Fit ReSurv models on the individual data.

This function fits and computes the reserves for the ReSurv models

Usage

ReSurv(
  IndividualDataPP,
  hazard_model = "COX",
  tie = "efron",
  baseline = "spline",
  continuous_features_scaling_method = "minmax",
  random_seed = 1,
  hparameters = list(),
  percentage_data_training = 0.8,
  grouping_method = "exposure",
  check_value = 1.85,
  eta = 0.5,
  simplifier = TRUE
)

# Default S3 method
ReSurv(
  IndividualDataPP,
  hazard_model = "COX",
  tie = "efron",
  baseline = "spline",
  continuous_features_scaling_method = "minmax",
  random_seed = 1,
  hparameters = list(),
  percentage_data_training = 0.8,
  grouping_method = "exposure",
  check_value = 1.85,
  eta = 0.5,
  simplifier = TRUE
)

# S3 method for class 'IndividualDataPP'
ReSurv(
  IndividualDataPP,
  hazard_model = "COX",
  tie = "efron",
  baseline = "spline",
  continuous_features_scaling_method = "minmax",
  random_seed = 1,
  hparameters = list(),
  percentage_data_training = 0.8,
  grouping_method = "exposure",
  check_value = 1.85,
  eta = 0.5,
  simplifier = TRUE
)

Arguments

IndividualDataPP

IndividualDataPP object to use for the ReSurv fit.

hazard_model

character, hazard model supported from our package, must be provided as a string. The model can be chosen from:

• "COX": Standard Cox model for the hazard.

• "NN": Deep Survival Neural Network.

• "XGB": eXtreme Gradient Boosting.

tie

Handling of ties in the Cox fit, passed to survival::coxph(): "efron" (default), "breslow", or "exact". NN and XGB fitting use Efron handling.

baseline

Retained for compatibility. The baseline is estimated from the risk sets using the specified eta.

continuous_features_scaling_method

Scaling method: "minmax" or "standard".

random_seed

integer, random seed set for reproducibility

hparameters

list, hyperparameters for the machine learning models. It will be disregarded for the cox approach.

percentage_data_training

numeric, fraction in (0, 1] of observed data used for training; the remainder is used for validation in the NN and XGB models.

grouping_method

Retained for compatibility; currently ignored.

check_value

Retained for compatibility; currently ignored.

eta

Numeric in [0, 1], controlling the baseline estimate and hazard-to-development-factor conversion. Default is 0.5.

simplifier

logical, kept for compatibility. The simplified forecast frame is always used.

Value

A ReSurvFit list containing model.out (design matrix and fitted backend model), hazard_frame (risk scores, baseline, hazards, development factors and survival probabilities), data_information (preprocessing and reserving metadata), and fit_information (model name, training loss is_lkh, validation loss os_lkh, and eta). Use predict() or predictReserve() to obtain claim-count predictions.

Details

The model fit uses the theoretical framework of Hiabu et al. (2023), that relies on the correspondence between hazard models and development factors:

Neural networks use the native R torch backend. Install its runtime with torch::install_torch() before fitting a neural network.

The ReSurv package assumes proportional hazard models. Given an i.i.d. sample \(\left\{y_i,x_i\right\}_{i=1, \ldots, n}\) the individual hazard at time \(t\) is:

\(\lambda_i(t)=\lambda_0(t)e^{y_i(x_i)}\)

Composed of a baseline \(\lambda_0(t)\) and a proportional effect \(e^{y_i(x_i)}\).

Currently, the implementation allows to optimize the partial likelihood (concerning the proportional effects) using one of the following statistical learning approaches:

• COX

• Neural Networks

• eXtreme Gradient Boosting

References

Hiabu, M., Hofman, E., & Pittarello, G. (2023). A machine learning approach based on survival analysis for IBNR frequencies in non-life reserving. arXiv preprint arXiv:2312.14549.

Therneau, T. M., & Lumley, T. (2015). Package ‘survival’. R Top Doc, 128(10), 28-33.

Katzman, J. L., Shaham, U., Cloninger, A., Bates, J., Jiang, T., & Kluger, Y. (2018). DeepSurv: personalized treatment recommender system using a Cox proportional hazards deep neural network. BMC medical research methodology, 18(1), 1-12.

Chen, T., He, T., Benesty, M., & Khotilovich, V. (2019). Package ‘xgboost’. R version, 90, 1-66.

Examples

input_data_0 <- data_generator(
random_seed = 1964,
scenario = "alpha",
time_unit = 1,
years = 4,
period_exposure = 100)

individual_data <- IndividualDataPP(data = input_data_0,
categorical_features = "claim_type",
continuous_features = "AP",
accident_period = "AP",
calendar_period = "RP",
input_time_granularity = "years",
output_time_granularity = "years",
years=4)


resurv_fit_cox <- ReSurv(individual_data,
hazard_model = "COX",
eta = 0)