Fit ReSurv models on the individual data.

This function fits and computes the reserves for the ReSurv models

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
)

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

ties handling, default is the Efron approach.

baseline

handling the baseline hazard. Default is a spline.

continuous_features_scaling_method

method to preprocess the features

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, percentage of data used for training on the upper triangle.

grouping_method

character, use probability or exposure approach to group from input to output development factors. Choice between:

• "exposure"

• "probability"

Default is "exposure".

check_value

numeric, check hazard value on initial granularity, if above threshold we increase granularity to try and adjust the development factor.

Value

ReSurv fit. A list containing

• model.out: list containing the pre-processed covariates data for the fit (data) and the basic model output (model.out;COX, XGB or NN).

• is_lkh: numeric Training negative log likelihood.

• os_lkh: numeric Validation negative log likelihood. Not available for COX.

• hazard_frame: data.frame containing the fitted hazard model with the corresponding covariates. It contains:

  • expg: fitted risk score.

  • baseline: fitted baseline.

  • hazard: fitted hazard rate (expg*baseline).

  • f_i: fitted development factors.

  • cum_f_i: fitted cumulative development factors.

  • S_i:fitted survival function.

  • S_i_lag:fitted survival function (lag version, for further information see ?dplyr::lag).

  • S_i_lead:fitted survival function (lead version, for further information see ?dplyr::lead).

• hazard_model: string chosen hazard model (COX, NN or XGB)

• IndividualDataPP: starting IndividualDataPP object.

Details

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

To be completed with final notation of the paper.

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

Munir, H., Emil, H., & Gabriele, P. (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.