atefitmean {precmed}

Doubly robust estimator of and inference for the average treatment effect for continuous data

Description

Doubly robust estimator of the average treatment effect between two treatments, which is the rate ratio of treatment 1 over treatment 0 for count outcomes. Bootstrap is used for inference.

Usage

atefitmean(
  data,
  cate.model,
  ps.model,
  ps.method = "glm",
  minPS = 0.01,
  maxPS = 0.99,
  interactions = TRUE,
  n.boot = 500,
  plot.boot = FALSE,
  seed = NULL,
  verbose = 0
)

Arguments

data

A data frame containing the variables in the outcome and propensity score models; a data frame with n rows (1 row per observation).

cate.model

A formula describing the outcome model to be fitted. The outcome must appear on the left-hand side.

ps.model

A formula describing the propensity score model to be fitted. The treatment must appear on the left-hand side. The treatment must be a numeric vector coded as 0/1. If data are from a RCT, specify ps.model as an intercept-only model.

ps.method

A character value for the method to estimate the propensity score. Allowed values include one of: 'glm' for logistic regression with main effects only (default), or 'lasso' for a logistic regression with main effects and LASSO penalization on two-way interactions (added to the model if interactions are not specified in ps.model). Relevant only when ps.model has more than one variable.

minPS

A numerical value between 0 and 1 below which estimated propensity scores should be truncated. Default is 0.01.

maxPS

A numerical value between 0 and 1 above which estimated propensity scores should be truncated. Must be strictly greater than minPS. Default is 0.99.

interactions

A logical value indicating whether the outcome model should be fitted separately by treatment arm with the variables in cate.model, which is equivalent to assuming treatment-covariate interaction by all of the variables in cate.model. If TRUE, the outcome model will be fitted separately by treatment arms only if at least 10 patients received each treatment option. Default is TRUE.

n.boot

A numeric value indicating the number of bootstrap samples used. Default is 500.

plot.boot

A logical value indicating whether histograms of the bootstrapped treatment effect estimates should be produced at every n.boot/10-th iteration and whether the final histogram should be outputted. Default is FALSE.

seed

An optional integer specifying an initial randomization seed for reproducibility. Default is NULL, corresponding to no seed.

verbose

An integer value indicating whether intermediate progress messages and histograms should be printed. 1 indicates messages are printed and 0 otherwise. Default is 0.

Details

This helper function estimates the average treatment effect (ATE) between two treatment groups in a given dataset specified by y, trt, x.cate, x.ps, time. The ATE is estimated with a doubly robust estimator that accounts for imbalances in covariate distributions between the two treatment groups with inverse probability treatment weighting. For count outcomes, the estimated ATE is the estimated rate ratio between treatment 1 versus treatment 0. Both original and log-transformed ATEs are returned, as well as the rate in either treatment group. If inference = TRUE, the variability of the estimated rate ratio is also calculated using bootstrap. Additional variability outputs include standard error of the log rate ratio, 95% confidence interval of the rate ratio, p-value, and a histogram of the log rate ratio.

Value

Return a list of 8 elements:

• log.rate.ratio: A numeric value of the estimated log rate ratio.

• se.boot.log.rate.ratio: A numeric value of the bootstrap standard error of log rate ratio.

• rate.ratio: A numeric value of the estimated rate ratio.

• rate.ratio0: A numeric value of the estimated rate in the group trt=0.

• rate.ratio1: A numeric value of the estimated rate in the group trt=1.

• rate.ratio.CIl: A numeric value of the lower limit 95% bootstrap confidence interval for estimated rate ratio.

• rate.ratio.CIu: A numeric value of the upper limit 95% bootstrap confidence interval for estimated rate ratio.

• pvalue: A numeric value of the p-value derived from the bootstrapped values based on a Chi-squared distribution.

• warning: A warning message produced if the treatment variable was not coded as 0/1. The key to map the original coding of the variable to a 0/1 key is displayed in the warning to facilitate the interpretation of the remaining of the output.

• plot: If plot.boot is TRUE, a histogram displaying the distribution of the bootstrapped log rate ratios. The red vertical reference line in the histogram represents the estimated log rate ratio.

Examples

# This module is not implemented yet!