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Using bal.tab() with a Censoring Indicator

Source: R/class-bal.tab.cens.R
class-bal.tab.cens.Rd

When bal.tab() is given a censoring indicator marked with .cens() rather than a treatment, its target is the full at-risk sample, and what matters is whether the units still under observation resemble that sample once weighted. This page outlines the output in this case.

Balance is therefore assessed between two samples built from the same units:

  • Uncensored: the units with C == 0, carrying the censoring weights.

  • Full: every at-risk unit, i.e., every unit with a non-missing C, carrying a weight of 1.

Setting un = TRUE adds the same comparison with the uncensored units unweighted, which is the imbalance the weights were estimated to remove.

The two samples are compared using the same statistics available for binary treatments (mean.diffs, variance.ratios, ks.statistics, and ovl.coefficients), because internally they are stacked into a binary comparison. The two samples name their own columns rather than taking a binary treatment's positional 0 and 1, so the balance table has M.Uncensored and SD.Uncensored for the uncensored sample and M.Full and SD.Full for the full one, and Diff is the difference between the full sample and the uncensored one.

bal.plot() works too, showing the weighted uncensored sample against the unweighted full sample.

Allowable arguments

Every argument to bal.tab() applies as it does with a binary treatment, with the following exceptions.

s.d.denom

allowable values are "full" (the default), which uses the standard deviation of the covariate in the full at-risk sample; "uncensored", which uses that of the uncensored sample; and "pooled", "all", "weighted", and "hedges", which behave as they do for a binary treatment.

estimand and focal

do not apply and are ignored with a warning. The target is the full at-risk sample.

subclass

applies: subclassifying is itself a way of solving a censoring problem, in that within each subclass the uncensored units should resemble every at-risk unit in it. See "With subclasses" below.

match.strata

does not apply.

cluster and imp apply as usual, and produce a bal.tab.cluster or bal.tab.imp object whose per-cluster or per-imputation components are the censoring balance tables described here.

Among longitudinal treatments

A censoring indicator can appear among a list of longitudinal treatments, as in list(A1 ~ x, .cens(C1) ~ x, A2 ~ x), which is how a joint treatment-and-censoring model is written for WeightIt::weightitMSM(); bal.tab() also accepts such a weightitMSM object directly. Each entry of the list gets a table of its own kind, and each is assessed among the units still under observation entering it, so the full sample a censoring indicator is compared against is the risk set at that time point rather than the original cohort, and a treatment after it is assessed only among the units it did not censor. A list that mixes censoring with treatment gets no balance summary across time points. See class-bal.tab.msm.

With subclasses

Subclassification is an alternative to weighting for solving a censoring problem: within each subclass, the units still under observation should resemble every at-risk unit in that subclass. Supplying subclass therefore produces a bal.tab.cens object that also inherits from bal.tab.subclass, with a balance table for each subclass and a summary across them, as described at class-bal.tab.subclass.

The summary across subclasses is subclassification expressed as censoring weights: a unit still under observation in subclass \(k\) receives \(n_k / n_{k1}\), where \(n_k\) is the number of at-risk units in the subclass and \(n_{k1}\) the number of them still under observation, and the full sample is left unweighted. This is the same summary one would get from supplying those weights to a censoring model directly.

The sample sizes have one column per subclass, with Full, Uncensored, and Censored rows.

Output

The output is a bal.tab.cens object, which inherits from bal.tab.bin and bal.tab (or from bal.tab.subclass when subclass is supplied), and has the same elements as an ordinary binary-treatment bal.tab object. Its Observations component differs: it has a single Total column, because the target sample is the same in every row, and the rows

  • Full: the number (or effective number) of at-risk units,

  • Uncensored: the number of units still under observation,

  • Adjusted (or one row per set of weights): their effective number once weighted,

  • Censored: the number of units censored, omitted when there are none.

Uncensored and Censored sum to Full.

See also