Compute a BCa bootstrap confidence interval for the Mann-Whitney parameter. The code is based on the slides found here: http://users.stat.umn.edu/~helwig/notes/bootci-Notes.pdf

bca_mannwhitney(
  treat,
  covar,
  out,
  nboot,
  treat_form,
  out_levels,
  out_form,
  mannwhitney_est,
  out_model,
  alpha = 0.05
)

Arguments

treat	A `numeric` vector containing treatment status. Missing values are not allowed unless the corresponding entry in `out` is also missing. Only values of 0 or 1 are treated as actual treatment levels. Any other value is assumed to encode a value for which the outcome is missing and the corresponding outcome value is ignored.
covar	A `data.frame` containing the covariates to include in the working proportional odds model.
out	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
nboot	Number of bootstrap replicates used to compute bootstrap confidence intervals.
treat_form	The right-hand side of a regression formula for the working model of treatment probability as a function of covariates
out_levels	A `numeric` vector containing all ordered levels of the outcome.
out_form	The right-hand side of a regression formula for the working proportional odds model. NOTE: THIS FORMULA MUST NOT SUPPRESS THE INTERCEPT.
mannwhitney_est	The point estimate of the Mann-Whitney parameter.
out_model	Which R function should be used to fit the proportional odds model. Options are `"polr"` (from the `MASS` package), "vglm" (from the `VGAM` package), or `"clm"` (from the `ordinal` package).
alpha	Level of confidence interval.

Confidence interval for the Mann-Whitney parameter