This function computes pseudo values based on a first order Taylor
series, also known as the "infinitesimal jackknife" (IJ) or "dfbeta"
residuals. To be completely correct the results of this function
could perhaps be
called `IJ pseudo values' or even pseudo psuedo-values.
For moderate to large data, however, the resulta will
be almost identical, numerically, to the ordinary jackknife.

A primary advantage of this approach is computational speed.
Other features, neither good nor bad, are that they will agree with
robust standard errors of other survival package estimates,
which are based on the IJ, and that the mean of the estimates, over
subjects, is exactly the underlying survival estimate.

For the `type`

variable, `surv`

is an acceptable synonym for
`pstate`

, `chaz`

for `cumhaz`

, and
`rmst`

,`rmts`

and `auc`

are equivalent to `sojourn`

.
All of these are case insensitive.

If the orginal `survfit`

call produced multiple curves, the internal
computations are done separately for each curve.
The result from this routine is simply n times the IJ value, where n is
the number of uniue subjects in the respective curve.
(If the the `survfit`

call included and `id`

option, n is
the number of unique id values, otherwise the number of rows in the data set.)
IJ values are well defined for all variants of the Aalen-Johansen
estimate, as computed by the `survfit`

function; indeed, they are
the basis for standard errors of the result.

Understanding of the properties of the pseudo-values is still
evolving. Validity has been verified for the probability in state and
sojourn times whenever all subjects start in the same state;
this includes for instance the usual Kaplan-Meier and competing risks cases.
On the other hand, one must be cautious when the data includes
left-truncation (Parner); and pseudo-values for the cumulative hazard
have not been widely explored.
When a given subject is spread across multiple (time1, time2) windows
with different weights for each of those portions, which can happen
with time-dependent inverse probability of censoring (IPW) weights for
instance, the current thought is to set both collapse and weight to
FALSE, with clustering and weighting as part of the subsequent GEE
model; but this is quite tentative.
As understanding evolves, treat this routine's results as a reseach
tool, not production, for these more complex models.