Which labelling reproduces a reported contrast?

A reported odds ratio, risk ratio or risk difference depends on which group is the reference, which outcome is the event and which margin of the table holds the groups. relchk() recomputes the contrast from the table under every such reading and says which ones reproduce the reported value: the labelling the report states, another one, or none.

Usage

relchk(
  x,
  value,
  type = "or",
  group = NULL,
  ref = NULL,
  event = NULL,
  digits = NULL,
  tol = NULL
)

Arguments

x: The table of counts, groups in rows and outcomes in columns: a matrix, a 2-d table, a data frame of numeric columns, or a list of numeric vectors of one length (the columns). At least 2 x 2; counts finite and at least 0 with no NA, no row or column all 0, and no label missing or given twice. Rows and columns without names are labelled "1", "2", ... .
value: The reported value: one finite number.
type: The kind of contrast the report claims: "or" (odds ratio), "rr" (risk ratio) or "rd" (risk difference).
group, ref, event: The labelling the report claims, each NULL (not stated) or a label (matched exactly, case included; a factor by its label) or a position: group and ref name rows of x, event a column.
digits: The decimals value was rounded to: a reading matches when it lies within half a unit of the last decimal, at either end, so that both rounding conventions at the half are accepted. By default the fewest decimals that print value exactly (give digits = 2 for a value reported as 2.30). Give digits or tol, not both.
tol: Instead of digits, the largest difference allowed: one number from 0. Either way, a reading also matches when it differs only in the last few bits.

Value

An object of class relchk, a list: verdict ("holds": a reading the claim allows matches; "other": only readings it does not allow match; "none"), ok (TRUE when the claim holds), value, tol (the difference allowed), digits (NA when tol was given or no decimals print value exactly; then tol is 0), type, claim (the stated group, ref and event, NA where not stated) and reads, a data frame with one row per reading: grp ("rows" or "cols": the margin holding the groups), type, group, ref, event, value, match and claim (TRUE for the readings the claim allows: groups in rows, the kind type, and the stated labels).

Details

A reading compares group group with group ref for outcome event, the other outcomes pooled as non-events: with a and b the events and non-events of group, c and d those of ref, the odds ratio is a d / (b c), the risk ratio (a / (a + b)) / (c / (c + d)) and the risk difference a / (a + b) - c / (c + d). Every ordered pair of groups and every outcome is read, with the groups in the rows and, the table transposed, in the columns, and all three kinds of contrast.

No correction is made for zero cells: a reading whose denominator is 0 is Inf (a positive numerator) or NaN (0 over 0) and matches nothing. Counts need not be whole numbers (weighted totals are read as they are).

For a 2 x 2 table the odds ratio inverts when the reference group or the event changes and is unchanged when both change or the table is transposed; the risk ratio inverts with the reference group, and the risk difference changes sign with either; proof("relchk") names the Lean theorems.

Examples

tab <- matrix(c(20, 10, 80, 90), 2,
              dimnames = list(c("A", "B"), c("yes", "no")))
# 2.25 is the odds ratio of A against B for "yes"
relchk(tab, 2.25, ref = "B", event = "yes")
#> relchk: reported 2.25, to 2 decimals
#> claim: or, ref B, event yes
#> verdict: the claim holds
#>   grp type group ref event value claim
#>  rows   or     B   A    no  2.25 FALSE
#>  rows   or     A   B   yes  2.25  TRUE
#>  cols   or    no yes     B  2.25 FALSE
#>  cols   or   yes  no     A  2.25 FALSE
# 0.44 is the same contrast read with the reference group swapped
relchk(tab, 0.44, ref = "B", event = "yes")
#> relchk: reported 0.44, to 2 decimals
#> claim: or, ref B, event yes
#> verdict: only readings the claim does not allow match
#>   grp type group ref event     value claim
#>  rows   or     B   A   yes 0.4444444 FALSE
#>  rows   or     A   B    no 0.4444444 FALSE
#>  cols   or    no yes     A 0.4444444 FALSE
#>  cols   or   yes  no     B 0.4444444 FALSE
# a risk ratio reported as an odds ratio
relchk(tab, 2.0, type = "or", digits = 1)
#> relchk: reported 2, to 1 decimal
#> claim: or
#> verdict: only readings the claim does not allow match
#>   grp type group ref event value claim
#>  rows   rr     A   B   yes     2 FALSE