OLS Combined-Likelihood Inference for KK Designs
Source:R/inference_continuous_KK_ols_one_lik.R
InferenceContinKKOLSOneLik.RdFits a single stacked OLS regression over matched-pair differences and reservoir observations for KK matching-on-the-fly designs with continuous responses, using the treatment indicator and, optionally, all recorded covariates as predictors. Note that warm starts are disabled for this class as OLS is a closed-form estimator and does not benefit from initialization.
Details
Model. Let \(m\) be the number of matched pairs and
\(n_R = n_{RT} + n_{RC}\) the number of unmatched reservoir subjects. The
design matrix stacks two blocks: \(m\) matched-pair difference rows
(each row's response is the within-pair outcome difference, coded with an
implicit unit treatment column and covariate differences \(X_{d}\)), and
\(n_R\) reservoir rows (raw covariates plus a treatment/matching-status
indicator column). The stacked regression is fit by ordinary least squares
(lm.fit), and \(\hat\beta_T\) is the coefficient on
the treatment/matched-difference column, i.e. an additive mean-difference
estimand on the outcome's natural scale. If only matched pairs exist,
j_treat = 1; if only reservoir data exist, j_treat = 2; if
both exist, the combined design uses j_treat = 2. If neither
matched pairs nor a treatment-and-control-populated reservoir exist, the
estimate is marked nonestimable ("no_usable_matched_or_reservoir_data").
Variance. Standard errors use the HC2 heteroskedasticity-consistent
sandwich estimator (ols_hc2_post_fit_cpp), not the classical OLS
variance, so the Wald confidence interval/p-value are robust to
heteroskedasticity across the matched/reservoir blocks.
Likelihood tier. likelihood_tier = "full": this is a genuine
Gaussian likelihood (not a quasi-likelihood or partial likelihood), so
score, gradient, and likelihood-ratio testing types are available in
addition to Wald, and an exact (not higher-order-accurate) Bartlett
correction reproduces base R's lm() classical partial F-test exactly
under the classical homoskedastic-Gaussian-errors assumption (a stronger
assumption than the HC2-robust Wald path uses, so the two paths need not
agree numerically).
Assumptions. Continuous response; independent matched pairs and/or
independent reservoir subjects; no censoring
(assertNoCensoring() is enforced); a
KK matching-on-the-fly design
(DesignSeqOneByOneKK14 or subclass).
References
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
. (KK14 in REFERENCES.md.)
See also
InferenceContinKKOLSIVWC
for the inverse-variance-weighted-combination alternative to this
one-likelihood combined-fit approach; analogous Python API:
statsmodels GLM/OLS.
Super class
Inference -> InferenceContinKKOLSOneLik
Methods
Public methods
+ 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$get_treatment()Inference$initialize()Inference$is_nonestimable()Inference$set_optimization_alg()Inference$set_seed()Inference$supports()
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$add_all_subject_responses(rnorm(10))
inf = InferenceContinKKOLSOneLik$new(seq_des)
inf$compute_estimate()
#> [1] 1.282994
# }