Weibull AFT Inference for Survival Responses

Fits a Weibull Accelerated Failure Time (AFT) model for survival responses: \(\log T_i = \beta_0 + \beta_T W_i + X_i^\top \gamma + \sigma \epsilon_i\), \(\epsilon_i \sim\) standard extreme-value (Gumbel-minimum), so that \(T_i\) is marginally Weibull-distributed with shape \(1/\sigma\) and treatment-dependent scale, by maximum likelihood (fast_weibull_regression_cpp). \(\hat\beta_T\) is a log-time-ratio (log acceleration factor): \(\exp(\hat\beta_T)\) is the estimated multiplicative effect of treatment on survival time (an AFT model, not a proportional-hazards model — the Weibull distribution is the one location where AFT and proportional-hazards parameterizations coincide, since \(\exp(-\beta_T/\sigma)\) also equals the treatment hazard ratio). likelihood_tier = "full": likelihood-ratio, score, gradient, and Wald tests are all available when the model converges, plus parametric-likelihood-bootstrap calibration of the likelihood-ratio test. Right-censored and interval-censored observations enter the likelihood via their appropriate survival/density contributions. Validity requires the Weibull shape assumption for the (log-)survival-time distribution and, when interpreted causally, the usual design-based/model-based assumptions.

References

Kalbfleisch, J. D., and Prentice, R. L. (2002). The Statistical Analysis of Failure Time Data (2nd ed.). Wiley, for the Weibull AFT model and its equivalence to a proportional-hazards model.

See also

Comparable Python API: lifelines WeibullAFTFitter. See also: Proportional hazards model (Wikipedia, for the AFT/PH equivalence note).

Super class

Inference -> InferenceSurvivalWeibullRegr

Methods

Public methods

• InferenceSurvivalWeibullRegr$set_custom_randomization_statistic_function()

• InferenceSurvivalWeibullRegr$set_custom_randomization_statistic_cpp()

• InferenceSurvivalWeibullRegr$approximate_randomization_distribution_beta_hat_T()

• InferenceSurvivalWeibullRegr$supports_rand_pval_for_incidence()

• InferenceSurvivalWeibullRegr$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()

---

InferenceSurvivalWeibullRegr$set_custom_randomization_statistic_function()

Usage

InferenceSurvivalWeibullRegr$set_custom_randomization_statistic_function(
  custom_randomization_statistic_function
)

---

InferenceSurvivalWeibullRegr$set_custom_randomization_statistic_cpp()

Usage

InferenceSurvivalWeibullRegr$set_custom_randomization_statistic_cpp(fn)

---

InferenceSurvivalWeibullRegr$approximate_randomization_distribution_beta_hat_T()

Usage

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

---

InferenceSurvivalWeibullRegr$supports_rand_pval_for_incidence()

Usage

InferenceSurvivalWeibullRegr$supports_rand_pval_for_incidence()

---

InferenceSurvivalWeibullRegr$clone()

The objects of this class are cloneable with this method.

Usage

InferenceSurvivalWeibullRegr$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

# \donttest{
seq_des = DesignSeqOneByOneBernoulli$new(n = 10, response_type = 'survival')
for (i in 1:10) {
  seq_des$add_one_subject_to_experiment_and_assign(data.frame(x1 = rnorm(1)))
}
seq_des$add_all_subject_responses(runif(10))
inf = InferenceSurvivalWeibullRegr$new(seq_des)
inf$compute_estimate()
#> [1] -1.284267
# }
# \donttest{
inf$set_seed(1)
inf$compute_lik_ratio_bootstrap_two_sided_pval(delta = 0, B = 9, show_progress = FALSE)
#> [1] 0.2
# }