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Robust Parametric Survival Regression (AFT) with Warm-Start and Random-Restart Fallback

Source: R/helper_robust_regression.R
robust_survreg_with_surv_object.Rd

Fits a parametric accelerated-failure-time (AFT) survival regression via survreg on surv_object ~ . over the columns of cov_matrix_or_vector, with two layers of robustness against survreg's well-known sensitivity to starting values and near-collinear design matrices:

  1. Preprocessing: near-collinear columns of the design matrix are dropped first via drop_highly_correlated_cols then drop_linearly_dependent_cols, before any fitting is attempted.

  2. Warm start (Weibull only): when dist = "weibull", a fast closed-form-gradient Weibull fit (fast_weibull_regression) is attempted first; if it succeeds and returns a finite log-likelihood, its coefficients and \(\log(\hat\sigma)\) are passed to survreg as the init vector, which typically converges the true MLE in a single survreg call. If this warm-started fit is unavailable, fails, or produces NA coefficients, fitting falls through to the general random-restart loop below (for all other dist values, this warm start is skipped entirely).

  3. Random-restart loop: starting from an all-zero init vector, survreg is called repeatedly (perturbing init by an independent standard-normal jitter, init + rnorm(length(init)), after every failed attempt) until a fit with no NA coefficients is obtained or num_max_iter attempts are exhausted, at which point NULL is returned.

survreg.control(maxiter = 100, rel.tolerance = 1e-9, outer.max = 10) is used throughout (tighter than survreg's own defaults) to reduce the chance of a spuriously "converged" fit at a poor optimum.

Usage

robust_survreg_with_surv_object(
  surv_object,
  cov_matrix_or_vector,
  dist = "weibull",
  num_max_iter = 50
)

Arguments

surv_object

The survival object (built from the response vector and censoring vector via Surv).

cov_matrix_or_vector

The design matrix (or a single covariate vector) of predictors, excluding the intercept (one is added by the internal ~ . formula).

dist

The parametric AFT distribution family passed to survreg (default "weibull"); only "weibull" triggers the closed-form warm start.

num_max_iter

Maximum number of random-restart attempts if the (possibly warm-started) direct fit fails or does not converge (default 50).

Value

The fitted survreg model object, or NULL if no attempt converged to a fit with no NA coefficients within num_max_iter tries.

Examples

X = matrix(rnorm(500), 100, 5)
y = runif(100)
dead = rbinom(100, 1, 0.5)
surv = survival::Surv(y, dead)
robust_survreg_with_surv_object(surv, X)
#> Call:
#> survival::survreg(formula = surv_reg_formula, data = cov_matrix_or_vector_data_frame, 
#>     dist = dist, init = init_vals, control = survival::survreg.control(maxiter = 100, 
#>         rel.tolerance = 1e-09, outer.max = 10))
#> 
#> Coefficients:
#> (Intercept)          X1          X2          X3          X4          X5 
#> -0.12930510 -0.04882018  0.06032909  0.02179087  0.03177262  0.03758216 
#> 
#> Scale= 0.6189695 
#> 
#> Loglik(model)= -43.6   Loglik(intercept only)= -44.2
#> 	Chisq= 1.06 on 5 degrees of freedom, p= 0.957 
#> n= 100