Exact Test for 2x2 Tables with Automatic Zero-Cell Mid-p Default

Performs an exact test for 2x2 contingency tables using exact2x2. If any cell count in the 2x2 table is zero (min(tab) == 0) and midp is unspecified, the function defaults to the mid-p version of Central Fisher's exact test (midp = TRUE). This prevents the extreme conservatism and loss of power of standard conditional exact tests on boundary tables. When all cells are non-zero, it defaults to the standard Central Fisher's exact test (midp = FALSE), which guarantees central confidence intervals that invert the two one-sided tests.

Usage

exact2x2(
  x,
  y = NULL,
  data = NULL,
  variable = NULL,
  by = NULL,
  midp = NULL,
  conf.level = 0.95,
  alternative = "two.sided",
  tsmethod = "central",
  group = NULL,
  type = NULL,
  test.args = NULL,
  adj.vars = NULL,
  tbl = NULL,
  continuous_variable = NULL,
  ...
)

Arguments

x

A 2x2 numeric matrix, table, or a categorical vector. Can also be a data frame if variable and by are supplied (by name).

y

Optional second categorical vector when x is a vector.

data

Optional data frame when used with variable and by.

variable

Character string of the column name to test when called by gtsummary.

by

Character string of the grouping/stratifying column when called by gtsummary.

midp

Logical. If NULL (the default), automatically set to TRUE when any table cell is 0, and FALSE when all cells are positive. Can be explicitly set to TRUE or FALSE to override.

conf.level

Confidence level for the returned confidence interval (default 0.95).

alternative

Alternative hypothesis direction: "two.sided" (default), "greater", or "less".

tsmethod

Two-sided method passed to exact2x2: "two.sided" (Central Fisher's exact test, default), "minlike", or "blaker".

group, type, test.args, adj.vars, tbl, continuous_variable

Unused; accepted and ignored so this function satisfies gtsummary's custom-test calling convention (see tests) instead of leaking into ... and reaching exact2x2.

...

Additional arguments passed to exact2x2.

Value

A tibble with columns:

estimate

Estimated odds ratio (conditional MLE or median unbiased estimate).

p.value

Two-sided or one-sided p-value (mid-p adjusted when midp = TRUE).

conf.low

Lower bound of the confidence interval.

conf.high

Upper bound of the confidence interval.

statistic

Point estimate of the odds ratio (for gtsummary compatibility).

method

Descriptive name of the exact test performed.

alternative

Alternative hypothesis.

midp

Logical flag indicating whether mid-p adjustment was used.

has_zero

Logical flag indicating whether any cell in the table was zero.

Details

The function accepts a 2x2 table/matrix, two categorical vectors x and y, or data, variable and by by name for direct compatibility as a custom test in gtsummary's add_p. A table with an all-zero row or column (for example an unused factor level) is reduced to the observed levels first, so a binary variable with an empty extra level is still tested as 2x2.

Examples

# 2x2 table with a zero cell: automatically triggers mid-p adjustment
tab_zero <- matrix(c(0, 10, 5, 15), nrow = 2,
                   dimnames = list(c("Treated", "Control"), c("Event", "No Event")))
exact2x2(tab_zero)
#> # A tibble: 1 × 9
#>   estimate p.value conf.low conf.high statistic method         alternative midp 
#>      <dbl>   <dbl>    <dbl>     <dbl>     <dbl> <chr>          <chr>       <lgl>
#> 1        0   0.109        0      1.52         0 Central Fishe… two.sided   TRUE 
#> # ℹ 1 more variable: has_zero <lgl>

# 2x2 table without zero cells: standard Central Fisher's exact test
tab_nonzero <- matrix(c(12, 8, 5, 15), nrow = 2)
exact2x2(tab_nonzero)
#> # A tibble: 1 × 9
#>   estimate p.value conf.low conf.high statistic method         alternative midp 
#>      <dbl>   <dbl>    <dbl>     <dbl>     <dbl> <chr>          <chr>       <lgl>
#> 1     4.32  0.0536    0.982      21.9      4.32 Central Fishe… two.sided   FALSE
#> # ℹ 1 more variable: has_zero <lgl>