inspect_ipw_weights.RdProduces the individual weights that are associated with each observed event
present in the input data used to fit an IP weighted risk model represented
as an ipw object. The weights are presented as a collection of event
weights tables that are segregated according to whether the corresponding
events were part of the "main result" or a bootstrap iteration and which
treatment group (if applicable) the corresponding subject was a member of.
inspect_ipw_weights(ipw_fit, events_only = FALSE)An ipw object
Either TRUE or FALSE specifying whether to only
include subjects for whom a noncensored non-competing-risk event occurred
before the latest input to times in the original IPW model fit call
A named list with entries main and bootstrap.
The main entry is a length-1 named list with a name given by the string
" " (i.e. a string with one space) if there were no treatment groups
specified in the original IPW model fit call, otherwise it is a named
list where the names are given by the names of the treatment groups (and
hence the length of the list is equal to the number of treatment groups).
Each element in the list contains an event weights table with a form that
is described later in this section.
The bootstrap entry is an unnamed list with length equal to the number
of bootstrap iterations specified in the original IPW model fit call.
Each entry in the list has the same form as for the main entry
The event weights tables each have the following columns. The rows are
ordered in such a way that for row k and row m such that k is less
than m then the minimum of the event time or the censoring time
associated with row k is no greater than the event time associated with
row m.
id: the subject ID
event_time: the time at which a (possibly competing risk) event
occurred. If no event was observed before the censoring time for a given
subject then the corresponding entry is missing
censor_time: the time at which censoring was observed. In the case that
an event occurred before censoring for a given subject then the
corresponding entry is missing
competing_risk: whether a competing risk event occurred before
censoring for each subject
weight_bootstrap: the bootstrap iteration weight associated with each
subject
weight_treatment: the treatment weight associated with each subject
weight_noncensored: the censoring weight associated with each subject
weight_nonmissing: the missingness weight associated with each subject
weight_subject: the total weight associated with each subject. This is
given by the product of weight_bootstrap, weight_treatment,
weight_noncensored, and weight_nonmissing
weight_risk: the weight that each subject contributes to the overall
risk estimate. If a given subject does not observe a non-competing-risk
event before their censoring time then they contribute nothing (i.e. have
an entry with a value of 0) to the risk estimate. Otherwise, the amount
of risk that they contribute is equal to the subject's corresponding
entry in weight_subject
weight_cumulative: the cumulative weight for the current entry and
previously occurring entries. In more detail, the k-th entry in
weight_cumulative is given by the sum of the first k entries of
weight_total
cumulative_risk: the cumulative risk associated with the corresponding
event or censoring time for each subject. In more detail, let k be a
row in the subject weights table such that there are no other rows in the
table after row k with the same subject time as for row k. Then the
estimated probability that an subject occurs no later than the event or
censoring time associated with row k is equal to the cumulative risk
entry associated with row k. For some other row m such that there is
another row in the table after row m with the same subject time as for
row m then the corresponding cumulative risk entry is not useful
variance: the conservative variance estimate using the influence
function for the cumulative risk estimate associated with the
corresponding event or censoring time for each subject
The event tables produced by inspect_event_weights are arranged at the top
level according to whether the results correspond to the "main results" or to
a bootstrap iteration. The main results refers to the results that are
obtained without performing any reweighting of the input data, in contrast to
the bootstrap iterations for which reweighting is performed. The main results
are always produced, and there can be zero or more event tables corresponding
to bootstrap iterations.
The event tables are further divided according to which treatment group, if applicable, each of the subjects belonged to. In the case that no treatment groups were specified in the original IPW model fit call then all of the events are included in the same event table corresponding to the appropriate main results or bootstrap iteration.
Note that when the input to events_only is TRUE then subjects that did
not have an observed noncensored and non-competing-risk event before the
largest input to times in the original IPW model fit call are not included
in any of the event tables. Furthermore, if there are subjects with missing
observations in any of the covariates for any of the nuisance models, if
applicable, than such subjects are omitted from the table (such patients can
optionally be accounted for through missingness weights).
There are four primary weights that are associated with each entry in a given event table:
The bootstrap iteration weights. For the main results these weights all have a value of 1. Otherwise these are the weights that are given to the subjects in an event table corresponding to a given bootstrap iteration
The treatment weights. These are the inverses of the estimated probabilities of belonging to the treatment associated with a given event table, if applicable. In the case that no treatment groups were specified in the original IPW model fit call then all of the weights have a value of 1
The censoring weights. These are the inverses of the estimated probabilities of not being censored by the time at which each event occurred or censoring occurred, whichever came first
The missingness weights. These are the inverses of the estimated probabilities of not having missing data among any of the covariates that are specified for any of the treatment model, censoring model, or outcome model, as applicable. If there is no missing data then these weights are all 1
Furthermore, for a patient to contribute towards the overall cumulative risk then they have to have observed a non-competing-risk event occurring before a censoring event.