Proportion difference estimation

The analysis function estimate_proportion_diff() creates a layout element to estimate the difference in proportion of responders within a studied population. The primary analysis variable, vars, is a logical variable indicating whether a response has occurred for each record. See the method parameter for options of methods to use when constructing the confidence interval of the proportion difference. A stratification variable can be supplied via the strata element of the variables argument.

Usage

estimate_proportion_diff(
  lyt,
  vars,
  variables = list(strata = NULL),
  conf_level = 0.95,
  method = c("waldcc", "wald", "cmh", "cmh_sato", "cmh_mn", "ha", "newcombe",
    "newcombecc", "strat_newcombe", "strat_newcombecc"),
  weights_method = "cmh",
  var_labels = vars,
  na_str = default_na_str(),
  nested = TRUE,
  show_labels = "hidden",
  table_names = vars,
  section_div = NA_character_,
  ...,
  na_rm = TRUE,
  .stats = c("diff", "diff_ci"),
  .stat_names = NULL,
  .formats = c(diff = "xx.x", diff_ci = "(xx.x, xx.x)"),
  .labels = NULL,
  .indent_mods = c(diff = 0L, diff_ci = 1L)
)

s_proportion_diff(
  df,
  .var,
  .ref_group,
  .in_ref_col,
  variables = list(strata = NULL),
  conf_level = 0.95,
  method = c("waldcc", "wald", "cmh", "cmh_sato", "cmh_mn", "ha", "newcombe",
    "newcombecc", "strat_newcombe", "strat_newcombecc"),
  weights_method = "cmh",
  ...
)

a_proportion_diff(
  df,
  ...,
  .stats = NULL,
  .stat_names = NULL,
  .formats = NULL,
  .labels = NULL,
  .indent_mods = NULL
)

Arguments

lyt

(PreDataTableLayouts)
layout that analyses will be added to.

vars

(character)
variable names for the primary analysis variable to be iterated over.

variables

(named list of string)
list of additional analysis variables.

conf_level

(proportion)
confidence level of the interval.

method

(string)
the method used for the confidence interval estimation.

weights_method

(string)
weights method. Can be either "cmh" or "heuristic" and directs the way weights are estimated.

var_labels

(character)
variable labels.

na_str

(string)
string used to replace all NA or empty values in the output.

nested

(flag)
whether this layout instruction should be applied within the existing layout structure _if possible (TRUE, the default) or as a new top-level element (FALSE). Ignored if it would nest a split. underneath analyses, which is not allowed.

show_labels

(string)
label visibility: one of "default", "visible" and "hidden".

table_names

(character)
this can be customized in the case that the same vars are analyzed multiple times, to avoid warnings from rtables.

section_div

(string)
string which should be repeated as a section divider after each group defined by this split instruction, or NA_character_ (the default) for no section divider.

...

additional arguments for the lower level functions.

na_rm

(flag)
whether NA values should be removed from x prior to analysis.

.stats

(character)
statistics to select for the table.

Options are: 'diff', 'diff_ci'

.stat_names

(character)
names of the statistics that are passed directly to name single statistics (.stats). This option is visible when producing rtables::as_result_df() with make_ard = TRUE.

.formats

(named character or list)
formats for the statistics. See Details in analyze_vars for more information on the "auto" setting.

.labels

(named character)
labels for the statistics (without indent).

.indent_mods

(named integer)
indent modifiers for the labels. Defaults to 0, which corresponds to the unmodified default behavior. Can be negative.

df

(data.frame)
data set containing all analysis variables.

.var

(string)
single variable name that is passed by rtables when requested by a statistics function.

.ref_group

(data.frame or vector)
the data corresponding to the reference group.

.in_ref_col

(flag)
TRUE when working with the reference level, FALSE otherwise.

Value

estimate_proportion_diff() returns a layout object suitable for passing to further layouting functions, or to rtables::build_table(). Adding this function to an rtable layout will add formatted rows containing the statistics from s_proportion_diff() to the table layout.

s_proportion_diff() returns a named list of elements diff and diff_ci.

a_proportion_diff() returns the corresponding list with formatted rtables::CellValue().

Details

The possible methods are:

"waldcc": Wald confidence interval with continuity correction (Agresti and Coull 1998) .
"wald": Wald confidence interval without continuity correction (Agresti and Coull 1998) .
"cmh": Cochran-Mantel-Haenszel (CMH) confidence interval (Mantel and Haenszel 1959) .
"cmh_sato": CMH confidence interval with Sato variance estimator (Sato et al. 1989) .
"cmh_mn": CMH confidence interval with Miettinen and Nurminen confidence interval (Miettinen and Nurminen 1985) .
"ha": Anderson-Hauck confidence interval (Hauck and Anderson 1986) .
"newcombe": Newcombe confidence interval without continuity correction (Newcombe 1998) .
"newcombecc": Newcombe confidence interval with continuity correction (Newcombe 1998) .
"strat_newcombe": Stratified Newcombe confidence interval without continuity correction (Yan and Su 2010) .
"strat_newcombecc": Stratified Newcombe confidence interval with continuity correction (Yan and Su 2010) .

Functions

estimate_proportion_diff(): Layout-creating function which can take statistics function arguments and additional format arguments. This function is a wrapper for rtables::analyze().
s_proportion_diff(): Statistics function estimating the difference in terms of responder proportion.
a_proportion_diff(): Formatted analysis function which is used as afun in estimate_proportion_diff().

Note

When performing an unstratified analysis, methods "cmh", "cmh_sato", "strat_newcombe", and "strat_newcombecc" are not permitted.

References

Agresti A, Coull BA (1998). “Approximate is Better than "Exact" for Interval Estimation of Binomial Proportions.” The American Statistician, 52(2), 119–126. doi:10.1080/00031305.1998.10480550 .

Hauck WW, Anderson S (1986). “A Comparison of Large-Sample Confidence Interval Methods for the Difference of Two Binomial Probabilities.” The American Statistician, 40(4), 318–322. doi:10.2307/2684618 , 2025-12-08.

Mantel N, Haenszel W (1959). “Statistical aspects of the analysis of data from retrospective studies of disease.” Journal of the National Cancer Institute, 22(4), 719–748.

Miettinen OS, Nurminen M (1985). “Comparative analysis of two rates.” Statistics in Medicine, 4(2), 213–226. doi:10.1002/sim.4780040211 .

Newcombe RG (1998). “Interval estimation for the difference between independent proportions: comparison of eleven methods.” Statistics in Medicine, 17(8), 873-890. doi:10.1002/(SICI)1097-0258(19980430)17:8<873::AID-SIM779>3.0.CO;2-I .

Sato T, Greenland S, Robins JM (1989). “On the variance estimator for the Mantel-Haenszel Risk Difference.” Biometrics, 45(4), 1323–1324. http://www.jstor.org/stable/2531784.

Yan X, Su XG (2010). “Stratified Wilson and Newcombe Confidence Intervals for Multiple Binomial Proportions.” Stat. Biopharm. Res., 2(3), 329–335.

Examples

## "Mid" case: 4/4 respond in group A, 1/2 respond in group B.
nex <- 100 # Number of example rows
dta <- data.frame(
  "rsp" = sample(c(TRUE, FALSE), nex, TRUE),
  "grp" = sample(c("A", "B"), nex, TRUE),
  "f1" = sample(c("a1", "a2"), nex, TRUE),
  "f2" = sample(c("x", "y", "z"), nex, TRUE),
  stringsAsFactors = TRUE
)

l <- basic_table() %>%
  split_cols_by(var = "grp", ref_group = "B") %>%
  estimate_proportion_diff(
    vars = "rsp",
    conf_level = 0.90,
    method = "ha"
  )

build_table(l, df = dta)
#>                                        A         B
#> ——————————————————————————————————————————————————
#> Difference in Response rate (%)       12.0        
#>   90% CI (Anderson-Hauck)         (-5.4, 29.4)    

s_proportion_diff(
  df = subset(dta, grp == "A"),
  .var = "rsp",
  .ref_group = subset(dta, grp == "B"),
  .in_ref_col = FALSE,
  conf_level = 0.90,
  method = "ha"
)
#> $diff
#> diff_ha 
#>      12 
#> attr(,"label")
#> [1] "Difference in Response rate (%)"
#> 
#> $diff_ci
#> diff_ci_ha_l diff_ci_ha_u 
#>    -5.374519    29.374519 
#> attr(,"label")
#> [1] "90% CI (Anderson-Hauck)"
#> 

# CMH example with strata
s_proportion_diff(
  df = subset(dta, grp == "A"),
  .var = "rsp",
  .ref_group = subset(dta, grp == "B"),
  .in_ref_col = FALSE,
  variables = list(strata = c("f1", "f2")),
  conf_level = 0.90,
  method = "cmh"
)
#> $diff
#> diff_cmh 
#> 12.27932 
#> attr(,"label")
#> [1] "Difference in Response rate (%)"
#> 
#> $diff_ci
#> diff_ci_cmh_l diff_ci_cmh_u 
#>     -2.657093     27.215725 
#> attr(,"label")
#> [1] "90% CI (CMH, without correction)"
#> 

a_proportion_diff(
  df = subset(dta, grp == "A"),
  .stats = c("diff"),
  .var = "rsp",
  .ref_group = subset(dta, grp == "B"),
  .in_ref_col = FALSE,
  conf_level = 0.90,
  method = "ha"
)
#> RowsVerticalSection (in_rows) object print method:
#> ----------------------------
#>   row_name formatted_cell indent_mod                       row_label
#> 1     diff             12          0 Difference in Response rate (%)