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

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

Usage

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

Arguments

data: A data frame containing the variables in the outcome, propensity score, and inverse probability of censoring models (if specified); 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 (PS) model to be fitted. The treatment must appear on the left-hand side. The treatment must be a numeric vector coded as 0 or 1. If data are from a randomized controlled trial, specify ps.model = ~1 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 assume treatment-covariate interaction by x. If TRUE, interactions will be assumed 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.
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 should be printed. 1 indicates messages are printed and 0 otherwise. Default is 0.

Value

Return an item of the class atefit with the following elements:

log.rate.ratio: A vector of numeric values of the estimated ATE (expressed as a log rate ratio of trt=1 over trt=0), the bootstrap standard error, the lower and upper limits of 95% confidence interval, and the p-value.
rate0: A numeric value of the estimated rate in the group trt=0.
rate1: A numeric value of the estimated rate in the group trt=1.
trt.boot: Estimated log rate ratios in each bootstrap sample.
warning: A warning message produced if the treatment variable was not coded as 0 or 1. The key to map the original coding of the variable to a 0-1 coding is displayed in the warning to facilitate the interpretation of the remaining of the output.

Details

This helper function estimates the average treatment effect (ATE) between two treatment groups in a given dataset. 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.

Examples

output <- atefitcount(data = countExample,
                      cate.model = y ~ age + female + previous_treatment +
                                   previous_cost + previous_number_relapses +
                                   offset(log(years)),
                      ps.model = trt ~ age + previous_treatment,
                      verbose = 1, n.boot = 50, seed = 999)
#> Warning: Variable trt was recoded to 0/1 with drug0->0 and drug1->1.
#> 
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output
#> Average treatment effect:
#> 
#>                  estimate        SE   CI.lower  CI.upper    pvalue
#> log.rate.ratio 0.06311746 0.1624482 -0.2552752 0.3815101 0.6976173
#> 
#> Estimated event rates:
#> 
#>        estimate
#> rate1 0.2860635
#> rate0 0.2685660
#> 
#> Warning: Variable trt was recoded to 0/1 with drug0->0 and drug1->1.
plot(output)