Non-parametric Wilcoxon-based Compound Inference for KK Matching-on-the-Fly Designs
Source:R/inference_all_KK_wilcox_ivwc.R
InferenceAllKKWilcoxIVWC.RdFits a non-parametric, rank-based compound (inverse-variance-weighted, IVWC)
estimator of the treatment effect under a
DesignSeqOneByOne-family KK
matching-on-the-fly design (see
DesignSeqOneByOneKK14). For matched
pairs, the sub-estimate \(\hat\beta_m\) is the Hodges-Lehmann
estimate from a Wilcoxon signed-rank test on the within-pair differences (the
median of the Walsh averages \((d_i+d_j)/2\)); for reservoir (unmatched)
subjects, \(\hat\beta_r\) is the Hodges-Lehmann estimate from a Wilcoxon
rank-sum (Mann-Whitney \(U\)) test on treated-vs-control reservoir responses
(the median of all pairwise differences). The two are combined by classical
inverse-variance weighting,
$$\hat\beta_T = w^* \hat\beta_m + (1-w^*)\, \hat\beta_r, \qquad
w^* = \frac{\widehat{\mathrm{Var}}(\hat\beta_r)}{\widehat{\mathrm{Var}}(\hat\beta_r)
+ \widehat{\mathrm{Var}}(\hat\beta_m)},$$
with variance the standard inverse-variance-pooled form (see
$compute_estimate()'s method-level documentation for the full formula
and fallback behavior when only one sub-estimate is usable). Because it is
built from Hodges-Lehmann/Wilcoxon estimators rather than sample means, this
method is robust to outliers and does not assume a specific parametric
distribution for the response — but it does not currently support censored
survival data or incidence (binary) responses (see $initialize()), and
its jackknife methods all report explicit non-estimability rather than
computing a (statistically unreliable) delete-1 jackknife of the
Hodges-Lehmann functional.
References
Hodges, J. L., and Lehmann, E. L. (1963). "Estimates of Location Based on Rank Tests." The Annals of Mathematical Statistics, 34(2), 598-611, doi:10.1214/aoms/1177704172 , for the Hodges-Lehmann estimator underlying both sub-estimates; Kapelner, A., and Krieger, A. M. (2014). "Matching on-the-fly: Sequential allocation with higher power and efficiency." Biometrics, 70(2), 378-388, doi:10.1111/biom.12148 , for the KK matching-on-the-fly design and the inverse-variance combination of matched-pair and reservoir estimates.
Legacy class. Not fully tested in comprehensive_tests.R.
Super class
Inference -> InferenceAllKKWilcoxIVWC
Methods
Public methods
+ inherited public methods from Inference
Inference$capabilities()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$supports()
InferenceAllKKWilcoxIVWC$new()
Usage
InferenceAllKKWilcoxIVWC$new(
des_obj,
model_formula = NULL,
verbose = FALSE,
smart_cold_start_default = NULL
)Arguments
des_objA completed
Designobject whose entire n subjects are assigned and response y is recorded within.model_formulaOptional formula for covariate adjustment. If
NULL(default), the formula from the design object is used and its pre-computed design matrix is reused. If a formula is provided, a new design matrix is constructed from the design's imputed covariates.verboseWhether to print progress messages.
smart_cold_start_defaultWhether to use smart cold start values by default for likelihood-based models. Explicit starts always override this object-level policy.
NULL(default) consults the global cold-start dispatch policy.
Examples
# \donttest{
seq_des = DesignSeqOneByOneKK14$new(n = 10, response_type = 'continuous')
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(rnorm(10))
inf = InferenceAllKKWilcoxIVWC$new(seq_des)
inf$compute_estimate()
#> [1] 0.5302245
# }