Package 'drord' reference manual

Title:	Doubly-Robust Estimators for Ordinal Outcomes
Description:	Efficient covariate-adjusted estimators of quantities that are useful for establishing the effects of treatments on ordinal outcomes (Benkeser, Diaz, Luedtke 2020 <doi:10.1111/biom.13377>)
Authors:	David Benkeser [aut, cre, cph]
Maintainer:	David Benkeser <[email protected]>
License:	MIT + file LICENSE
Version:	1.0.1.9000
Built:	2025-03-01 03:21:00 UTC
Source:	https://github.com/benkeser/drord

Compute a BCa confidence interval

Description

Compute a BCa confidence interval

Usage

bca_interval(pt_est, boot_samples, jack_samples, alpha = 0.05)
bca_interval(pt_est, boot_samples, jack_samples, alpha = 0.05)

Arguments

`pt_est`	The point estimate of the parameter of interest
`boot_samples`	A collection of bootstrap realizations of the estimator of the parameter of interest
`jack_samples`	A vector of jackknife estimates of the parameter of interest.
`alpha`	Confidence intervals have nominal level 1-`alpha`.

Value

2-length vector containing BCa confidence interval limits.

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

Description

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

Usage

bca_logodds(
  treat,
  covar,
  out,
  nboot,
  treat_form,
  out_levels,
  out_form,
  out_model,
  logodds_est,
  alpha = 0.05
)
bca_logodds(
  treat,
  covar,
  out,
  nboot,
  treat_form,
  out_levels,
  out_form,
  out_model,
  logodds_est,
  alpha = 0.05
)

Arguments

`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`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.
`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).
`logodds_est`	The estimated log-odds.
`alpha`	Level of confidence interval.

Value

matrix with treatment-specific log-odds CIs and CI for difference.

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

Description

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

Usage

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

Value

Confidence interval for the Mann-Whitney parameter

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

Description

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

Usage

bca_marg_dist(
  treat,
  covar,
  out,
  nboot,
  treat_form,
  out_levels,
  out_form,
  out_model,
  marg_cdf_est,
  marg_pmf_est,
  alpha = 0.05
)
bca_marg_dist(
  treat,
  covar,
  out,
  nboot,
  treat_form,
  out_levels,
  out_form,
  out_model,
  marg_cdf_est,
  marg_pmf_est,
  alpha = 0.05
)

Arguments

`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`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.
`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).
`marg_cdf_est`	Point estimate of treatment-specific CDF.
`marg_pmf_est`	Point estimate of treatment-specific PMF.
`alpha`	Level of confidence interval.

Value

List (cdf, pmf) of lists (treat=1, treat=0) of confidence intervals for distributions.

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

Description

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

Usage

bca_wmean(
  treat,
  covar,
  out,
  nboot,
  treat_form,
  out_levels,
  out_form,
  out_weights,
  out_model,
  wmean_est,
  alpha = 0.05
)
bca_wmean(
  treat,
  covar,
  out,
  nboot,
  treat_form,
  out_levels,
  out_form,
  out_weights,
  out_model,
  wmean_est,
  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.
`out_weights`	A vector of `numeric` weights with length equal to the length of `out_levels`.
`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).
`wmean_est`	The estimated weighted means + estimated covariance matrix.
`alpha`	Level of confidence interval.

Value

matrix with treatment-specific weighted mean CIs and CI for difference.

Used to compute treatment-specific BCa intervals for the CDF and PMF

Description

Used to compute treatment-specific BCa intervals for the CDF and PMF

Usage

compute_trt_spec_bca_intervals(
  dist = c("cdf", "pmf"),
  trt = c(1, 0),
  marg_est,
  boot_samples,
  jack_samples,
  alpha
)
compute_trt_spec_bca_intervals(
  dist = c("cdf", "pmf"),
  trt = c(1, 0),
  marg_est,
  boot_samples,
  jack_samples,
  alpha
)

Arguments

`dist`	Which one? CDF or PMF?
`trt`	Which treatment?
`marg_est`	The point estimate
`boot_samples`	A collection of bootstrap realizations of the estimator of the parameter of interest
`jack_samples`	A vector of jackknife estimates of the parameter of interest.
`alpha`	Confidence intervals have nominal level 1-`alpha`.

Value

List of pointwise and simultaneous confidence intervals for dist.

Compute simultaneous confidence interval for treatment-specific marginal distribution

Description

Compute simultaneous confidence interval for treatment-specific marginal distribution

Usage

compute_trt_spec_marg_dist_ptwise_ci(pt_est, cov_est, alpha, cdf = TRUE)
compute_trt_spec_marg_dist_ptwise_ci(pt_est, cov_est, alpha, cdf = TRUE)

Arguments

`pt_est`	The point estimate of the treatment-specific marginal CDF/PMF
`cov_est`	Covariance matrix estimates.
`alpha`	Confidence intervals have nominal level 1-`alpha`.
`cdf`	Is this for CDF or PMF?

Value

Confidence interval

Compute simultaneous confidence interval for treatment-specific marginal distribution

Description

Compute simultaneous confidence interval for treatment-specific marginal distribution

Usage

compute_trt_spec_marg_dist_simul_ci(
  pt_est,
  trt_spec_marg_dist_eif,
  remove_last = TRUE,
  alpha
)
compute_trt_spec_marg_dist_simul_ci(
  pt_est,
  trt_spec_marg_dist_eif,
  remove_last = TRUE,
  alpha
)

Arguments

`pt_est`	The point estimate of the treatment-specific marginal CDF/PMF
`trt_spec_marg_dist_eif`	The EIF estimates for the treatment-specific marginal CDF/PMF estimates
`remove_last`	Should the last level be removed? Should be set equal to `TRUE` for CDF computations and `FALSE` for PMF computations.
`alpha`	Confidence intervals have nominal level 1-`alpha`.

Value

Confidence interval

Simulated COVID-19 outcomes for hospitalized patients.

Description

A simulated dataset containing outcomes, (hypothetical) treatment, and age group

Usage

covid19
covid19

Format

A data frame with 500 rows and 3 variables:

out: study outcome, here 1 represents death, 2 intubation, 3 no adverse outcome
age_grp: age category with 1 the youngest and 7 the oldest
treat: hypothetical treatment, here 1 represents an (effective) active treatment and 0 a control

Doubly robust estimates of for evaluating effects of treatments on ordinal outcomes.

Description

The available parameters for evaluating treatment efficacy are:

Difference in (weighted) means: The outcome levels are treated numerically, with each level possibly assigned a weight. The difference in average outcomes is computed.
Log odds ratio: The comparison describes the average log-odds (treatment level 1 versus 0) of the cumulative probability for each level of the outcome.
Mann-Whitney: The probability that a randomly-selected individual receiving treatment 1 will have a larger outcome value than a randomly selected individual receiving treatment 0 (with ties assigned weight 1/2).

Usage

drord(
  out,
  treat,
  covar,
  out_levels = sort(unique(out)),
  out_form = paste0(colnames(covar), collapse = "+"),
  out_weights = rep(1, length(out_levels)),
  out_model = "pooled-logistic",
  treat_form = "1",
  param = c("weighted_mean", "log_odds", "mann_whitney"),
  ci = "wald",
  alpha = 0.05,
  nboot = 1000,
  return_models = TRUE,
  est_dist = TRUE,
  stratify = FALSE,
  ...
)
drord(
  out,
  treat,
  covar,
  out_levels = sort(unique(out)),
  out_form = paste0(colnames(covar), collapse = "+"),
  out_weights = rep(1, length(out_levels)),
  out_model = "pooled-logistic",
  treat_form = "1",
  param = c("weighted_mean", "log_odds", "mann_whitney"),
  ci = "wald",
  alpha = 0.05,
  nboot = 1000,
  return_models = TRUE,
  est_dist = TRUE,
  stratify = FALSE,
  ...
)

Arguments

`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`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_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.
`out_weights`	A vector of `numeric` weights with length equal to the length of `out_levels`.
`out_model`	Which R function should be used to fit the proportional odds model. The recommended option is `"pooled-logistic"`. Other options available include `"polr"` (from the `MASS` package), "vglm" (from the `VGAM` package), or `"clm"` (from the `ordinal` package).
`treat_form`	The right-hand side of a regression formula for the working model of treatment probability as a function of covariates
`param`	A vector of `characters` indicating which of the three treatment effect parameters should be estimated (`"weighted_mean", "log_odds",` and/or `"mann_whitney"`).
`ci`	A vector of `characters` indicating which confidence intervals should be computed (`"bca"` and/or `"wald"`)
`alpha`	Confidence intervals have nominal level 1-`alpha`.
`nboot`	Number of bootstrap replicates used to compute bootstrap confidence intervals.
`return_models`	If `TRUE` the fitted working proportional odds models and treatment probability models are returned.
`est_dist`	A `boolean` indicating whether estimates of the CDF and PMF should be computed and returned. For real data analysis, we generally recommend leaving as `TRUE`; however, when studying performance in simulations, it can save time to set to `FALSE`.
`stratify`	If `TRUE`, then a fully stratified estimator is computed, i.e., the empirical CDF of each treatment arm is estimated stratifying by levels of `covar`. For now, this option is limited to univariate covariates.
`...`	Other options (not currently used).

Details

In each case, estimates are constructed by obtaining a doubly robust estimate of the cumulative distribution function (CDF) for each treatment group. This is achieved by fitting a (working) proportional odds model that includes inverse probability of treatment weights. The inclusion of these weights ensures that, so long as the working model includes intercept terms, the resultant estimate of the CDF is an augmented inverse probability of treatment weighted estimate. This implies that the estimate is nonparametric efficient if the working model contains the truth; however, even if the working model does not contain the truth, the CDF estimates are consistent and asymptotically normal with variance expected to dominate that of an unadjusted estimate of the same treatment effect.

The CDF estimates are subsequently mapped into estimates of each requested parameter for evaluating treatment effects. The double robustness and efficiency properties of the CDF estimates extend to these quantities as well. Confidence intervals and hypothesis tests can be carried out in closed form using Wald-style intervals and tests or using a nonparametric corrected and accelerated bootstrap (BCa). Inference for the CDF and probability mass function is also returned and can be used for subsequent visualizations (see plot.drord).

Value

An object of class drord. In addition to information related to how drord was called, the output contains the following:

log_odds: inference pertaining to the log-odds parameter. NULL if this parameter not requested in call to drord.
mann_whitney: inference pertaining to the Mann-Whitney parameter. NULL if this parameter not requested in call to drord.
weighted_mean: inference pertaining to weighted mean parameter. NULL if this parameter not requested in call to drord.
cdf: inference pertaining to the treatment-specific CDFs. See the plot method for a convenient way of visualizing this information. NULL if est_dist = FALSE in call to drord.
pmf: inference pertaining to the treatment-specific PMFs. See the plot method for a convenient way of visualizing this information. NULL if est_dist = FALSE in call to drord.
treat_mod: the fitted model for the probability of treatment as a function of covariates. NULL if return_models = FALSE
out_mod: the proportional odds model fit in each treatment arm. named entries in list indicate the corresponding treatment arm. NULL if return_models = FALSE or stratify = TRUE.

Examples

data(covid19)

# get estimates of all parameters based on main-effects 
# proportional odds model and intercept-only propensity model
fit <- drord(out = covid19$out, treat = covid19$treat, 
             covar = covid19[, "age_grp", drop = FALSE])

# get estimates of all parameters based on proportional odds and
# propensity model that treats age_grp as categorical
fit2 <- drord(out = covid19$out, treat = covid19$treat, 
              covar = covid19[, "age_grp", drop = FALSE],
				 out_form = "factor(age_grp)",
				 treat_form = "factor(age_grp)")

# obtain estimator stratified by age group 
fit3 <- drord(out = covid19$out, treat = covid19$treat, 
              covar = covid19[, "age_grp", drop = FALSE],
				 stratify = TRUE)

# demonstration with missing outcome data
covid19$out[1:5] <- NA

# propensity model should now adjust for covariates to address
# the potential for informative missingness
fit4 <- drord(out = covid19$out, treat = covid19$treat, 
              covar = covid19[, "age_grp", drop = FALSE],
				 treat_form = "age_grp")
data(covid19)

# get estimates of all parameters based on main-effects 
# proportional odds model and intercept-only propensity model
fit <- drord(out = covid19$out, treat = covid19$treat, 
             covar = covid19[, "age_grp", drop = FALSE])

# get estimates of all parameters based on proportional odds and
# propensity model that treats age_grp as categorical
fit2 <- drord(out = covid19$out, treat = covid19$treat, 
              covar = covid19[, "age_grp", drop = FALSE],
				 out_form = "factor(age_grp)",
				 treat_form = "factor(age_grp)")

# obtain estimator stratified by age group 
fit3 <- drord(out = covid19$out, treat = covid19$treat, 
              covar = covid19[, "age_grp", drop = FALSE],
				 stratify = TRUE)

# demonstration with missing outcome data
covid19$out[1:5] <- NA

# propensity model should now adjust for covariates to address
# the potential for informative missingness
fit4 <- drord(out = covid19$out, treat = covid19$treat, 
              covar = covid19[, "age_grp", drop = FALSE],
				 treat_form = "age_grp")

Get EIF estimates for treatment-specific PMF at a particular level of the outcome

Description

Get EIF estimates for treatment-specific PMF at a particular level of the outcome

Usage

eif_pmf_k(k, out, treat, trt_level, trt_spec_prob_est, trt_k_spec_pmf_est)
eif_pmf_k(k, out, treat, trt_level, trt_spec_prob_est, trt_k_spec_pmf_est)

Arguments

`k`	The level of the outcome.
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`trt_level`	Treatment level
`trt_spec_prob_est`	Estimated propensity for `trt_level`.
`trt_k_spec_pmf_est`	Estimated conditional PMF for `trt_level` at `k`.

Get EIF estimates for treatment-specific CDF at a particular level of the outcome

Description

Get EIF estimates for treatment-specific CDF at a particular level of the outcome

Usage

eif_theta_k(k, out, treat, trt_level, trt_spec_prob_est, trt_k_spec_cdf_est)
eif_theta_k(k, out, treat, trt_level, trt_spec_prob_est, trt_k_spec_cdf_est)

Arguments

`k`	The level of the outcome.
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`trt_level`	Treatment level
`trt_spec_prob_est`	Estimated propensity for `trt_level`.
`trt_k_spec_cdf_est`	Estimated conditional CDF for `trt_level` at `k`.

Map an estimate of the conditional PMF into an estimate of the conditional CDF

Description

Map an estimate of the conditional PMF into an estimate of the conditional CDF

Usage

estimate_cdf(pmf_est)
estimate_cdf(pmf_est)

Arguments

pmf_est

A list of the treatment-specific PMF estimates

Value

A list of treatment-specific CDF estimates

Compute confidence interval/s for the log-odds parameters

Description

Compute confidence interval/s for the log-odds parameters

Usage

estimate_ci_logodds(
  logodds_est,
  cdf_est,
  out_form,
  covar,
  treat_prob_est,
  treat,
  treat_form,
  out,
  ci,
  alpha = 0.05,
  nboot,
  out_levels,
  out_model,
  ...
)
estimate_ci_logodds(
  logodds_est,
  cdf_est,
  out_form,
  covar,
  treat_prob_est,
  treat,
  treat_form,
  out,
  ci,
  alpha = 0.05,
  nboot,
  out_levels,
  out_model,
  ...
)

Arguments

`logodds_est`	The point estimates for log-odds.
`cdf_est`	A list of treatment-specific CDF estimates.
`out_form`	The right-hand side of a regression formula for the working proportional odds model. NOTE: THIS FORMULA MUST NOT SUPPRESS THE INTERCEPT.
`covar`	A `data.frame` containing the covariates to include in the working proportional odds model.
`treat_prob_est`	Estimated probability of treatments, output from call to `estimate_treat_prob`.
`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`treat_form`	The right-hand side of a regression formula for the working model of treatment probability as a function of covariates
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`ci`	A vector of `characters` indicating which confidence intervals should be computed (`"bca"` and/or `"wald"`)
`alpha`	Confidence intervals have nominal level 1-`alpha`.
`nboot`	Number of bootstrap replicates used to compute bootstrap confidence intervals.
`out_levels`	A `numeric` vector containing all ordered levels of the outcome.
`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).
`...`	Other options (not currently used).

Value

List with wald and bca-estimated confidence intervals for the weighted mean parameters.

Compute confidence interval/s for the Mann-Whitney parameter

Description

Compute confidence interval/s for the Mann-Whitney parameter

Usage

estimate_ci_mannwhitney(
  mannwhitney_est,
  cdf_est,
  pmf_est,
  treat_prob_est,
  treat_form,
  out_form,
  treat,
  ci,
  out,
  alpha,
  nboot,
  out_levels,
  covar,
  out_model
)
estimate_ci_mannwhitney(
  mannwhitney_est,
  cdf_est,
  pmf_est,
  treat_prob_est,
  treat_form,
  out_form,
  treat,
  ci,
  out,
  alpha,
  nboot,
  out_levels,
  covar,
  out_model
)

Arguments

`mannwhitney_est`	The point estimates for log-odds.
`cdf_est`	The estimated conditional CDF.
`pmf_est`	The estimated conditional PMF.
`treat_prob_est`	Estimated probability of treatments, output from call to `estimate_treat_prob`.
`treat_form`	The right-hand side of a regression formula for the working model of treatment probability as a function of covariates
`out_form`	The right-hand side of a regression formula for the working proportional odds model. NOTE: THIS FORMULA MUST NOT SUPPRESS THE INTERCEPT.
`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.
`ci`	A vector of `characters` indicating which confidence intervals should be computed (`"bca"` and/or `"wald"`)
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`alpha`	Confidence intervals have nominal level 1-`alpha`.
`nboot`	Number of bootstrap replicates used to compute bootstrap confidence intervals.
`out_levels`	A `numeric` vector containing all ordered levels of the outcome.
`covar`	A `data.frame` containing the covariates to include in the working proportional odds model.
`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).

Value

List with wald and bca-estimated confidence intervals for the Mann-Whitney parameter.

Compute confidence interval/s for the treatment specific PMF and CDF.

Description

Compute confidence interval/s for the treatment specific PMF and CDF.

Usage

estimate_ci_marg_dist(
  marg_cdf_est,
  marg_pmf_est,
  cdf_est,
  pmf_est,
  covar,
  treat_prob_est,
  treat_form,
  out_form,
  treat,
  ci,
  out_levels,
  out_model,
  out,
  alpha,
  nboot
)
estimate_ci_marg_dist(
  marg_cdf_est,
  marg_pmf_est,
  cdf_est,
  pmf_est,
  covar,
  treat_prob_est,
  treat_form,
  out_form,
  treat,
  ci,
  out_levels,
  out_model,
  out,
  alpha,
  nboot
)

Arguments

`marg_cdf_est`	Point estimate of treatment-specific CDF.
`marg_pmf_est`	Point estimate of treatment-specific PMF.
`cdf_est`	Estimates of treatment-specific conditional CDF.
`pmf_est`	Estimates of treatment-specific conditional PMF.
`covar`	A `data.frame` containing the covariates to include in the working proportional odds model.
`treat_prob_est`	Estimated probability of treatments, output from call to `estimate_treat_prob`.
`treat_form`	The right-hand side of a regression formula for the working model of treatment probability as a function of covariates
`out_form`	The right-hand side of a regression formula for the working proportional odds model. NOTE: THIS FORMULA MUST NOT SUPPRESS THE INTERCEPT.
`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.
`ci`	A vector of `characters` indicating which confidence intervals should be computed (`"bca"` and/or `"wald"`)
`out_levels`	A `numeric` vector containing all ordered levels of the outcome.
`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).
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`alpha`	Confidence intervals have nominal level 1-`alpha`.
`nboot`	Number of bootstrap replicates used to compute bootstrap confidence intervals.

Value

List of lists (cdf and pmf) with wald and bca-estimated confidence intervals for the marginal treatment-specific distribution functions.

Compute confidence interval/s for the weight mean parameters

Description

Compute confidence interval/s for the weight mean parameters

Usage

estimate_ci_wmean(
  out,
  treat,
  covar,
  wmean_est,
  alpha = 0.05,
  out_levels = order(unique(out)),
  out_form = NULL,
  out_weights = rep(1, length(out_levels)),
  out_model,
  treat_form = "1",
  ci = c("bca", "wald"),
  nboot = 10000
)
estimate_ci_wmean(
  out,
  treat,
  covar,
  wmean_est,
  alpha = 0.05,
  out_levels = order(unique(out)),
  out_form = NULL,
  out_weights = rep(1, length(out_levels)),
  out_model,
  treat_form = "1",
  ci = c("bca", "wald"),
  nboot = 10000
)

Arguments

`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`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.
`wmean_est`	The point estimates for weighted means
`alpha`	Confidence intervals have nominal level 1-`alpha`.
`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.
`out_weights`	A vector of `numeric` weights with length equal to the length of `out_levels`.
`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).
`treat_form`	The right-hand side of a regression formula for the working model of treatment probability as a function of covariates
`ci`	A vector of `characters` indicating which confidence intervals should be computed (`"bca"` and/or `"wald"`)
`nboot`	Number of bootstrap replicates used to compute bootstrap confidence intervals.

Value

List with wald and bca-estimated confidence intervals for the weighted mean parameters.

Map an estimate of treatment-specific PMF into an estimate of treatment specific conditional mean for each observation.

Description

Map an estimate of treatment-specific PMF into an estimate of treatment specific conditional mean for each observation.

Usage

estimate_cond_mean(trt_spec_pmf_est, ordered_out_levels, ordered_out_weights)
estimate_cond_mean(trt_spec_pmf_est, ordered_out_levels, ordered_out_weights)

Arguments

`trt_spec_pmf_est`	The treatment-specific PMF estimates
`ordered_out_levels`	Self explanatory
`ordered_out_weights`	Self explanatory

Value

Vector of estimated conditional means

Obtain an estimate of the efficient influence function for the treatment-specific weighted mean parameter

Description

Obtain an estimate of the efficient influence function for the treatment-specific weighted mean parameter

Usage

estimate_eif_wmean(
  trt_spec_cond_mean_est,
  trt_spec_prob_est,
  trt_level,
  out,
  treat
)
estimate_eif_wmean(
  trt_spec_cond_mean_est,
  trt_spec_prob_est,
  trt_level,
  out,
  treat
)

Arguments

`trt_spec_cond_mean_est`	Conditional mean for `trt_level`
`trt_spec_prob_est`	Propensity for `trt_level`
`trt_level`	Treatment level
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`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.

implements a plug-in estimator of equation (2) in Diaz et al

Description

implements a plug-in estimator of equation (2) in Diaz et al

Usage

estimate_logodds(cdf_est)
estimate_logodds(cdf_est)

Arguments

cdf_est

A list of treatment-specific CDF estimates

Value

Log odds of treatment = 1, = 0, and the difference.

Compute the estimate of Mann-Whitney based on conditional CDF and PMF

Description

Compute the estimate of Mann-Whitney based on conditional CDF and PMF

Usage

estimate_mannwhitney(cdf_est, pmf_est)
estimate_mannwhitney(cdf_est, pmf_est)

Arguments

`cdf_est`	Conditional CDF estimates
`pmf_est`	Conditional PMF estimates

Value

Mann-Whitney point estimate

Get a treatment-specific estimate of the conditional PMF. Essentially this is a wrapper function for `fit_trt_spec_reg`, which fits the proportion odds model in a given treatment arm.

Description

Get a treatment-specific estimate of the conditional PMF. Essentially this is a wrapper function for fit_trt_spec_reg, which fits the proportion odds model in a given treatment arm.

Usage

estimate_pmf(
  out,
  treat,
  covar,
  out_levels,
  out_form = NULL,
  out_model,
  treat_prob_est,
  stratify = FALSE,
  return_models = TRUE,
  ...
)
estimate_pmf(
  out,
  treat,
  covar,
  out_levels,
  out_form = NULL,
  out_model,
  treat_prob_est,
  stratify = FALSE,
  return_models = TRUE,
  ...
)

Arguments

`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`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_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.
`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).
`treat_prob_est`	Estimated probability of treatments, output from call to `estimate_treat_prob`.
`stratify`	Boolean indicating whether to use nonparametric maximum likelihood (i.e., a stratified estimator). If `out_form = "1"`, then a covariate-unadjusted estimate is computed.
`return_models`	If `TRUE` the fitted working proportional odds models and treatment probability models are returned.
`...`	Other options (not used).

Value

A list with fm the fitted model for treatment 1 and 0 (or, if !return_models then NULL) and pmf the estimated PMF under treatment 1 and 0 evaluated on each observation.

Estimate probability of receiving each level of treatment

Description

Estimate probability of receiving each level of treatment

Usage

estimate_treat_prob(treat, covar, treat_form, return_models)
estimate_treat_prob(treat, covar, treat_form, return_models)

Arguments

`treat`	A `numeric` vector containing treatment status. 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.
`covar`	A `data.frame` containing the covariates to include in the working proportional odds model.
`treat_form`	The right-hand side of a regression formula for the working model of treatment probability as a function of covariates
`return_models`	If `TRUE` the fitted working proportional odds models and treatment probability models are returned.

Value

A list where the first element is estimate of Pr(treat = 1 | covar) for covar equal to inputted values of covar and second element is estimate of Pr(treat = 0 | covar) for covar equal to inputted values of covar

Compute the estimate of the weighted mean parameter based on estimated PMF in each treatment arm.

Description

Compute the estimate of the weighted mean parameter based on estimated PMF in each treatment arm.

Usage

estimate_wmean(
  pmf_est,
  treat,
  out,
  out_levels,
  out_weights,
  treat_prob_est,
  return_cov = TRUE
)
estimate_wmean(
  pmf_est,
  treat,
  out,
  out_levels,
  out_weights,
  treat_prob_est,
  return_cov = TRUE
)

Arguments

`pmf_est`	List of treatment-specific PMF estimates.
`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.
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`out_levels`	A `numeric` vector containing all ordered levels of the outcome.
`out_weights`	A vector of `numeric` weights with length equal to the length of `out_levels`.
`treat_prob_est`	Estimated probability of treatments, output from call to `estimate_treat_prob`.
`return_cov`	If `TRUE` the estimated covariance matrix is returned.

Value

List with estimates of treatment-specific means and difference in means. If return_cov = TRUE, also includes covariance matrix estimates.

Get the covariance matrix for beta

Description

Get the covariance matrix for beta

Usage

evaluate_beta_cov(cdf_est, theta_cov)
evaluate_beta_cov(cdf_est, theta_cov)

Arguments

`cdf_est`	Estimated CDFs
`theta_cov`	Covariance matrix for CDF estimates

Value

Estimated covariance matrix for log-odds ratio parameters

Compute the estimated gradient of the Mann-Whitney parameter. Needed to derive standard error for Wald confidence intervals.

Description

Compute the estimated gradient of the Mann-Whitney parameter. Needed to derive standard error for Wald confidence intervals.

Usage

evaluate_mannwhitney_gradient(cdf_est, pmf_est)
evaluate_mannwhitney_gradient(cdf_est, pmf_est)

Arguments

`cdf_est`	Conditional CDF estimates
`pmf_est`	Conditional PMF estimates

Value

3-length vector for delta method calculus

Get eif estimates for treatment-specific CDF

Description

Get eif estimates for treatment-specific CDF

Usage

evaluate_marg_cdf_eif(cdf_est, treat_prob_est, treat, out, out_levels)
evaluate_marg_cdf_eif(cdf_est, treat_prob_est, treat, out, out_levels)

Arguments

`cdf_est`	Estimated conditional CDF for `trt_level`.
`treat_prob_est`	Estimated propensity for `trt_level`.
`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`out_levels`	A `numeric` vector containing all ordered levels of the outcome.

Value

a list of eif estimates

Evaluate pointwise confidence interval for marginal CDF.

Description

Evaluate pointwise confidence interval for marginal CDF.

Usage

evaluate_marg_cdf_ptwise_ci(marg_cdf_est, marg_cdf_eif, alpha)
evaluate_marg_cdf_ptwise_ci(marg_cdf_est, marg_cdf_eif, alpha)

Arguments

`marg_cdf_est`	The point estimate of the marginal CDF distribution
`marg_cdf_eif`	The EIF estimates for the marginal CDF estimates
`alpha`	Confidence intervals have nominal level 1-`alpha`.

Value

List by treatment of simultaneous confidence intervals

Evaluate simultaneous confidence interval for marginal PMF or CDF.

Description

Evaluate simultaneous confidence interval for marginal PMF or CDF.

Usage

evaluate_marg_dist_simul_ci(
  marg_dist_est,
  marg_dist_eif,
  alpha,
  remove_last = FALSE
)
evaluate_marg_dist_simul_ci(
  marg_dist_est,
  marg_dist_eif,
  alpha,
  remove_last = FALSE
)

Arguments

`marg_dist_est`	The point estimate of the marginal CDF/PMF distribution
`marg_dist_eif`	The EIF estimates for the marginal CDF/PMF estimates
`alpha`	Confidence intervals have nominal level 1-`alpha`.
`remove_last`	Should the last level be removed? Should be set equal to `TRUE` for CDF computations and `FALSE` for PMF computations.

Value

List by treatment of simultaneous confidence intervals

Get eif estimates for treatment-specific PMF

Description

Get eif estimates for treatment-specific PMF

Usage

evaluate_marg_pmf_eif(pmf_est, treat_prob_est, treat, out, out_levels)
evaluate_marg_pmf_eif(pmf_est, treat_prob_est, treat, out, out_levels)

Arguments

`pmf_est`	Estimated conditional PMF for `trt_level`.
`treat_prob_est`	Estimated propensity for `trt_level`.
`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`out_levels`	A `numeric` vector containing all ordered levels of the outcome.

Value

a list of eif estimates

Evaluate pointwise confidence interval for marginal PMF.

Description

Evaluate pointwise confidence interval for marginal PMF.

Usage

evaluate_marg_pmf_ptwise_ci(marg_pmf_est, marg_pmf_eif, alpha)
evaluate_marg_pmf_ptwise_ci(marg_pmf_est, marg_pmf_eif, alpha)

Arguments

`marg_pmf_est`	The point estimate of the marginal PMF distribution
`marg_pmf_eif`	The EIF estimates for the marginal PMF estimates
`alpha`	Confidence intervals have nominal level 1-`alpha`.

Value

List by treatment of simultaneous confidence intervals

get a covariance matrix for the estimated CDF

Description

get a covariance matrix for the estimated CDF

Usage

evaluate_theta_cov(cdf_est, treat_prob_est, treat, out, out_levels)
evaluate_theta_cov(cdf_est, treat_prob_est, treat, out, out_levels)

Arguments

`cdf_est`	The estimates of the treatment-specific CDFs
`treat_prob_est`	List of estimated probability of treatments, output from call to `estimate_treat_prob`.
`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`out_levels`	A `numeric` vector containing all ordered levels of the outcome.

Value

Estimated covariance matrix for CDF estimates

Get a matrix of eif estimates for treatment-specific PMF

Description

Get a matrix of eif estimates for treatment-specific PMF

Usage

evaluate_trt_spec_pmf_eif(
  trt_spec_pmf_est,
  trt_spec_prob_est,
  trt_level,
  treat,
  out,
  out_levels
)
evaluate_trt_spec_pmf_eif(
  trt_spec_pmf_est,
  trt_spec_prob_est,
  trt_level,
  treat,
  out,
  out_levels
)

Arguments

`trt_spec_pmf_est`	Estimated conditional PMF for `trt_level`.
`trt_spec_prob_est`	Estimated propensity for `trt_level`.
`trt_level`	Treatment level
`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`out_levels`	A `numeric` vector containing all ordered levels of the outcome.

Value

a matrix of EIF estimates

get a matrix of eif estimates for the treatment-specific CDF estimates

Description

get a matrix of eif estimates for the treatment-specific CDF estimates

Usage

evaluate_trt_spec_theta_eif(
  trt_spec_cdf_est,
  trt_spec_prob_est,
  trt_level,
  treat,
  out,
  out_levels
)
evaluate_trt_spec_theta_eif(
  trt_spec_cdf_est,
  trt_spec_prob_est,
  trt_level,
  treat,
  out,
  out_levels
)

Arguments

`trt_spec_cdf_est`	Estimated conditional CDF for `trt_level`.
`trt_spec_prob_est`	Estimated propensity for `trt_level`.
`trt_level`	Treatment level
`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.
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`out_levels`	A `numeric` vector containing all ordered levels of the outcome.

Value

matrix of EIF estimates for CDF.

Helper function to fit a treatment specific outcome regression. If there are more than 2 observed levels of the outcome for the specified treatment arm, then `polr` is used from the `MASS` package. Otherwise logistic regression is used. In both cases, inverse probability of treatment weights are included in the regression. If there are levels of the outcome that are not observed in this treatment group, then 0's are added in. The function returns a matrix with named columns corresponding to each outcome (ordered numerically). The entries represent the estimated covariate-conditional treatment-specific PMF.

Description

Helper function to fit a treatment specific outcome regression. If there are more than 2 observed levels of the outcome for the specified treatment arm, then polr is used from the MASS package. Otherwise logistic regression is used. In both cases, inverse probability of treatment weights are included in the regression. If there are levels of the outcome that are not observed in this treatment group, then 0's are added in. The function returns a matrix with named columns corresponding to each outcome (ordered numerically). The entries represent the estimated covariate-conditional treatment-specific PMF.

Usage

fit_trt_spec_reg(
  trt_level,
  trt_spec_prob_est,
  out,
  treat,
  covar,
  out_levels,
  out_form = NULL,
  out_model,
  stratify,
  ...
)
fit_trt_spec_reg(
  trt_level,
  trt_spec_prob_est,
  out,
  treat,
  covar,
  out_levels,
  out_form = NULL,
  out_model,
  stratify,
  ...
)

Arguments

`trt_level`	Which level of treatment to fit the proportional odds model for
`trt_spec_prob_est`	A vector of estimates of Pr(`treat` = `trt_level` \| `covar`).
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`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_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.
`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).
`stratify`	Boolean indicating whether to use nonparametric maximum likelihood (i.e., a stratified estimator). If `out_form = "1"`, then a covariate-unadjusted estimate is computed.
`...`	Other options (not used).

Compute one log odds based on a given data set.

Description

Compute one log odds based on a given data set.

Usage

get_one_logodds(treat, covar, treat_form, out_model, out, out_levels, out_form)
get_one_logodds(treat, covar, treat_form, out_model, out, out_levels, out_form)

Arguments

`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`covar`	A `data.frame` containing the covariates to include in the working proportional odds model.
`treat_form`	The right-hand side of a regression formula for the working model of treatment probability as a function of covariates
`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).
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`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.

Value

Estimated log odds for these input data.

Compute one estimate of Mann-Whitney parameter based on a given data set.

Description

Compute one estimate of Mann-Whitney parameter based on a given data set.

Usage

get_one_mannwhitney(
  treat,
  covar,
  treat_form,
  out,
  out_levels,
  out_form,
  out_model
)
get_one_mannwhitney(
  treat,
  covar,
  treat_form,
  out,
  out_levels,
  out_form,
  out_model
)

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.
`treat_form`	The right-hand side of a regression formula for the working model of treatment probability as a function of covariates
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`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.
`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).

Value

Estimate of Mann-Whitney parameter for these input data.

Compute one estimate of the marginal CDF/PMF on a given data set.

Description

Compute one estimate of the marginal CDF/PMF on a given data set.

Usage

get_one_marg_dist(
  treat,
  covar,
  treat_form,
  out_model,
  out,
  out_levels,
  out_form
)
get_one_marg_dist(
  treat,
  covar,
  treat_form,
  out_model,
  out,
  out_levels,
  out_form
)

Arguments

`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`covar`	A `data.frame` containing the covariates to include in the working proportional odds model.
`treat_form`	The right-hand side of a regression formula for the working model of treatment probability as a function of covariates
`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).
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`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.

Value

List of estimated cdf/pmf for these input data.

Compute one weighted mean based on a given data set.

Description

Compute one weighted mean based on a given data set.

Usage

get_one_wmean(
  treat,
  covar,
  treat_form,
  out,
  out_levels,
  out_form,
  out_model,
  out_weights
)
get_one_wmean(
  treat,
  covar,
  treat_form,
  out,
  out_levels,
  out_form,
  out_model,
  out_weights
)

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.
`treat_form`	The right-hand side of a regression formula for the working model of treatment probability as a function of covariates
`out`	A `numeric` vector containing the outcomes. Missing outcomes are allowed.
`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.
`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).
`out_weights`	A vector of `numeric` weights with length equal to the length of `out_levels`.

Get a response from model formula

Description

Get a response from model formula

Usage

getResponseFromFormula(formula, data)
getResponseFromFormula(formula, data)

Arguments

`formula`	The model formula
`data`	The data frame associated with the model

Compute jackknife log-odds estimates.

Description

Compute jackknife log-odds estimates.

Usage

jack_logodds(treat, covar, out, treat_form, out_model, out_levels, out_form)
jack_logodds(treat, covar, out, treat_form, out_model, out_levels, out_form)

Arguments

`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`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.
`treat_form`	The right-hand side of a regression formula for the working model of treatment probability as a function of covariates
`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).
`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.

Value

Jackknife estimated log-odds

Compute Mann-Whitney log-odds estimates.

Description

Compute Mann-Whitney log-odds estimates.

Usage

jack_mannwhitney(
  treat,
  covar,
  out,
  treat_form,
  out_levels,
  out_form,
  out_model
)
jack_mannwhitney(
  treat,
  covar,
  out,
  treat_form,
  out_levels,
  out_form,
  out_model
)

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.
`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.
`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).

Value

Jackknife estimate of Mann-Whitney parameter

Compute jackknife distribution estimates.

Description

Compute jackknife distribution estimates.

Usage

jack_marg_cdf(treat, covar, out, treat_form, out_levels, out_form, out_model)
jack_marg_cdf(treat, covar, out, treat_form, out_levels, out_form, out_model)

Arguments

`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`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.
`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.
`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).

Value

Jackknife estimated distributions

Compute jackknife weighted mean estimates.

Description

Compute jackknife weighted mean estimates.

Usage

jack_wmean(
  treat,
  covar,
  out,
  treat_form,
  out_levels,
  out_form,
  out_weights,
  out_model
)
jack_wmean(
  treat,
  covar,
  out,
  treat_form,
  out_levels,
  out_form,
  out_weights,
  out_model
)

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.
`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.
`out_weights`	A vector of `numeric` weights with length equal to the length of `out_levels`.
`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).

Value

Jackknife-estimated weighted mean

Marginalize over empirical distribution to obtain marginal treatment-specific CDF estimate.

Description

Marginalize over empirical distribution to obtain marginal treatment-specific CDF estimate.

Usage

marginalize_cdf(cdf_est)
marginalize_cdf(cdf_est)

Arguments

cdf_est

Estimates of treatment-specific conditional CDF.

Marginalize over empirical distribution to obtain marginal treatment-specific PMF estimate.

Description

Marginalize over empirical distribution to obtain marginal treatment-specific PMF estimate.

Usage

marginalize_pmf(pmf_est)
marginalize_pmf(pmf_est)

Arguments

pmf_est

Estimates of treatment-specific conditional PMF.

Get one bootstrap computation of the log odds parameters.

Description

Get one bootstrap computation of the log odds parameters.

Usage

one_boot_logodds(
  treat,
  covar,
  out,
  treat_form,
  out_levels,
  out_form,
  out_model
)
one_boot_logodds(
  treat,
  covar,
  out,
  treat_form,
  out_levels,
  out_form,
  out_model
)

Arguments

`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`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.
`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.
`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).

Value

Estimates of log odds for a particular bootstrap sample.

Get one bootstrap computation of the Mann-Whitney parameter.

Description

Get one bootstrap computation of the Mann-Whitney parameter.

Usage

one_boot_mannwhitney(
  treat,
  covar,
  out,
  treat_form,
  out_levels,
  out_form,
  out_model
)
one_boot_mannwhitney(
  treat,
  covar,
  out,
  treat_form,
  out_levels,
  out_form,
  out_model
)

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.
`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.
`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).

Value

Estimates of Mann-Whitney parameter for a particular bootstrap sample.

Get one bootstrap computation of the CDF and PMF estimates

Description

Get one bootstrap computation of the CDF and PMF estimates

Usage

one_boot_marg_dist(
  treat,
  covar,
  out,
  treat_form,
  out_levels,
  out_form,
  out_model
)
one_boot_marg_dist(
  treat,
  covar,
  out,
  treat_form,
  out_levels,
  out_form,
  out_model
)

Arguments

`treat`	A `numeric` vector containing treatment status. Should only assume a value 0 or 1.
`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.
`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.
`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).

Value

Estimates of CDF and PMF for a particular bootstrap sample.

Get one bootstrap computation of the weighted mean parameters.

Description

Get one bootstrap computation of the weighted mean parameters.

Usage

one_boot_wmean(
  treat,
  covar,
  out,
  treat_form,
  out_levels,
  out_form,
  out_weights,
  out_model
)
one_boot_wmean(
  treat,
  covar,
  out,
  treat_form,
  out_levels,
  out_form,
  out_weights,
  out_model
)

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.
`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.
`out_weights`	A vector of `numeric` weights with length equal to the length of `out_levels`.
`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).

Value

Estimates of weighted mean for a particular bootstrap sample.

Print the output of a `"drord"` object.

Description

Print the output of a "drord" object.

Usage

## S3 method for class 'drord'
plot(
  x,
  treat_labels = c(1, 0),
  dist = "pmf",
  out_labels = if (dist == "pmf") {     x$out_levels } else {    
    x$out_levels[-length(x$out_levels)] },
  ...
)
## S3 method for class 'drord'
plot(
  x,
  treat_labels = c(1, 0),
  dist = "pmf",
  out_labels = if (dist == "pmf") {     x$out_levels } else {    
    x$out_levels[-length(x$out_levels)] },
  ...
)

Arguments

`x`	A `"drord"` object.
`treat_labels`	Labels for the treatment variables (treat = 1 followed by treat = 0).
`dist`	Which distribution to plot. Valid options are `"cdf"` or `"pmf"`.
`out_labels`	Labels for the ordered outcome levels. If `dist = "cdf"`, the highest level of outcome will be dropped.
`...`	Other arguments (not used)

Value

A list with named entries plot (a ggplot2 object) and plot_data, the data.frame from which the plot is made. The latter is included for additional modifications to the plot that are desired.

Fits a proportional odds model via pooled logistic regression.

Description

The outcome in data (indicated in the form object) should be an ordered factor.

Usage

POplugin(form, data, weights = 1)
POplugin(form, data, weights = 1)

Arguments

`form`	The model formula
`data`	The data set used to fit the model
`weights`	Either equal to 1 (no weights) or a vector of length equal to nrow(data)

Value

A list with the fitted glm, the original data, levels of the outcome, and the outcome name

Predict method for a `POplugin` object

Description

Predict method for a POplugin object

Usage

## S3 method for class 'POplugin'
predict(object, newdata = NULL)
## S3 method for class 'POplugin'
predict(object, newdata = NULL)

Arguments

`object`	An object of class `POplugin`
`newdata`	A `data.frame` on which to predict

Value

A data frame with nrow = number of rows in newdata (or the orignal data frame) and with the number of columns equal to the number of levels of the outcome observed in the original data frame

Print the output of a `"drord"` object.

Description

Print the output of a "drord" object.

Usage

## S3 method for class 'drord'
print(x, ci = "bca", ...)
## S3 method for class 'drord'
print(x, ci = "bca", ...)

Arguments

`x`	A `"drord"` object
`ci`	Which confidence interval should be printed. Defaults to BCa, but it BCa was not computed in call to `drord`, defaults back to Wald.
`...`	Other arguments (not used)

Trimmed logistic function

Description

Trimmed logistic function

Usage

trimmed_logit(x)
trimmed_logit(x)

Arguments

`x`	A numeric between 0 and 1

Compute a Wald confidence interval for the weighted mean

Description

Compute a Wald confidence interval for the weighted mean

Usage

wald_ci_wmean(wmean_est, alpha)
wald_ci_wmean(wmean_est, alpha)

Arguments

`wmean_est`	The estimated weighted means + estimated covariance matrix.
`alpha`	Level of confidence interval.

Value

matrix with treatment-specific weighted mean CIs and CI for difference.

Package 'drord'

Help Index

Compute a BCa confidence interval

Description

Usage

Arguments

Value

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

Description

Usage

Arguments

Value

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

Description

Usage

Arguments

Value

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

Description

Usage

Arguments

Value

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

Description

Usage

Arguments

Value

Used to compute treatment-specific BCa intervals for the CDF and PMF

Description

Usage

Arguments

Value

Compute simultaneous confidence interval for treatment-specific marginal distribution

Description

Usage

Arguments

Value

Compute simultaneous confidence interval for treatment-specific marginal distribution

Description

Usage

Arguments

Value

Simulated COVID-19 outcomes for hospitalized patients.

Description

Usage

Format

Doubly robust estimates of for evaluating effects of treatments on ordinal outcomes.

Description

Usage

Arguments

Details

Value

Examples

Get EIF estimates for treatment-specific PMF at a particular level of the outcome

Description

Usage

Arguments

Get EIF estimates for treatment-specific CDF at a particular level of the outcome

Description

Usage

Arguments

Map an estimate of the conditional PMF into an estimate of the conditional CDF

Description

Usage

Arguments

Value

Compute confidence interval/s for the log-odds parameters

Description

Usage

Arguments

Value

Compute confidence interval/s for the Mann-Whitney parameter

Description

Usage

Arguments

Value

Compute confidence interval/s for the treatment specific PMF and CDF.

Description

Usage

Arguments

Get a treatment-specific estimate of the conditional PMF. Essentially this is a wrapper function for `fit_trt_spec_reg`, which fits the proportion odds model in a given treatment arm.