Sparse Group LASSO Cox Regression - Comprehensive Guide

Note: The sparsegrouplasso() function is designed for use within jamovi’s GUI. The code examples below show the R syntax for reference.

Sparse Group LASSO for Survival Analysis

Overview

Sparse Group LASSO combines group-level variable selection with within-group sparsity for penalized Cox proportional hazards models. Unlike standard Group LASSO (which includes or excludes entire groups), Sparse Group LASSO can retain a group while dropping individual variables within it. This is implemented via glmnet’s elastic net Cox regression with penalty.factor weighting for group structure.

The module supports 5 grouping strategies (factor-based, custom, pathway-based, variable-type, correlation-based), 4 model selection criteria (CV deviance, AIC, BIC, EBIC), adaptive weighting from initial ridge/LASSO/univariate models, repeated CV, bootstrap confidence intervals, and stability selection.

This analysis is particularly valuable for genomic survival studies where genes belong to pathways (retain pathway but drop uninformative genes), clinical prediction models where factors have multiple categories (drop unimportant levels), and any scenario requiring structured yet sparse variable selection.

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Datasets Used in This Guide

Dataset	N	Predictors	Events	Primary Use
sparsegrouplasso_lung	180	14 (mixed)	95	Lung cancer with 4 clinical domains
sparsegrouplasso_genepanel	100	40 (continuous)	43	8 gene pathways, signal in 3
sparsegrouplasso_small	50	6 (mixed)	19	Small cohort edge case

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1. Basic Analysis with Automatic Grouping

Default settings with continuous predictors

lung <- read.csv(paste0(data_path, "sparsegrouplasso_lung.csv"))
#> Error in `file()`:
#> ! cannot open the connection
str(lung[, c("time", "status", "age", "smoking_py", "tumor_size", "pdl1")])
#> Error in `[.data.frame`:
#> ! undefined columns selected

sparsegrouplasso(
  data = lung,
  time_var = "time",
  event_var = "status",
  outcomeLevel = "Dead",
  censorLevel = "Alive",
  pred_vars = c("age", "smoking_py", "tumor_size", "pdl1",
                "crp", "nlr", "albumin", "ldh"),
  pathway_info = NULL,
  group_definition = "factor_based",
  alpha_sgl = 0.95,
  cv_folds = 5,
  suitabilityCheck = TRUE
)
#> Error:
#> ! Argument 'time_var' contains 'time' which is not present in the dataset

Look for: suitability report (EPV, multicollinearity), summary table (optimal lambda, variables/groups selected), coefficients with hazard ratios, group structure showing which groups were selected, and the three default plots.

---

2. Mixed Continuous and Factor Predictors

Factor-based grouping with categorical variables

When factors are included, their dummy variables are automatically grouped together. This ensures e.g., all ecog levels are selected or dropped as a unit.

sparsegrouplasso(
  data = lung,
  time_var = "time",
  event_var = "status",
  outcomeLevel = "Dead",
  censorLevel = "Alive",
  pred_vars = c("age", "smoking_py", "sex", "ecog", "histology",
                "tumor_size", "pdl1"),
  pathway_info = NULL,
  group_definition = "factor_based",
  cv_folds = 5,
  suitabilityCheck = FALSE
)
#> Error:
#> ! Argument 'time_var' contains 'time' which is not present in the dataset

Look for: group structure table showing ecog (3 dummy vars in one group) and histology (2 dummy vars in one group) with descriptive names.

---

3. Alpha Parameter – Group vs Individual Sparsity

alpha = 0.3 (group-heavy)

sparsegrouplasso(
  data = lung,
  time_var = "time",
  event_var = "status",
  outcomeLevel = "Dead",
  censorLevel = "Alive",
  pred_vars = c("age", "smoking_py", "tumor_size", "pdl1",
                "crp", "nlr", "albumin", "ldh"),
  pathway_info = NULL,
  alpha_sgl = 0.3,
  cv_folds = 5,
  suitabilityCheck = FALSE
)
#> Error:
#> ! Argument 'time_var' contains 'time' which is not present in the dataset

alpha = 0.99 (individual sparsity)

sparsegrouplasso(
  data = lung,
  time_var = "time",
  event_var = "status",
  outcomeLevel = "Dead",
  censorLevel = "Alive",
  pred_vars = c("age", "smoking_py", "tumor_size", "pdl1",
                "crp", "nlr", "albumin", "ldh"),
  pathway_info = NULL,
  alpha_sgl = 0.99,
  cv_folds = 5,
  suitabilityCheck = FALSE
)
#> Error:
#> ! Argument 'time_var' contains 'time' which is not present in the dataset

Compare the two: lower alpha tends to select/exclude entire groups, higher alpha allows individual variable selection within retained groups.

---

4. Model Selection Criteria

AIC – moderate parsimony

sparsegrouplasso(
  data = lung,
  time_var = "time",
  event_var = "status",
  outcomeLevel = "Dead",
  censorLevel = "Alive",
  pred_vars = c("age", "smoking_py", "tumor_size", "pdl1",
                "crp", "nlr", "albumin", "ldh"),
  pathway_info = NULL,
  selection_criterion = "aic",
  cv_folds = 5,
  suitabilityCheck = FALSE
)
#> Error:
#> ! Argument 'time_var' contains 'time' which is not present in the dataset

BIC – strong parsimony

sparsegrouplasso(
  data = lung,
  time_var = "time",
  event_var = "status",
  outcomeLevel = "Dead",
  censorLevel = "Alive",
  pred_vars = c("age", "smoking_py", "tumor_size", "pdl1",
                "crp", "nlr", "albumin", "ldh"),
  pathway_info = NULL,
  selection_criterion = "bic",
  cv_folds = 5,
  suitabilityCheck = FALSE
)
#> Error:
#> ! Argument 'time_var' contains 'time' which is not present in the dataset

BIC typically selects fewer variables than CV deviance or AIC due to its stronger penalty for model complexity.

---

5. Custom Group Definition

sparsegrouplasso(
  data = lung,
  time_var = "time",
  event_var = "status",
  outcomeLevel = "Dead",
  censorLevel = "Alive",
  pred_vars = c("age", "smoking_py", "tumor_size", "pdl1",
                "crp", "nlr", "albumin", "ldh"),
  pathway_info = NULL,
  group_definition = "custom",
  custom_groups = "1,2;3,4;5,6;7,8",
  cv_folds = 5,
  suitabilityCheck = FALSE
)
#> Error:
#> ! Argument 'time_var' contains 'time' which is not present in the dataset

Format: semicolons separate groups, commas separate variable indices within groups. Here: {age,smoking_py}, {tumor_size,pdl1}, {crp,nlr}, {albumin,ldh}.

---

6. Adaptive Weights

Ridge-based adaptive weights

Uses initial ridge Cox estimates to weight the penalty – variables with stronger initial effects get less penalization.

sparsegrouplasso(
  data = lung,
  time_var = "time",
  event_var = "status",
  outcomeLevel = "Dead",
  censorLevel = "Alive",
  pred_vars = c("age", "smoking_py", "tumor_size", "pdl1",
                "crp", "nlr", "albumin", "ldh"),
  pathway_info = NULL,
  weight_type = "ridge_based",
  weight_power = 1,
  cv_folds = 5,
  suitabilityCheck = FALSE
)
#> Error:
#> ! Argument 'time_var' contains 'time' which is not present in the dataset

Look for: the Adaptive Weights table showing individual and group weights with rationale.

---

7. Bootstrap Confidence Intervals

sparsegrouplasso(
  data = lung,
  time_var = "time",
  event_var = "status",
  outcomeLevel = "Dead",
  censorLevel = "Alive",
  pred_vars = c("age", "smoking_py", "tumor_size", "pdl1"),
  pathway_info = NULL,
  confidence_intervals = TRUE,
  bootstrap_samples = 100,
  alpha_level = 0.05,
  cv_folds = 5,
  suitabilityCheck = FALSE
)
#> Error:
#> ! Argument 'time_var' contains 'time' which is not present in the dataset

Look for: CI Lower and CI Upper columns populated in the coefficients table, and selection frequency showing bootstrap inclusion rates.

---

8. Stability Selection

sparsegrouplasso(
  data = lung,
  time_var = "time",
  event_var = "status",
  outcomeLevel = "Dead",
  censorLevel = "Alive",
  pred_vars = c("age", "smoking_py", "tumor_size", "pdl1",
                "crp", "nlr", "albumin", "ldh"),
  pathway_info = NULL,
  stability_selection = TRUE,
  bootstrap_samples = 100,
  stability_threshold = 0.6,
  stability_subsample = 0.8,
  plot_stability = TRUE,
  cv_folds = 5,
  suitabilityCheck = FALSE
)
#> Error:
#> ! Argument 'time_var' contains 'time' which is not present in the dataset

Look for: stability results table with selection probability, first/last selected lambda, and the stability plot with threshold line.

---

9. Repeated Cross-Validation

sparsegrouplasso(
  data = lung,
  time_var = "time",
  event_var = "status",
  outcomeLevel = "Dead",
  censorLevel = "Alive",
  pred_vars = c("age", "smoking_py", "tumor_size", "pdl1",
                "crp", "nlr", "albumin", "ldh"),
  pathway_info = NULL,
  cv_repeats = 3,
  cv_folds = 5,
  suitabilityCheck = FALSE
)
#> Error:
#> ! Argument 'time_var' contains 'time' which is not present in the dataset

Repeated CV averages error curves across multiple random fold assignments for more stable lambda selection.

---

10. High-Dimensional Gene Panel

genepanel <- read.csv(paste0(data_path, "sparsegrouplasso_genepanel.csv"))
#> Error in `file()`:
#> ! cannot open the connection
gene_vars <- names(genepanel)[!names(genepanel) %in% c("time", "status")]
#> Error:
#> ! object 'genepanel' not found

sparsegrouplasso(
  data = genepanel,
  time_var = "time",
  event_var = "status",
  outcomeLevel = "Progressed",
  censorLevel = "Stable",
  pred_vars = gene_vars,
  pathway_info = NULL,
  group_definition = "correlation_based",
  correlation_threshold = 0.5,
  cv_folds = 3,
  n_lambda = 20,
  suitabilityCheck = TRUE
)
#> Error:
#> ! object 'genepanel' not found

With 40 predictors and 100 observations, this is a p > n/3 scenario where regularization is essential.

---

11. Small Sample Edge Case

small <- read.csv(paste0(data_path, "sparsegrouplasso_small.csv"))
#> Error in `file()`:
#> ! cannot open the connection

sparsegrouplasso(
  data = small,
  time_var = "time",
  event_var = "status",
  outcomeLevel = "Dead",
  censorLevel = "Alive",
  pred_vars = c("age", "tumor_size", "marker1", "marker2"),
  pathway_info = NULL,
  cv_folds = 3,
  suitabilityCheck = TRUE
)
#> Error:
#> ! object 'small' not found

The suitability report should flag the small sample size and low EPV.

---

12. Solution Path and Sparsity Pattern

sparsegrouplasso(
  data = lung,
  time_var = "time",
  event_var = "status",
  outcomeLevel = "Dead",
  censorLevel = "Alive",
  pred_vars = c("age", "smoking_py", "tumor_size", "pdl1",
                "crp", "nlr", "albumin", "ldh"),
  pathway_info = NULL,
  show_path = TRUE,
  plot_sparsity = TRUE,
  cv_folds = 5,
  suitabilityCheck = FALSE
)
#> Error:
#> ! Argument 'time_var' contains 'time' which is not present in the dataset

Look for: the regularization path table showing how variables enter/exit across lambda values, and the sparsity pattern plot.

---

References

• Simon N, Friedman J, Hastie T, Tibshirani R (2013). “A Sparse-Group Lasso.” Journal of Computational and Graphical Statistics, 22(2), 231-245.
• Friedman J, Hastie T, Tibshirani R (2025). glmnet: Lasso and Elastic-Net Regularized Generalized Linear Models. R package version 4.1-10.
• Therneau TM (2026). survival: Survival Analysis. R package version 3.8-6.
• Meinshausen N, Buhlmann P (2010). “Stability selection.” JRSS-B, 72(4), 417-473.