Clayton Copula / Standard Weibull Compound Inference for KK Designs
Source:R/inference_survival_GLMM_weibull_frailty_loggamma.R
InferenceSurvivalGLMMWeibullFrailtyLoggammaIVWC.RdThis class implements a compound estimator for KK matching-on-the-fly designs with survival responses using a Clayton copula with Weibull AFT margins for matched pairs and a standard Weibull AFT model for the reservoir. The two treatment-effect estimates (on the log-time ratio scale) are combined by inverse-variance weighting.
Details
Frailty distribution. The Clayton copula for a matched pair,
S(t1,t2) = (S1(t1)^-theta + S2(t2)^-theta - 1)^(-1/theta) with Weibull
margins S_i, is exactly the closed-form bivariate survival function
obtained by multiplying two conditionally-independent Weibull hazards by a
shared gamma frailty term Z ~ Gamma(1/theta, 1/theta) and
integrating Z out analytically (Clayton 1978; Oakes 1989); theta
is the frailty variance / dependence parameter (see ClaytonWeibullLikelihood
in fast_survival_models_optim.cpp, which builds the likelihood from the
per-subject Weibull cumulative hazards H1, H2). This is the classic
textbook Weibull-gamma shared-frailty model, fit here in its closed form (no
numerical integration required) rather than as an AFT Gaussian-random-intercept
model.
This is a different (and equally standard) frailty assumption from the
log-normal-frailty Weibull AFT GLMM implemented by
InferenceSurvivalGLMMWeibullFrailtyNormalIVWC /
InferenceSurvivalGLMMWeibullFrailtyNormalOneLik,
which instead places a Gaussian random intercept on the log-time (AFT) scale and
integrates it out by Gauss-Hermite quadrature. Prefer this Clayton-copula class
for the classic gamma-frailty / proportional-hazards dependence structure;
prefer the Weibull-frailty class for a Gaussian-random-intercept / GLMM-style
dependence structure.
References
Clayton DG (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:10.2307/2335289
Oakes D (1989). "Bivariate Survival Models Induced by Frailties." Journal of the American Statistical Association, 84(406), 487-493. doi:10.2307/2289934
Legacy class. Not fully tested in comprehensive_tests.R.
See also
InferenceSurvivalGLMMWeibullFrailtyNormalIVWC
for the corresponding log-normal-frailty IVWC estimator.
Super class
Inference -> InferenceSurvivalGLMMWeibullFrailtyLoggammaIVWC
Methods
Public methods
InferenceSurvivalGLMMWeibullFrailtyLoggammaIVWC$set_custom_randomization_statistic_function()InferenceSurvivalGLMMWeibullFrailtyLoggammaIVWC$set_custom_randomization_statistic_cpp()InferenceSurvivalGLMMWeibullFrailtyLoggammaIVWC$approximate_randomization_distribution_beta_hat_T()InferenceSurvivalGLMMWeibullFrailtyLoggammaIVWC$supports_rand_pval_for_incidence()InferenceSurvivalGLMMWeibullFrailtyLoggammaIVWC$compute_rand_two_sided_pval()
+ inherited public methods from Inference
Inference$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()