Doubly-Robust Estimators for Ordinal Outcomes • drord

Doubly robust estimators of treatment effects for ordinal outcomes

Description

drord is an R package that computes estimates of effect parameters that are useful for evaluating efficacy of treatments on ordinal outcomes. The effect estimates are covariate-adjusted, which means they can be used in observational settings or to gain efficiency in randomized trials.

The estimators implemented in the package are doubly robust, in that they are based on working models for the probability of treatment as a function of covariates (i.e., the propensity score) and for the CDF of the outcome as a function of covariates in each treatment arm. The latter working model is implemented via proportional odds models that are fit in each treatment arm separately. Estimates based on these two working models are combined to quantify the effects of the treatment on the ordinal outcome in three different ways:

Difference in (weighted) means: The outcome levels are treated numerically, with each level possibly assigned a weight. The effect is defined as the difference in average outcomes.
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. See Diaz et al. (2016) for further discussion of this parameter.
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). See Vermeulen et al. (2014) for further discussion.

Installation

A developmental release may be installed from GitHub via devtools with:

devtools::install_github("benkeser/drord")

Usage

Here we demonstrate calls to drord to compute treatment effects using a simulated data set of COVID-19 outcomes in hospitalized patients.

library(drord)
#> drord: Doubly robust estimators for ordinal outcomes
#> Version: 1.0.0

# load data
data(covid19)

# estimate treatment effects
fit <- drord(out = covid19$out, 
             covar = covid19[ , "age_grp", drop = FALSE],
             treat = covid19$treat)
#> Warning in eval(family$initialize): non-integer #successes in a binomial glm!

#> Warning in eval(family$initialize): non-integer #successes in a binomial glm!
# look at estimates
fit
#> $mann_whitney
#>       est  wald_cil  wald_ciu 
#> 0.5800689 0.5337929 0.6263449 
#> 
#> $log_odds
#>               est   wald_cil    wald_ciu
#> treat1 -1.2922742 -1.5719616 -1.01258678
#> treat0 -0.9163279 -1.1533670 -0.67928881
#> diff   -0.3759463 -0.7254384 -0.02645421
#> 
#> $weighted_mean
#>              est   wald_cil  wald_ciu
#> treat1 2.5554260 2.46316500 2.6476871
#> treat0 2.3721986 2.28768451 2.4567127
#> diff   0.1832275 0.06389974 0.3025552

There is a plot method included to visualize either the cumulative distribution or probability mass function of outcomes.

# plot of CDF
cdf_plot <- plot(fit, dist = "cdf", 
                 treat_labels = c("Treatment", "Control"),
                 out_labels = c("Death", "Death or intubation"))
cdf_plot$plot + ggsci::scale_fill_nejm()

The black bars are pointwise 95% confidence intervals; the gray bars are simultaneous 95% confidence intervals.

A similar plot can be made for the PMF.

# plot of PMF
pmf_plot <- plot(fit, dist = "pmf",
                 treat_labels = c("Treatment", "Control"),
                 out_labels = c("Death", "Intubation", "None"))
pmf_plot$plot + ggsci::scale_fill_nejm()

Issues

If you encounter any bugs or have any specific feature requests, please file an issue.

Citation

After using the drord R package, please cite both of the following:

@Manual{drordpackage,
  title = {drord: Doubly-Robust Estimators for Ordinal Outcomes},
  author = {David Benkeser},
  note = {R package version 1.0.1}
}

@article{benkeserdiazluedtke2020,
  title = {Improving Precision and Power in Randomized Trials for COVID-19 Treatments Using Covariate Adjustment, for Ordinal or Time to Event Outcomes},
  journal = {Biometrics},
  doi = {https://doi.org/10.1111/biom.13377}
}

License

The contents of this repository are distributed under the MIT license. See below for details:

The MIT License (MIT)

Copyright (c) 2020- David Benkeser

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
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The above copyright notice and this permission notice shall be included in all
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