)
summary(fgaugS2)
#> 
#>    n events
#>  100     13
#> 
#>  100 clusters
#> coeffients:
#>    Estimate     S.E.  dU^-1/2 P-value
#> Z1 -0.25559  0.27360  0.28698  0.3502
#> Z2  0.43883  0.54675  0.57407  0.4222
#> 
#> exp(coeffients):
#>    Estimate    2.5%  97.5%
#> Z1  0.77446 0.45301 1.3240
#> Z2  1.55089 0.53111 4.5287
#>