Find the plateau of near-optimal symptom combinations

Identifies every symptom combination whose balanced accuracy falls within delta percentage points of the best combination in the same search. The best-performing subset of PCL-5 items is rarely alone: typically a large set of alternatives performs indistinguishably well. Reporting the size of that plateau, rather than only the winner, is what separates "these six items are the right ones" from "any of these hundreds of six-item sets would do".

Usage

compute_plateau(fit, delta = 1)

Arguments

fit: A fitted exhaustive search from score_all_combinations.
delta: Numeric. Plateau width in percentage points of balanced accuracy: delta = 1 (the default) keeps every combination within one percentage point of the best. A vector is allowed, e.g. delta = c(1, 5) to report a primary and a secondary plateau in one call.

Value

An object of class ptsdiag_plateau: a list of two data frames.

summary: one row per delta, with delta, ba_best (the best balanced accuracy), ba_threshold (the lowest balanced accuracy still on the plateau), plateau_size (number of combinations), n_candidates (size of this rule form's candidate space) and plateau_proportion.
sets: one row per plateau member, with delta, rank, combination_id, balanced_accuracy and ba_gap (how far below the best it falls, in percentage points).

Details

The plateau is always computed within one rule form, because the candidate spaces differ in size. A six-item hierarchical search evaluates 13,685 combinations while the non-hierarchical search evaluates 38,760, so the same plateau count means very different things; plateau_proportion divides by the right denominator for the search that produced fit.

Comparisons use exact integer arithmetic rather than the rounded balanced accuracies. Writing N1 for the number of reference cases and N0 for the number of non-cases, the quantity tp * N0 + tn * N1 is an integer proportional to balanced accuracy, so combinations that genuinely tie are never separated by floating-point noise.

Examples

# \donttest{
# A compact 4-symptom search on a 120-row subset keeps the example fast
ptsd_data <- rename_ptsd_columns(simulated_ptsd[1:120, ],
                                 id_col = c("patient_id", "age", "sex"))
fit <- score_all_combinations(ptsd_data, n_symptoms = 4, n_required = 3,
                              show_progress = FALSE)

plateau <- compute_plateau(fit, delta = c(1, 5))
plateau$summary
#>   delta ba_best ba_threshold plateau_size n_candidates plateau_proportion
#> 1     1       1    0.9909910            8         4845        0.001651187
#> 2     5       1    0.9684685           39         4845        0.008049536
head(plateau$sets)
#>   delta rank combination_id balanced_accuracy    ba_gap
#> 1     1    1      6_7_11_12         1.0000000 0.0000000
#> 2     1    2       4_6_7_12         0.9954955 0.4504505
#> 3     1    3       4_6_7_11         0.9909910 0.9009009
#> 4     1    4      6_7_11_13         0.9909910 0.9009009
#> 5     1    5      6_7_11_17         0.9909910 0.9009009
#> 6     1    6      6_7_11_19         0.9909910 0.9009009
# }