Conditional-moment concentration for a discrete intervention

Assess the concentration of uncapped exposure-only ratios for one arm and assigned prefix. Observation probabilities define a separate averaging measure. Supply the study's threshold explicitly.

Usage

margot_lmtp_support_concentration(
  natural_mass,
  policy_mass,
  preceding_weight,
  reached,
  row_id,
  minimum,
  observation_weight = NULL
)

Arguments

natural_mass, policy_mass

Numeric probability matrices. Rows have names equal to row_id; matching column names identify discrete values or regions with a common ratio within each region. Each reached row sums to one, within a tolerance of 1e-12. Each entry must lie in [0, 1] exactly; the tolerance applies only to the row sum.

preceding_weight

Named numeric vector of products of exposure ratios before this assignment. Use ones for the first assignment.

reached

Named logical vector marking the current observation risk set.

row_id

Unique nonempty character identifiers in input order.

minimum

Study-selected concentration threshold in (0, 1]. Equality passes. This is a decision convention, not a validity guarantee.

observation_weight

Optional positive, named inverse-observation weights. They are normalised over all reached records, including records with zero preceding exposure weight. NULL uses equal averaging weights.

Value

A list with fraction, equivalent (fraction times reached count), n, and state (pass, fail, boundary_fail, or unassessable). Assessed inputs also give boundary_records and sole_failures. A required positive policy mass with zero natural mass on a positive-weight row gives boundary_fail and no fraction. Invalid or numerically unrepresentable inputs give unassessable.

Details

With normalised observation weights b, preceding exposure ratios W and m2 = sum(q^2/g), the fraction is (sum(b * W))^2 / sum(b * W^2 * m2). The observation weights enter once. Zero-W records remain in the averaging population; their current exposure divisions are skipped. Inputs are never trimmed. The fraction assesses the supplied fitted laws; it cannot establish positivity, identification or coverage.

Examples

ids <- c("a", "b")
g <- matrix(c(.2, .8, .2, .8), 2, byrow = TRUE,
  dimnames = list(ids, c("zero", "positive")))
q <- g
q[, ] <- rep(c(1, 0), each = 2)
margot_lmtp_support_concentration(g, q, setNames(c(1, 1), ids),
  setNames(c(TRUE, TRUE), ids), ids, minimum = .05)
#> $fraction
#> [1] 0.2
#> 
#> $equivalent
#> [1] 0.4
#> 
#> $n
#> [1] 2
#> 
#> $state
#> [1] "pass"
#> 
#> $boundary_records
#> [1] 0
#> 
#> $sole_failures
#> [1] 0
#>