Compute IPSI counterfactual initiation probabilities — margot_compute_ipsi

Takes a formatted transition matrix (for example, one of the formatted tables produced by `margot_transition_table()` such as `transition_tables$tables_data[[i]]` or the paired `knitr_kable` stored under `transition_tables$tables[[i]]`) and computes the natural initiation probability for baseline non-attenders along with the counterfactual probabilities implied by marginal incremental propensity score interventions (IPSIs) for a set of proposed deltas.

Usage

margot_compute_ipsi_probability(trans_matrix, deltas = c(2, 5, 10))

Arguments

trans_matrix: A data frame containing at least a `"From / To"` column, a `"State 1"` column, and a `"Total"` column. Must include a row identified as `"State 0"` under `"From / To"`, representing non-attenders at the prior wave. You can pass either the raw data frame or the `knitr_kable` object returned inside `margot_transition_table(... )$tables[[i]]` (the function automatically reads the attached `table_data` attribute).
deltas: Numeric vector of IPSI shift magnitudes (greater than 1). The defaults match the standard IPSI reporting set `c(2, 5, 10)`.

Value

A data frame with one row per delta containing the natural initiation probability `p`, its exact 95 counterfactual probability `p' = 1 - (1 - p) / delta`, and the fold increase `p'/p`. The result carries a `counts` attribute with the raw initiation and at-risk totals and the natural-probability interval used to compute `p`.

Examples

trans <- data.frame(
  `From / To` = c("State 0", "State 1"),
  `State 0` = c(27380, 330),
  `State 1` = c(845, 170),
  Total = c(28225, 500),
  check.names = FALSE
)
margot_compute_ipsi_probability(trans)
#>   delta delta_inverse natural_p natural_p_l natural_p_u counterfactual_p
#> 1     2           0.5  0.029938  0.02798067  0.03199286        0.5149690
#> 2     5           0.2  0.029938  0.02798067  0.03199286        0.8059876
#> 3    10           0.1  0.029938  0.02798067  0.03199286        0.9029938
#>   fold_increase
#> 1      17.20118
#> 2      26.92189
#> 3      30.16213
margot_compute_ipsi_probability(trans, deltas = c(1.5, 3))
#>   delta delta_inverse natural_p natural_p_l natural_p_u counterfactual_p
#> 1   1.5         0.667  0.029938  0.02798067  0.03199286         0.353292
#> 2   3.0         0.333  0.029938  0.02798067  0.03199286         0.676646
#>   fold_increase
#> 1      11.80079
#> 2      22.60158