One-Likelihood Clayton-Copula Weibull AFT Inference for KK Survival Designs

Estimates a treatment log-time-ratio \(\beta_T\) for right-censored survival outcomes collected under a KK matching-on-the-fly design (DesignSeqOneByOneKK14 or subclass) by maximizing a single combined likelihood: matched-pair survival times are modeled with a Weibull accelerated-failure-time (AFT) margin joined by a Clayton copula (dependence parameter \(\theta\)) to account for within-pair correlation induced by shared matching covariates, while unmatched reservoir subjects are modeled by the same Weibull AFT margin marginally (no dependence term). All subjects share one treatment coefficient, estimated jointly.

Details

Estimand. \(\beta_T\), the treatment coefficient of a Weibull AFT model \(\log T = \beta_0 + \beta_T W + X\beta + \sigma\epsilon\) with \(\epsilon\) extreme-value-distributed; \(\exp(\hat\beta_T)\) is the treatment-vs-control survival-time ratio (an acceleration factor). This is a distinct scale from the log hazard ratio reported by Cox-based KK survival classes.

Model. .fit_clayton_weibull_aft() jointly optimizes the AFT regression coefficients, the Weibull shape (\(\log\sigma\)), and the Clayton copula dependence parameter (\(\log\theta\)) by direct maximum likelihood over the combined matched-pair-copula / reservoir-marginal log-likelihood; right-censoring enters as the usual survival contribution (density for observed failures, survival function for censored times). likelihood_tier = "full", so a parametric likelihood bootstrap (simulate_under_lik_null, which draws new pair times from the fitted Clayton copula and new singleton times from the marginal Weibull) is available alongside Wald inference.

Assumptions. Weibull AFT margin correctly specified; Clayton copula correctly captures within-pair dependence (a positive-dependence, single-parameter Archimedean copula); independent censoring given covariates; a KK matching-on-the-fly design supplying the matched/ reservoir partition.

References

Clayton, D. G. (1978). "A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence." Biometrika, 65(1), 141-151. doi:10.1093/biomet/65.1.141 . (Clayton1978 in REFERENCES.md.)

Oakes, D. (1989). "Bivariate survival models induced by frailties." Journal of the American Statistical Association, 84(406), 487-493. doi:10.1080/01621459.1989.10478795 . (Oakes1989 in REFERENCES.md.)

See also

Analogous Python API for AFT/copula survival models: lifelines WeibullAFTFitter, copulas. Copula (probability theory) (orientation).

Super class

Inference -> InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik

Methods

Public methods

• InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$set_custom_randomization_statistic_function()

• InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$set_custom_randomization_statistic_cpp()

• InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$approximate_randomization_distribution_beta_hat_T()

• InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$supports_rand_pval_for_incidence()

• InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$compute_rand_two_sided_pval()

• InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$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$get_treatment()
• Inference$initialize()
• Inference$is_nonestimable()
• Inference$set_optimization_alg()
• Inference$set_seed()
• Inference$supports()

---

InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$set_custom_randomization_statistic_function()

Usage

InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$set_custom_randomization_statistic_function(
  custom_randomization_statistic_function
)

---

InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$set_custom_randomization_statistic_cpp()

Usage

InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$set_custom_randomization_statistic_cpp(
  fn
)

---

InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$approximate_randomization_distribution_beta_hat_T()

Usage

InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$approximate_randomization_distribution_beta_hat_T(
  r = 501,
  delta = 0,
  transform_responses = "none",
  show_progress = TRUE,
  permutations = NULL,
  debug = FALSE,
  zero_one_logit_clamp = .Machine$double.eps
)

---

InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$supports_rand_pval_for_incidence()

Usage

InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$supports_rand_pval_for_incidence(

)

---

InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$compute_rand_two_sided_pval()

Usage

InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$compute_rand_two_sided_pval(
  r = 501,
  delta = 0,
  transform_responses = "none",
  na.rm = TRUE,
  show_progress = TRUE,
  permutations = NULL,
  zero_one_logit_clamp = .Machine$double.eps
)

---

InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$clone()

The objects of this class are cloneable with this method.

Usage

InferenceSurvivalGLMMWeibullFrailtyLoggammaOneLik$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.