Poisson Super Learner.

Poisson SuperLearner

The package provides an implementation of piecewise-constant hazard models for time-to-event analysis of survival and competing risks data. The piecewise-constant hazard models can be combined in an ensemble, the Poisson Superlearner, via cross-validated risk minimization for flexible hazard estimation. It enables estimation of survival functions and absolute risk predictions.

The package provides:

• Flexible specification of base learners (e.g. penalized and unpenalized Poisson regression).
• Automatic time-splitting into piecewise-constant hazard intervals.
• Cross-validated ensemble learning.
• Absolute risk prediction at arbitrary time horizons.

Installation

# install.packages("devtools")
# devtools::install_github("gpitt71/poissonsuperlearner")

library(poissonsuperlearner)

Example: Piecewise-Constant Hazard Model

Fit a single PCH model and obtain absolute risk predictions.

library(poissonsuperlearner)

set.seed(42)

# Simulate synthetic survival data
d <- simulateStenoT1(
  n = 50,
  scenario = "alpha"
)

# Define an unpenalized Poisson hazard learner
l_glm <- Learner_glmnet(
  covariates = c("sex", "diabetes_duration"),
  cross_validation = FALSE,
  lambda = 0
)

# Fit piecewise-constant hazard model
fit_glm <- fit_learner(
  data = d,
  id = "id",
  status = "event",
  event_time = "time",
  learner = l_glm,
  number_of_nodes = 5
)

# Absolute risk prediction at time horizon t = 5
predictRisk(fit_glm, newdata = d[1, ], times = 5)

What happens internally?

• The follow-up time is split into number_of_nodes intervals.
• A Poisson regression is fitted to the expanded dataset.
• The estimated hazards are integrated to produce survival and absolute risk.

Example: Superlearner for Piecewise Hazards

Combine multiple hazard learners into an ensemble.

library(poissonsuperlearner)

set.seed(42)

d <- simulateStenoT1(
  n = 50,
  scenario = "alpha"
)

# Base learner 1: unpenalized Poisson regression
l_glm <- Learner_glmnet(
  covariates = c("sex", "diabetes_duration"),
  cross_validation = FALSE,
  lambda = 0
)

# Base learner 2: Lasso-penalized Poisson regression
l_lasso <- Learner_glmnet(
  covariates = c("value_Smoking", "value_LDL"),
  cross_validation = TRUE,
  alpha = 1
)

learners_list <- list(
  glm   = l_glm,
  lasso = l_lasso
)

# Fit the superlearner
sl_fit <- Superlearner(
  data = d,
  id = "id",
  status = "event",
  event_time = "time",
  learners = learners_list,
  number_of_nodes = 5
)

# Absolute risk prediction from the ensemble
predictRisk(sl_fit, newdata = d[1, ], times = 5)

Superlearner workflow

1. Each base learner is fitted on cross-validation folds.
2. Out-of-sample Poisson deviance is computed.
3. A meta-learner combines the base hazard predictions.
4. Final hazards are aggregated and converted to absolute risk.

For competing risks, learners may also be a list of cause-specific learner libraries, one library per cause. Predictions can be requested from the stacked ensemble (model = "sl"), the discrete super learner (model = "discrete_sl"), or named/indexed base learners.

Main Functions

• Learner_glmnet() - define a Poisson hazard learner.
• Learner_gam() - define a Poisson GAM hazard learner.
• Learner_hal() - define a HAL-style Poisson hazard learner.
• fit_learner() - fit a single piecewise-constant hazard model.
• Superlearner() - fit an ensemble of hazard learners.
• predict() - obtain hazards, survival, and absolute risk predictions.
• predictRisk() - obtain risk matrices compatible with riskRegression.

Typical Use Case

poissonsuperlearner is designed for:

• Survival analysis via Poisson representations.
• Flexible hazard modeling with regularization.
• Ensemble-based absolute risk prediction.
• Methodological research in time-to-event modeling.

The package focuses on modular learners, transparent cross-validation, and direct control of the piecewise hazard structure.