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Adaptive LASSO Cox Regression for Variable Selection in Survival Analysis

Source: vignettes/jsurvival-adaptivelasso-comprehensive.Rmd
jsurvival-adaptivelasso-comprehensive.Rmd

Note: The adaptivelasso() function is designed for use within jamovi’s GUI. The code examples below show the R syntax for reference. To run interactively, use devtools::load_all() and call the R6 class directly: adaptivelassoClass$new(options = adaptivelassoOptions$new(...), data = mydata).

Adaptive LASSO Cox Regression

Overview

The Adaptive LASSO Cox Regression module (adaptivelasso) performs penalized variable selection for Cox proportional hazards models using data-driven adaptive weights. Unlike standard LASSO, the adaptive LASSO assigns differential penalties to each coefficient based on an initial estimate of their importance. This achieves the oracle property – meaning that asymptotically, it selects the true model as if the true sparse structure were known in advance.

This matters in practice because standard LASSO can over-shrink large coefficients and under-shrink small ones, producing biased estimates. The adaptive variant corrects this by penalizing unimportant variables more aggressively while leaving truly important predictors relatively unpenalized, yielding sparser models with less bias.

Key capabilities:

  • Five weight methods (ridge, univariate Cox, full Cox, marginal correlation, equal)
  • Elastic net mixing for handling correlated predictors
  • Cross-validated lambda selection with deviance or C-index criteria
  • Stability selection via bootstrap for robust variable identification
  • Proportional hazards testing and influence diagnostics
  • Risk group stratification with survival predictions
  • Six visualization types (regularization path, CV curve, stability, survival curves, baseline hazard, diagnostics)

What is Adaptive LASSO?

Mathematical Formulation

The Cox proportional hazards model is:

h(t)=h0(t)exp⁡(β1x1+β2x2+⋯+βpxp)h(t) = h_0(t) \exp(\beta_1 x_1 + \beta_2 x_2 + \cdots + \beta_p x_p)

Standard LASSO penalizes all coefficients equally:

Maximize:ℓ(β)−λ∑j=1p|βj|\text{Maximize:} \quad \ell(\beta) - \lambda \sum_{j=1}^{p} |\beta_j|

Adaptive LASSO uses data-driven weights ŵj\hat{w}_j:

Maximize:ℓ(β)−λ∑j=1pŵj|βj|\text{Maximize:} \quad \ell(\beta) - \lambda \sum_{j=1}^{p} \hat{w}_j |\beta_j|

where ŵj=1/|β̂jinit|γ\hat{w}_j = 1 / |\hat{\beta}_j^{init}|^{\gamma} and β̂jinit\hat{\beta}_j^{init} is an initial consistent estimator of βj\beta_j. The power parameter γ>0\gamma > 0 controls how aggressively the weights differentiate between important and unimportant predictors.

Why Adaptive Weights Matter

The key insight is that variables with large initial coefficient estimates receive smaller penalties (low ŵj\hat{w}_j), while variables with near-zero initial estimates receive larger penalties (high ŵj\hat{w}_j). This asymmetry is what grants the oracle property.

Weight Methods Comparison

Method Initial Estimator When to Use
Ridge (default) Ridge-penalized Cox coefficients High-dimensional data (p > n), correlated predictors
Univariate Cox Individual Cox regressions per variable Moderate dimensions, uncorrelated predictors
Full Cox Standard multivariable Cox model Low dimensions (p << n), well-conditioned design
Marginal Correlation Correlation with survival outcome Quick screening, very large p
Equal (Standard LASSO) All weights = 1 (no adaptation) Baseline comparison, when initial estimates are unreliable

LASSO vs Adaptive LASSO

Property Standard LASSO Adaptive LASSO
Variable selection consistency No (in general) Yes (oracle property)
Coefficient bias Systematically biased Reduced bias for true signals
Penalty structure Uniform across all variables Differential, data-driven
Computational cost Lower (single-stage) Higher (two-stage: initial + penalized)
Best for Quick screening, exploratory Confirmatory analysis, final models

Datasets Used in This Guide

The package includes three test datasets designed for adaptive LASSO analysis:

Dataset N Events Event Rate Predictors Strata Description
adaptivelasso_test_data 180 122 68% 12 (6 numeric + 6 factor) center (3 levels) Standard clinical scenario
adaptivelasso_small_data 40 11 28% 6 (2 numeric + 4 factor) center (2 levels) Small sample / edge case
adaptivelasso_highdim_data 80 61 76% 17 (9 numeric + 8 factor) – High-dimensional with genomic features

1. Basic Usage (Default Settings)

1.1 Minimal Example

A minimal adaptive LASSO analysis requires only the time variable, event indicator, event level, and predictor variables. All other options use sensible defaults (ridge weights, alpha=1.0, 10-fold CV, deviance criterion).

data("adaptivelasso_test_data", package = "ClinicoPath")

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  suitabilityCheck = TRUE,
  show_coefficients = TRUE,
  show_cv_results = TRUE,
  plot_selection_path = TRUE,
  plot_cv_curve = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

The suitability assessment (traffic-light system) evaluates:

  • Events per variable (EPV): Are there enough events relative to the number of predictors?
  • Sample size adequacy: Is n large enough for stable estimation?
  • Event rate: Are events too rare or too common?
  • Missing data: Are there problematic amounts of missingness?
  • Multicollinearity: Are predictors highly correlated?
  • Variable types: Are there enough numeric predictors for penalized regression?

1.2 With Stratification

When there is a known grouping variable (e.g., treatment center, study site) that should not be penalized but accounted for as a stratum, use the strata option. This fits separate baseline hazards for each stratum while sharing the regression coefficients.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  strata = "center",
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = TRUE,
  plot_selection_path = TRUE,
  plot_cv_curve = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Stratification is particularly useful when the center effect is a nuisance variable you want to adjust for without estimating its coefficient.

2. Weight Methods Comparison

The choice of weight method determines the initial coefficient estimates used to calculate adaptive penalties. This section compares all five methods on the same dataset. Look at which variables are selected and the magnitude of adaptive weights to understand how each method behaves.

2.1 Ridge Weights (Default)

Ridge regression always produces non-zero coefficients, making it a stable source of initial weights even in high-dimensional or correlated settings.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  weight_method = "ridge",
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_selection_path = FALSE,
  show_cv_results = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

2.2 Univariate Cox Weights

Each predictor is fitted in a separate univariate Cox model. Variables with strong marginal associations get small weights (less penalized), while marginally weak predictors get large weights. This does not account for confounding between variables.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  weight_method = "univariate",
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_selection_path = FALSE,
  show_cv_results = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

2.3 Full Cox Weights

Uses the full multivariable Cox model for initial estimates. This accounts for confounding but can be unstable when p is close to n or when there is multicollinearity. Best reserved for low-dimensional problems.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  weight_method = "cox",
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_selection_path = FALSE,
  show_cv_results = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

2.4 Marginal Correlation Weights

Uses the correlation between each predictor and the survival outcome (via concordance or similar measure). Fast to compute, suitable as a rough screen in very high-dimensional settings.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  weight_method = "correlation",
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_selection_path = FALSE,
  show_cv_results = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

2.5 Equal Weights (Standard LASSO)

Setting weights to equal recovers the standard LASSO – no adaptation. This is useful as a baseline comparison to see how much the adaptive weighting changes the variable selection.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  weight_method = "equal",
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_selection_path = FALSE,
  show_cv_results = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

What to compare across methods: The “Adaptive Weight” column in the coefficients table shows how aggressively each variable is penalized. Variables with small weights are protected from shrinkage; variables with large weights are strongly penalized. Different weight methods may select different variables – this is expected and informative about which predictors are robust across estimation strategies.

3. Elastic Net and Adaptive Penalty

3.1 Alpha Sensitivity

The alpha parameter controls the mix between L1 (LASSO) and L2 (ridge) penalties. Values between 0 and 1 give elastic net behavior, which is helpful when predictors are correlated and you want grouped selection.

Alpha = 1.0 (Pure LASSO): Maximum sparsity. Variables are either in or out.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  alpha = 1.0,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_selection_path = FALSE,
  show_cv_results = TRUE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Alpha = 0.5 (Elastic Net): Compromise between LASSO and ridge. Correlated predictors tend to be selected or excluded together.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  alpha = 0.5,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_selection_path = FALSE,
  show_cv_results = TRUE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Alpha = 0.0 (Pure Ridge): No variable selection – all coefficients are shrunk but none set exactly to zero. This is not typically the goal of adaptive LASSO, but it is useful as a comparison.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  alpha = 0.0,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_selection_path = FALSE,
  show_cv_results = TRUE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

3.2 Gamma Sensitivity

The gamma parameter controls how sharply the adaptive weights differentiate between strong and weak predictors. Higher gamma gives more aggressive selection.

Gamma = 0.5 (Mild adaptation): Weights are less extreme. More variables tend to survive selection.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  gamma = 0.5,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_selection_path = FALSE,
  show_cv_results = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Gamma = 1.0 (Default): Standard adaptive LASSO.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  gamma = 1.0,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_selection_path = FALSE,
  show_cv_results = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Gamma = 2.0 (Strong adaptation): Weights are very extreme. Only the strongest predictors survive; marginal predictors are aggressively excluded.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  gamma = 2.0,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_selection_path = FALSE,
  show_cv_results = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Guidance: Use gamma=0.5 for exploratory analysis (retain more variables), gamma=1.0 as the default, and gamma=2.0 when you need a very sparse final model. In high-dimensional settings, larger gamma helps control false selections.

4. Cross-Validation Options

4.1 Different CV Measures

The cross-validation criterion determines what the model optimizes during lambda selection. The two available measures are partial likelihood deviance and Harrell’s C-index.

Deviance (default): Optimizes the partial likelihood. This is the standard choice and is computationally efficient.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  cv_folds = 10,
  cv_measure = "deviance",
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = TRUE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

C-index (Harrell’s concordance): Optimizes discrimination ability – the probability that for a random pair of patients, the one with the higher risk score has the earlier event. This focuses on ranking rather than calibration.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  cv_folds = 10,
  cv_measure = "C",
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = TRUE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Choosing between deviance and C-index:

  • Use deviance (default) for general-purpose model building and when calibration matters.
  • Use C-index when discrimination (ranking patients correctly) is the primary goal, such as for prognostic risk scores.

4.2 Custom Lambda Sequence

Instead of the automatic lambda sequence, you can specify a custom range. This is useful when you want to explore a specific penalty region or when the automatic range does not cover the optimal region well.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  lambda_sequence = "custom",
  lambda_custom_max = 0.5,
  lambda_custom_min = 0.0001,
  n_lambda = 50,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = TRUE,
  show_selection_path = TRUE,
  show_diagnostics = FALSE,
  plot_selection_path = TRUE,
  plot_cv_curve = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

4.3 Single Lambda

Fix the penalty parameter to a single value. This bypasses cross-validation and fits the model at exactly the specified lambda. Useful for comparing models at specific penalty levels, or when you have a pre-determined lambda from prior analysis.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  lambda_sequence = "single",
  lambda_single = 0.01,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

4.4 Varying the Number of CV Folds

More folds give better bias-variance trade-off in the CV estimate but increase computation time. Fewer folds (e.g., 5) are faster; more folds (e.g., 15-20) are more stable.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  cv_folds = 5,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = TRUE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

4.5 Lambda Path Resolution

The n_lambda parameter controls how many lambda values are evaluated along the regularization path. More values give a smoother path but take longer. The lambda_min_ratio parameter controls how far down the path extends.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  n_lambda = 200,
  lambda_min_ratio = 0.0001,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = TRUE,
  show_diagnostics = FALSE,
  plot_selection_path = TRUE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

5. Stability Selection

Stability selection runs the adaptive LASSO on many bootstrap subsamples and tracks how frequently each variable is selected. Variables selected consistently across subsamples are considered “stably selected” and are more likely to be truly important. This provides stronger evidence than a single-run selection.

5.1 Basic Stability Selection 

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  stability_selection = TRUE,
  stability_threshold = 0.6,
  bootstrap_samples = 100,
  subsampling_ratio = 0.8,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE,
  plot_stability = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

The stability results table shows:

  • Selection Frequency: How often each variable was selected across bootstrap samples (0 to 1).
  • Stability Score: A normalized score reflecting selection reliability.
  • Stable Selection: “Yes” if the selection frequency exceeds the threshold, “No” otherwise.
  • Error Bound: An upper bound on the expected number of false selections (Meinshausen and Buhlmann, 2010).

5.2 Varying Threshold

A higher threshold is more conservative – fewer variables are declared “stably selected” but you have more confidence in those that are. A lower threshold is more liberal.

Conservative threshold (0.9):

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  stability_selection = TRUE,
  stability_threshold = 0.9,
  bootstrap_samples = 100,
  subsampling_ratio = 0.8,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE,
  plot_stability = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Liberal threshold (0.5):

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  stability_selection = TRUE,
  stability_threshold = 0.5,
  bootstrap_samples = 100,
  subsampling_ratio = 0.8,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE,
  plot_stability = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Practical guidance: A threshold of 0.6 is a reasonable default. For confirmatory analysis or when false selections are costly, use 0.8–0.9. For exploratory screening, 0.5 is acceptable.

6. Model Diagnostics

6.1 Proportional Hazards Test

The Cox model assumes that hazard ratios are constant over time. The proportional hazards (PH) test evaluates this assumption for each selected variable using scaled Schoenfeld residuals.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  proportional_hazards = TRUE,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = TRUE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

A significant p-value (< 0.05) in the PH test suggests that the effect of that variable changes over time. If the PH assumption is violated, consider stratification by that variable or a time-varying coefficient approach.

6.2 Influence Diagnostics

Influence diagnostics identify observations that have an outsized effect on the model estimates. This includes dfbeta values (change in each coefficient when an observation is removed) and leverage measures.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  influence_diagnostics = TRUE,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = TRUE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE,
  plot_diagnostics = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

6.3 Goodness of Fit

The goodness-of-fit assessment reports overall model performance including concordance statistics (C-index), model deviance, and calibration measures. This tells you how well the model discriminates between patients and how well-calibrated the predictions are.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  goodness_of_fit = TRUE,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = TRUE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

6.4 All Diagnostics Combined

For a comprehensive diagnostic assessment, enable all three diagnostic options together.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  proportional_hazards = TRUE,
  influence_diagnostics = TRUE,
  goodness_of_fit = TRUE,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = TRUE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE,
  plot_diagnostics = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

7. Risk Groups and Predictions

7.1 Risk Stratification

The adaptive LASSO model computes a linear predictor (risk score) for each patient. Patients are then divided into risk groups based on quantiles of this score. The risk group table shows the number of subjects, events, median survival, and hazard ratios relative to the lowest-risk group.

Three risk groups (default):

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  risk_groups = 3,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE,
  plot_survival_curves = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Two risk groups (high vs low):

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  risk_groups = 2,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE,
  plot_survival_curves = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Five risk groups (fine-grained stratification):

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  risk_groups = 5,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE,
  plot_survival_curves = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

7.2 Survival Predictions at Time Points

The time_points option specifies at which time points to estimate the baseline survival probability. These predictions are useful for communicating prognosis in clinical terms (“the 5-year survival probability is…”).

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  baseline_survival = TRUE,
  time_points = "5, 10, 15, 20, 25",
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE,
  plot_baseline_hazard = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

The predictions table shows the baseline survival estimate with 95% confidence intervals at each requested time point. Individual patient survival can be derived by combining the baseline survival with their risk score:

S(t|x)=S0(t)exp⁡(β̂Tx)S(t | x) = S_0(t)^{\exp(\hat{\beta}^T x)}

8. Visualization Options

8.1 All Plots Enabled

This example enables all six plot types simultaneously. In practice you would typically enable only the plots relevant to your analysis stage.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade"),
  stability_selection = TRUE,
  bootstrap_samples = 50,
  proportional_hazards = TRUE,
  influence_diagnostics = TRUE,
  goodness_of_fit = TRUE,
  baseline_survival = TRUE,
  time_points = "5, 10, 20",
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_selection_path = TRUE,
  show_cv_results = TRUE,
  show_diagnostics = TRUE,
  plot_selection_path = TRUE,
  plot_cv_curve = TRUE,
  plot_stability = TRUE,
  plot_survival_curves = TRUE,
  plot_baseline_hazard = TRUE,
  plot_diagnostics = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

What each plot shows:

Plot Content
Regularization Path Coefficient trajectories vs. log(lambda). Shows which variables enter/leave the model as penalty changes.
CV Curve Cross-validation error vs. log(lambda) with confidence bands. Vertical lines mark lambda.min and lambda.1se.
Stability Selection Bar chart of selection frequencies across bootstrap samples. Variables above the threshold line are stably selected.
Risk Group Survival Kaplan-Meier curves stratified by adaptive LASSO risk groups. Well-separated curves indicate good discrimination.
Baseline Hazard Estimated baseline hazard and cumulative hazard from the Breslow estimator. Helps assess the temporal risk pattern.
Diagnostics Residual plots, influential observations, and PH assessment. Identify model violations and outliers.

9. Advanced Options

9.1 Tied Times Methods

Tied survival times (multiple events at the same time) require approximation in the partial likelihood. Two methods are available.

Breslow (default): Faster, adequate when ties are not excessive.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  tie_method = "breslow",
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Efron: Better approximation to the exact partial likelihood, especially when there are many tied event times. Slightly more computationally intensive.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  tie_method = "efron",
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

When to use Efron: If your data has many tied event times (e.g., survival measured in months rather than days), Efron provides a better approximation. For continuous time measurements with few ties, both methods give nearly identical results.

9.2 Standardization

Standardizing predictors before fitting ensures that the penalty is applied fairly across variables measured on different scales. This is strongly recommended when variables have different units (e.g., age in years vs. tumor size in cm vs. Ki-67 percentage).

With standardization (default, recommended):

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  standardize = TRUE,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Without standardization (use with caution):

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  standardize = FALSE,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Without standardization, variables on larger scales (e.g., age 30–90) will be penalized more heavily than variables on smaller scales (e.g., albumin 2–5). Only disable standardization if all predictors are already on the same scale.

9.3 Convergence Settings

The coordinate descent algorithm used internally has convergence and iteration parameters. The defaults are adequate for most problems. Adjust only when you receive convergence warnings.

Tighter convergence (more precise but slower):

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  convergence_threshold = 1e-10,
  max_iterations = 50000,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

More relaxed convergence (faster, for exploration):

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  convergence_threshold = 1e-5,
  max_iterations = 5000,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = FALSE,
  show_selection_path = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

9.4 Reproducibility (Random Seed)

The random_seed option ensures that cross-validation folds and bootstrap samples are identical across runs. Always report the seed used in publications.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  random_seed = 42,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = TRUE,
  show_selection_path = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default
# Different seed may produce slightly different fold assignments and results
adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin"),
  random_seed = 999,
  suitabilityCheck = FALSE,
  show_coefficients = TRUE,
  show_cv_results = TRUE,
  show_selection_path = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

If the same variables are selected regardless of the seed, that is strong evidence of genuine signal. If selection changes substantially across seeds, consider using stability selection for more robust results.

10. Edge Cases

10.1 Small Sample

The small dataset (n=40, 11 events) tests the function’s behavior under challenging conditions: low EPV, few events, and limited statistical power.

data("adaptivelasso_small_data", package = "ClinicoPath")

adaptivelasso(
  data = adaptivelasso_small_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "biomarker_a", "biomarker_b",
                 "gender", "stage"),
  strata = "center",
  suitabilityCheck = TRUE,
  show_coefficients = TRUE,
  show_cv_results = TRUE,
  show_diagnostics = TRUE,
  plot_selection_path = TRUE,
  plot_cv_curve = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Expected suitability flags:

  • EPV: 11 events / 6 predictors = 1.8 (likely red – very low)
  • Sample size: n=40 (likely yellow or red)
  • Event rate: 28% (acceptable but low event count)

With such small samples, results should be interpreted with extreme caution. The adaptive LASSO may select zero variables (empty model) as the most honest answer, or it may select one or two variables with wide confidence intervals.

10.2 High-Dimensional Data

The high-dimensional dataset (n=80, 17 predictors including genomic features) tests the scenario where the number of candidate predictors is large relative to the sample size.

data("adaptivelasso_highdim_data", package = "ClinicoPath")

adaptivelasso(
  data = adaptivelasso_highdim_data,
  time = "time",
  event = "event",
  event_level = "Dead",
  predictors = c("gene_a", "gene_b", "gene_c", "gene_d",
                 "crp", "il6", "tnf", "fibrinogen",
                 "molecular_subtype", "grade", "lymph_node",
                 "margin_status", "receptor_status",
                 "bmi", "hemoglobin", "platelet", "ldh"),
  weight_method = "ridge",
  gamma = 1.0,
  suitabilityCheck = TRUE,
  stability_selection = TRUE,
  bootstrap_samples = 50,
  show_coefficients = TRUE,
  show_cv_results = TRUE,
  show_diagnostics = FALSE,
  plot_selection_path = TRUE,
  plot_cv_curve = TRUE,
  plot_stability = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

In high-dimensional settings, ridge weights are recommended because they always produce non-zero initial estimates. Univariate or full Cox weights may be unstable. Stability selection adds an extra layer of robustness for identifying truly important features.

10.3 Data Suitability Assessment

The suitability check runs automated assessments and produces a traffic-light report (green/yellow/red). This example demonstrates the suitability check with many predictors.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size", "ki67_index", "hemoglobin",
                 "crp_level", "albumin", "gender", "stage", "grade",
                 "treatment", "smoking_status"),
  suitabilityCheck = TRUE,
  show_coefficients = FALSE,
  show_selection_path = FALSE,
  show_cv_results = FALSE,
  show_diagnostics = FALSE,
  plot_selection_path = FALSE,
  plot_cv_curve = FALSE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

The suitability assessment never blocks the analysis – it is advisory. Even with red flags, the model will still run, but results should be interpreted accordingly.

10.4 Minimal Predictors

When only two or three predictors are available, the adaptive LASSO may not add much over standard Cox regression. This tests the boundary case.

adaptivelasso(
  data = adaptivelasso_test_data,
  time = "time",
  event = "event",
  event_level = "Event",
  predictors = c("age", "tumor_size"),
  suitabilityCheck = TRUE,
  show_coefficients = TRUE,
  show_cv_results = TRUE,
  show_diagnostics = TRUE,
  plot_selection_path = TRUE,
  plot_cv_curve = TRUE
)
#> Error in `adaptivelasso()`:
#> ! argument "censor_level" is missing, with no default

Interpreting Results

Coefficients Table

Column Meaning
Variable Predictor name (with dummy level for factors)
Coefficient Log hazard ratio (positive = increased risk, negative = protective)
Hazard Ratio exp(coefficient) – multiplicative effect on hazard per unit change
SE Standard error from post-selection unpenalized Cox refit
Lower CI / Upper CI 95% confidence interval for the hazard ratio
Adaptive Weight The penalty weight applied to this variable (smaller = less penalized)

Cross-Validation Results

Column Meaning
Lambda Min Lambda with minimum CV error (retains more variables)
Lambda 1SE Most parsimonious lambda within 1 SE of minimum (recommended default)
Min CV Error CV error at lambda.min
1SE CV Error CV error at lambda.1se
Variables (Min) Number of selected variables at lambda.min
Variables (1SE) Number of selected variables at lambda.1se

C-index Interpretation

C-index Discrimination Clinical Utility
0.50–0.60 Poor Limited utility
0.60–0.70 Fair May inform decisions
0.70–0.80 Good Useful for stratification
0.80–0.90 Excellent Strong clinical utility
> 0.90 Outstanding May indicate overfitting

Common Pitfalls and Best Practices

Pitfalls to Avoid

  1. Choosing weight method without considering data dimensions. Full Cox weights (cox) fail or are unstable when p is close to or exceeds n. Use ridge weights as the safe default.

  2. Ignoring the oracle property’s asymptotic nature. The oracle property is an asymptotic result. In small samples, adaptive LASSO may not outperform standard LASSO. Use stability selection to assess robustness.

  3. Over-interpreting post-selection p-values. Confidence intervals and p-values from the refitted unpenalized Cox model are conditional on the selected variables and tend to be anti-conservative. They are informative but should not be treated as formal hypothesis tests.

  4. Setting gamma too high with noisy initial estimates. If the initial estimates are unreliable (small sample, many predictors), a high gamma amplifies this noise. Start with gamma=1.0 and only increase after verifying that initial weights are sensible.

  5. Forgetting to standardize. Without standardization, the penalty is applied unevenly across variables measured on different scales. Always keep standardize = TRUE unless you have a specific reason not to.

  6. Not checking the proportional hazards assumption. A penalized Cox model still assumes proportional hazards. Violations can invalidate the selected model.

  7. Feature selection on the full dataset (data leakage). If you select features on all patients, then validate on the same data, performance estimates are biased. Feature selection should be done within the training set only. Cross-validation within the adaptive LASSO partially addresses this, but external validation is still needed for unbiased assessment.

Best Practices

  1. Use ridge weights as the default – they are stable across data dimensions.
  2. Always run suitability check before interpreting results.
  3. Use stability selection for confirmatory analysis to strengthen variable selection evidence.
  4. Compare weight methods – if the same variables are selected across methods, you have stronger evidence.
  5. Report the full specification: weight method, alpha, gamma, lambda selection rule, CV folds, seed.
  6. Validate externally when possible. Internal CV performance is optimistic.
  7. Follow TRIPOD guidelines for transparent reporting of prediction models.
  8. Combine with clinical knowledge – adaptive LASSO selects statistically important variables, but clinical relevance requires domain expertise.

When to Use Adaptive LASSO vs Other Methods

Scenario Recommended Method
Many predictors, want sparse model Adaptive LASSO
Standard LASSO but want less bias Adaptive LASSO
Correlated predictors, grouped selection Adaptive LASSO (alpha < 1) or Elastic Net
p >> n, genomic/radiomic features Adaptive LASSO with ridge weights
Few predictors, traditional inference Standard Cox regression
Quick exploratory screen Standard LASSO (weight_method = "equal")
Baseline comparison Standard LASSO, then compare with adaptive
Grouped variables (e.g., gene pathways) Group LASSO
Function Module Use When
LASSO Cox (lassocox) jsurvival Standard LASSO without adaptive weights
Adaptive LASSO (adaptivelasso) jsurvival Oracle-property variable selection (this function)
Group LASSO (grouplasso) jsurvival Select/exclude grouped variables together
NCV Reg Cox (ncvregcox) jsurvival Non-convex penalties (SCAD, MCP)
High-Dim Cox (highdimcox) jsurvival Very high-dimensional data (p >> n)
PLS Cox (plscox) jsurvival Dimension reduction via partial least squares
Survival Analysis jsurvival Standard Kaplan-Meier with log-rank test
Multivariable Survival jsurvival Standard Cox with no regularization

References

  • Zou H. The adaptive lasso and its oracle properties. J Am Stat Assoc. 2006;101(476):1418-1429.
  • Zhang HH, Lu W. Adaptive Lasso for Cox’s proportional hazards model. Biometrika. 2007;94(3):691-703.
  • Tibshirani R. The lasso method for variable selection in the Cox model. Stat Med. 1997;16(4):385-395.
  • Simon N, et al. Regularization paths for Cox’s proportional hazards model via coordinate descent. J Stat Softw. 2011;39(5):1-13.
  • Meinshausen N, Buhlmann P. Stability selection. J R Stat Soc B. 2010;72(4):417-473.
  • Collins GS, et al. Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis (TRIPOD). BMJ. 2015;350:g7594.