Recurrent events regression with terminal event

Fits Ghosh-Lin IPCW Cox-type model

recreg(
  formula,
  data,
  cause = 1,
  death.code = c(2),
  cens.code = 0,
  cens.model = ~1,
  weights = NULL,
  offset = NULL,
  Gc = NULL,
  wcomp = NULL,
  augmentation.type = c("lindyn.augment", "lin.augment"),
  ...
)

Arguments

formula

formula with 'Event' outcome

data

data frame

cause

of interest (1 default)

death.code

codes for death (terminating event, 2 default)

cens.code

code of censoring (0 default)

cens.model

for stratified Cox model without covariates

weights

weights for score equations

offset

offsets for model

Gc

censoring weights for time argument, default is to calculate these with a Kaplan-Meier estimator, should then give G_c(T_i-)

wcomp

weights for composite outcome, so when cause=c(1,3), we might have wcomp=c(1,2).

augmentation.type

of augmentation when augmentation model is given

...

Additional arguments to lower level funtions

Details

For Cox type model : $$ E(dN_1(t)|X) = \mu_0(t)dt exp(X^T \beta) $$ by solving Cox-type IPCW weighted score equations $$ \int (Z - E(t)) w(t) dN_1(t) $$ where $$w(t) = G(t) (I(T_i \wedge t < C_i)/G_c(T_i \wedge t))$$ and $$E(t) = S_1(t)/S_0(t)$$ and $$S_j(t) = \sum X_i^j w_i(t) \exp(X_i^T \beta)$$.

The iid decomposition of the beta's are on the form $$ \int (Z - E ) w(t) dM_1 + \int q(s)/p(s) dM_c $$ and returned as iid.

Events, deaths and censorings are specified via stop start structure and the Event call, that via a status vector and cause (code), censoring-codes (cens.code) and death-codes (death.code) indentifies these. See example and vignette.

Author

Thomas Scheike

Examples

## data with no ties
data(base1cumhaz)
data(base4cumhaz)
data(drcumhaz)
Lam1 <- base1cumhaz;  Lam2 <- base4cumhaz;  LamD <- drcumhaz
## simulates recurrent events of types 1 and 2 and with terminal event D and censoring
rr <- simRecurrentII(100,Lam1,cumhaz2=Lam2,death.cumhaz=LamD,cens=3/5000)
rr <- count.history(rr)
rr$cens <- 0
nid <- max(rr$id)
rr$revnr <- revcumsumstrata(rep(1,nrow(rr)),rr$id-1,nid)
rr$x <- rnorm(nid)[rr$id]
rr$statusG <- rr$status
rr <- dtransform(rr,statusG=3,death==1)
dtable(rr,~statusG+status+death)
#> 
#>                death   0   1
#> statusG status              
#> 0       0             42   0
#>         1              0   0
#>         2              0   0
#> 1       0              0   0
#>         1            126   0
#>         2              0   0
#> 2       0              0   0
#>         1              0   0
#>         2             13   0
#> 3       0              0  58
#>         1              0   0
#>         2              0   0
dcut(rr) <- gx~x

ll <- recreg(Event(start,stop,statusG)~x+cluster(id),data=rr,cause=1,death.code=3)
summary(ll)
#> 
#>    n events
#>  239    126
#> 
#>  100 clusters
#> coeffients:
#>    Estimate      S.E.   dU^-1/2 P-value
#> x -0.097581  0.144494  0.086683  0.4995
#> 
#> exp(coeffients):
#>   Estimate    2.5% 97.5%
#> x  0.90703 0.68333 1.204
#> 
#> 

## censoring stratified after quartiles of x
lls <- recreg(Event(start, stop, statusG)~x+cluster(id),data=rr,cause=1,
              death.code=3,cens.model=~strata(gx))
summary(lls)
#> 
#>    n events
#>  239    126
#> 
#>  100 clusters
#> coeffients:
#>    Estimate      S.E.   dU^-1/2 P-value
#> x -0.080601  0.127179  0.081397  0.5262
#> 
#> exp(coeffients):
#>   Estimate    2.5%  97.5%
#> x  0.92256 0.71902 1.1837
#> 
#>