Quantile Regression Compound Estimator for KK Matching-on-the-Fly Designs (Proportion Outcomes)

A variance-weighted compound quantile regression estimator for KK matching-on-the-fly designs with proportion responses. Inference is performed on the logit (log-odds) scale: responses \(y \in (0,1)\) are transformed via \(\text{logit}(y) = \log(y/(1-y))\) before quantile regression.

The estimator combines:

1. Quantile regression on logit-scale within-pair differences \(\text{logit}(y_T) - \text{logit}(y_C)\) (matched pairs)

2. Quantile regression of \(\text{logit}(y)\) on treatment and covariates (reservoir)

using the same variance-weighted combination logic as the OLS compound estimator.

The estimated treatment effect is a log-odds-ratio shift at quantile tau. At beta_T = 1 (one log-odds-ratio unit of treatment effect), the population treatment effect on the logit scale is exactly 1, so no skip_ci is needed.

Default quantile: tau = 0.5 (median regression). To target a different quantile — for example the 25th or 75th percentile — pass tau = 0.25 or tau = 0.75 to the constructor:

  inf = InferencePropKKQuantileRegrIVWC$
  new(seq_des, tau = 0.75)

Any value strictly between 0 and 1 is accepted.

Standard errors use Powell's "nid" sandwich estimator (non-iid), falling back to "iid" on failure. Asymptotic z-based inference is used throughout.

This class requires the quantreg package, which is listed in Suggests and is not installed automatically with EDI. Install quantreg before using this class.

Legacy class. Not fully tested in comprehensive_tests.R.

Super class

Inference -> InferencePropKKQuantileRegrIVWC

Methods

Public methods

• InferencePropKKQuantileRegrIVWC$new()

• InferencePropKKQuantileRegrIVWC$clone()

+ inherited public methods from Inference

• Inference$capabilities()
• Inference$compute_asymp_confidence_interval()
• Inference$compute_asymp_two_sided_pval()
• Inference$compute_estimate()
• Inference$compute_exact_confidence_interval()
• Inference$compute_exact_two_sided_pval_for_treatment_effect()
• Inference$duplicate()
• Inference$get_analysis_data()
• Inference$get_covariates()
• Inference$get_design_object()
• Inference$get_model_formula()
• Inference$get_nonestimable_reason()
• Inference$get_nonestimable_stage()
• Inference$get_optimization_alg()
• Inference$get_response()
• Inference$get_response_type()
• Inference$get_treatment()
• Inference$is_nonestimable()
• Inference$set_optimization_alg()
• Inference$set_seed()
• Inference$supports()

---

InferencePropKKQuantileRegrIVWC$new()

Initialize proportion-response KK IVWC quantile-regression inference on the logit response scale; see InferencePropKKQuantileRegrIVWC.

Usage

InferencePropKKQuantileRegrIVWC$new(
  des_obj,
  model_formula = NULL,
  tau = 0.5,
  verbose = FALSE,
  smart_cold_start_default = NULL
)

Arguments

des_obj

A DesignSeqOneByOne object whose entire n subjects are assigned and response y is recorded within.

model_formula

Optional formula for covariate adjustment. If NULL (default), the formula from the design object is used and its pre-computed design matrix is reused. If a formula is provided, a new design matrix is constructed from the design's imputed covariates.

tau

The quantile level for regression on the logit scale, strictly between 0 and 1. The default tau = 0.5 estimates the median log-odds-ratio treatment effect. Pass a different value (e.g. tau = 0.25 or tau = 0.75) to target a different percentile of the treatment effect distribution.

verbose

A flag indicating whether messages should be displayed to the user. Default is FALSE.

smart_cold_start_default

Whether to use smart cold start values.

---

InferencePropKKQuantileRegrIVWC$clone()

The objects of this class are cloneable with this method.

Usage

InferencePropKKQuantileRegrIVWC$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

# \donttest{
seq_des = DesignSeqOneByOneKK14$new(n = 10, response_type = 'proportion')
for (i in 1:10) {
  seq_des$add_one_subject_to_experiment_and_assign(data.frame(x1 = rnorm(1), x2 = rnorm(1)))
}
seq_des$add_all_subject_responses(runif(10))
inf = InferencePropKKQuantileRegrIVWC$new(seq_des)
inf$compute_estimate()
#> [1] 0.3697062
# }