Check reported odds ratios against a labelled table, under every relabelling

Recomputes the odds ratios a report gives for each group from the underlying table of counts, and says whether the reported values follow from the table as it is labelled. If they do not, it tries every reassignment of the group labels (and the two outcome columns swapped) and lists the relabellings that do reproduce the reported values. Use it when a published odds ratio looks implausible: a four-fold ratio reported as thirty-six-fold is typically reproduced exactly by one such relabelling, which shows the groups were mislabelled rather than the arithmetic wrong.

Usage

odds_ratio_check(counts, reference, reported, tolerance = 0.05)

Arguments

counts: Numeric matrix, data frame or table of counts with row names (the groups) and exactly two columns: outcome absent, then outcome present.
reference: Character string: the row name of the reference group.
reported: Named numeric vector of the odds ratios the report states, one per non-reference group, named by group. Extra names are ignored.
tolerance: Number, default 0.05: the relative tolerance for a match (5 percent), to allow for rounding in the report.

Value

A list with elements computed (named numeric odds ratios from the table as labelled), reported (the reported values, in the same order), consistent (logical), matches (a data frame with character relabelling, for example "B -> C, C -> B", and logical outcome_columns_swapped, one row per relabelling that reproduces the reported values) and verdict (a one-sentence character summary).

Details

With row $r$ holding $a_r$ (outcome absent) and $b_r$ (outcome present), the odds ratio of group $r$ against the reference $0$ is $$OR_r = \frac{b_r / a_r}{b_0 / a_0}.$$ A reported value matches when $|OR_r - \widehat{OR}_r| \le$ tolerance $\times |\widehat{OR}_r|$ for every non-reference group, and all values are finite. The search covers all $k!$ permutations of the row labels, each with and without the outcome columns swapped (the identity without a swap is the "as labelled" check), and is only run for $k \le 7$ groups. A zero cell gives an infinite or undefined odds ratio, which never matches.

Errors: counts not a matrix, data frame or table with two columns and row names; reference not a row name; reported not named by every non-reference row.

Examples

tab <- matrix(c(900, 100, 700, 300, 400, 600),
  ncol = 2, byrow = TRUE,
  dimnames = list(c("A", "B", "C"), c("no", "yes"))
)
# the odds ratios as labelled: B 3.86, C 13.5
odds_ratio_check(tab, "A", c(B = 3.857, C = 13.5))$consistent
#> [1] TRUE

# a report that swapped B and C
chk <- odds_ratio_check(tab, "A", c(B = 13.5, C = 3.857))
chk$matches
#>      relabelling outcome_columns_swapped
#> 1 B -> C, C -> B                   FALSE
chk$verdict
#> [1] "the reported odds ratios do NOT follow from the table as labelled; they are reproduced under a relabelling (B -> C, C -> B): the groups were mislabelled, not the software"

# every non-reference group needs a reported value
try(odds_ratio_check(tab, "A", c(B = 3.857)))
#> Error : odds_ratio_check: `reported` must be named by every non-reference row: ‘B’, ‘C’