Leave-One-Covariate-Out Inference with MiniPatch Ensembles (LOCO-MP) for Cox Models

Implements the LOCO-MP statistical inference framework (Gan, Zheng, & Allen 2022) for penalized Cox proportional hazards regression. Combines random minipatch ensembling (subsampling both observations/subjects and covariates) with out-of-bag Leave-One-Covariate-Out evaluation to produce distribution-free feature importance estimates, standard errors, asymptotic z-tests, and confidence intervals for survival models.

Usage

loco_mp_coxnet(
  formula = NULL,
  data = NULL,
  x = NULL,
  y = NULL,
  B = 100,
  n_ratio = 0.7,
  m_ratio = 0.5,
  penalty = NULL,
  mixture = 1,
  eval_time = NULL,
  subject_id = NULL,
  alpha = 0.05,
  p_adjust = c("bonferroni", "BH", "fdr", "holm", "none"),
  trunc = 0.05,
  parallel = FALSE,
  seed = NULL,
  covariates = c("path", "baseline"),
  ...
)

Arguments

formula: A formula with a Surv() outcome, e.g. Surv(time, status) ~ x1 + x2, or a [recipes::recipe()] whose outcome is a Surv column. A formula may not use `strata()` or `offset()`; see [coxnet()].
data: A data frame containing the variables in the model.
x: An optional predictor matrix (used if formula and data are NULL).
y: An optional Surv outcome object (used if formula and data are NULL).
B: Number of minipatches to generate. Default is 100.
n_ratio: Subsampling fraction for subjects/observations without replacement. Default is 0.7.
m_ratio: Subsampling fraction for predictors without replacement. Default is 0.5.
penalty: Penalty parameter for coxnet. If NULL, each minipatch is predicted at the smallest penalty on its own glmnet path, an almost unpenalized fit.
mixture: Elastic-net mixing parameter (\(\alpha \in [0, 1]\)). Default is 1 (lasso).
eval_time: Numeric vector of evaluation time points for IPCW Brier loss integration. If NULL, defaults to deciles of event times.
subject_id: Optional character column name identifying subjects for clustered / counting-process start/stop data. With a recipe, a single column with role "id" is used when NULL, as in [cv_coxnet()].
alpha: Significance level: the two-sided confidence intervals have level 1 - alpha, and autoplot() calls a predictor significant when its adjusted one-sided p-value is below alpha. Default is 0.05.
p_adjust: Multiple testing correction method for the one-sided p-values. Options include "bonferroni", "BH", "fdr", "holm", or "none". Default is "bonferroni".
trunc: Lower truncation threshold for Kaplan-Meier censoring weights. Default is 0.05.
parallel: Logical; if TRUE and future is available, runs patches in parallel.
seed: Optional random seed for reproducible subsampling. The caller's RNG state is restored on exit.
covariates: "path" (default) or "baseline": how the out-of-bag survival curve of a subject with start/stop rows uses the covariates, as in cv_coxnet. With "path" the cumulative hazard is integrated along the subject's covariate path, so no value from after an evaluation time predicts survival at it; "baseline" uses the first interval's covariates. The two agree for right-censored data.
...: Additional arguments passed to coxnet(), and so to glmnet, such as cox.ties, standardize, or penalty.factor. Not weights or offset.

Value

An S3 object of class "loco_mp_coxnet" (and "cbe_loco_mp_coxnet") containing:

results: A tibble with columns term, importance, std_error, statistic, p_value (one-sided, for importance > 0), p_adjusted, conf_low, conf_high (a two-sided interval at level 1 - alpha); see Details.
eval_time: Evaluation time grid used for IPCW loss integration.
B: Number of successfully fitted minipatches; a warning says when some failed.
n_ratio, m_ratio: Subsampling ratios used.
alpha: Significance level.
p_adjust: Multiple testing adjustment method.
covariates: How start/stop covariates were used; see covariates.

Details

**Tests and intervals.** For each predictor, `importance` is the mean, over the subjects that were out of bag in patches both with and without it, of the excess IPCW integrated Brier loss when it is left out. `p_value` is from a one-sided z test of `importance > 0`, the upper tail of the standard normal at `statistic`, and `p_adjusted` adjusts those one-sided p-values with `p_adjust`. `conf_low` and `conf_high` are a two-sided interval at level `1 - alpha`, not adjusted for multiple testing. The p-values and the interval therefore answer different questions: the interval excludes 0 when the unadjusted one-sided p-value is below `alpha / 2`, whereas `p_adjusted < alpha` is a one-sided, adjusted criterion. (With `p_adjust = "none"`, a predictor whose `p_value` is between `alpha / 2` and `alpha` passes the test but has an interval that still contains 0.) [autoplot()][autoplot.cbe_loco_mp_coxnet] colours a predictor "Significant" by `p_adjusted < alpha`, that is, by the one-sided adjusted test, not by whether its interval excludes 0.

**Data.** The predictors must be numeric, complete, and finite, and there must be at least 3 of them: each minipatch keeps 2 and leaves at least 1 out. This is checked once before any patch is fit. A minipatch that fails anyway (for example, one whose sampled subjects have no events) is dropped with a warning that gives the count and the first error; `B` in the result is the number that succeeded.

Examples

# \donttest{
if (requireNamespace("glmnet", quietly = TRUE) && requireNamespace("survival", quietly = TRUE)) {
  set.seed(42)
  n <- 60
  df <- data.frame(
    time = stats::rexp(n, 0.1) + 0.1,
    status = stats::rbinom(n, 1, 0.6),
    x1 = stats::rnorm(n),
    x2 = stats::rnorm(n),
    x3 = stats::rnorm(n)
  )
  fit <- loco_mp_coxnet(survival::Surv(time, status) ~ x1 + x2 + x3, data = df, B = 20)
  fit
  generics::tidy(fit)
}
#> # A tibble: 3 × 8
#>   term  importance std_error statistic p_value conf_low conf_high p_adjusted
#>   <chr>      <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>      <dbl>
#> 1 x3       0.00667    0.0191     0.349   0.364  -0.0308    0.0442      1    
#> 2 x2       0.00659    0.0126     0.523   0.300  -0.0181    0.0313      0.901
#> 3 x1      -0.00452    0.0124    -0.364   0.642  -0.0288    0.0198      1    
# }