Positivity / inverse-weight diagnostics for a fitted estimate

Reports the practical-positivity health of the inverse-probability weights that every concrete estimand relies on. The nuisance weight is \(1/(g(A\mid W)\, S_C(t)\, S_X(t))\) — the inverse of the probability of being assigned the regime's treatment and remaining uncensored (\(S_C\)) and, when a crossover model is used, not yet switched (\(S_X\)). Because these are multiplied, the denominator can become very small at later times, which (i) inflates the influence-function variance and (ii) triggers truncation that can bias the estimate. This is exactly the regime to watch with informative censoring and crossover.

For each intervention it returns the effective sample size \(\mathrm{ESS}(t) = (\sum_i w_{it})^2 / \sum_i w_{it}^2\) (as a fraction of \(n\)), the largest weight, the smallest observation probability (the positivity floor), and the share of weights sitting at the truncation bound — overall and at the worst time point. Read it alongside any estimate to judge whether the inference is trustworthy or weight-limited.

Usage

getPositivityDx(ConcreteEst, Verbose = TRUE)

Arguments

ConcreteEst: a "ConcreteEst" object from doConcrete().
Verbose: logical (default TRUE): print a short interpreted summary.

Value

invisibly, a list with summary (one row per intervention) and byTime (the per-evaluation-time ESS fraction, max weight, and minimum observation probability for each intervention).

Examples

if (FALSE) { # \dontrun{
est <- doConcrete(formatArguments(...))
getPositivityDx(est)
} # }