# Pseudo-observations for the expected number of years lost

### Description

Computes pseudo-observations for modeling using the number of years lost.

### Usage

1 |

### Arguments

`time` |
the follow up time. |

`event` |
the cause indicator, use 0 as censoring code and integers to name the other causes. |

`tmax` |
the maximum cut-off point time = the upper limit of the integral of the cumulative incidence function. If missing or larger than the maximum follow up time, it is replaced by the maximum follow up time. |

### Details

The function calculates the pseudo-observations for the expected number of years lost for each individual.
The pseudo-observations can be used for fitting a regression model with a generalized estimating equation.
No missing values in either `time`

or `event`

vector are allowed.

### Value

A list containing the following objects:

`cause` |
The ordered codes for different causes. |

`pseudo` |
A list of vectors- a vector for each of the causes, ordered by codes. Each value of a vector belongs to one individual (ordered as in the original data set). |

### References

Andersen P.K.: "A note on the decomposition of number of life years lost according to causes of death." *Research report, Department of Biostatistics, University of Copenhagen*, 2012 (2)

### See Also

`pseudoci`

,
`pseudomean`

,
`pseudosurv`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
library(KMsurv)
data(bmt)
bmt$icr <- bmt$d1 + bmt$d3
#compute the pseudo-observations:
pseudo = pseudoyl(time=bmt$t2, event=bmt$icr,tmax=2000)
#arrange the data - use pseudo observations for cause 2
a <- cbind(bmt,pseudo = pseudo$pseudo[[2]],id=1:nrow(bmt))
#fit a regression model for cause 2
library(geepack)
summary(fit <- geese(pseudo ~ z1 + as.factor(z8) + as.factor(group),
data = a, id=id, jack = TRUE, family=gaussian,
corstr="independence", scale.fix=FALSE))
#rearrange the output
round(cbind(mean = fit$beta,SD = sqrt(diag(fit$vbeta.ajs)),
Z = fit$beta/sqrt(diag(fit$vbeta.ajs)), PVal =
2-2*pnorm(abs(fit$beta/sqrt(diag(fit$vbeta.ajs))))),4)
``` |