Type:	Package
Title:	Machine Learning Models for Predicting Claim Counts
Version:	1.0.0
Description:	Prediction of claim counts using the feature based development factors introduced in the manuscript Hiabu M., Hofman E. and Pittarello G. (2023) <doi:10.48550/arXiv.2312.14549>. Implementation of Neural Networks, Extreme Gradient Boosting, and Cox model with splines to optimise the partial log-likelihood of proportional hazard models.
URL:	https://github.com/edhofman/ReSurv
BugReports:	https://github.com/edhofman/ReSurv/issues
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Depends:	tidyverse
Imports:	stats, dplyr, dtplyr, fastDummies, forecast, data.table, purrr, tidyr, tibble, ggplot2, survival, reshape2, bshazard, SynthETIC, rpart, reticulate, xgboost, SHAPforxgboost
SystemRequirements:	Python (>= 3.8.0)
Encoding:	UTF-8
Suggests:	knitr, rmarkdown
VignetteBuilder:	knitr, rmarkdown
RoxygenNote:	7.3.2
NeedsCompilation:	no
Packaged:	2024-11-14 08:40:52 UTC; gpitt
Author:	Emil Hofman [aut, cre, cph], Gabriele Pittarello [aut, cph], Munir Hiabu [aut, cph]
Maintainer:	Emil Hofman <emil_hofman@hotmail.dk>
Repository:	CRAN
Date/Publication:	2024-11-14 16:00:10 UTC

Individual Data Pre-Processing

Description

This function pre-processes the data for the application of a ReSurv model.

Usage

IndividualDataPP(
  data,
  id = NULL,
  continuous_features = NULL,
  categorical_features = NULL,
  accident_period,
  calendar_period,
  input_time_granularity = "months",
  output_time_granularity = "quarters",
  years = NULL,
  calendar_period_extrapolation = FALSE,
  continuous_features_spline = NULL,
  degrees_cf = 3,
  degrees_of_freedom_cf = 4,
  degrees_cp = 3,
  degrees_of_freedom_cp = 4
)

Arguments

Details

The input accident_period is coded as AP_i. The input development periods are derived as DP_i=calendar_period-accident_period+1.

The reverse time development factors are DP_rev_i = DP_max-DP_i, where DP_max is the maximum number of development times: DP_i =1,\ldots,DP_max. Given the parameter years, DP_max is derived internally from our package.

As for the truncation time, TR_i = AP_i-1.

AP_i, DP_i, DP_rev_i and TR_i are converted to AP_o, DP_o, DP_rev_o and TR_o (from the input_time_granularity to the output_time_granularity) using a multiplicative conversion factor. E.g., AP_o = AP_i * CF.

The conversion factor is computed as

CF=\frac{{\nu}^i}{({\nu}^o)^{-1}},

where {\nu}^i and {\nu}^o are the fraction of a year corresponding to input_time_granularity and output_time_granularity. {\nu}^i and {\nu}^o take values 1/360, 1/12, 1/4, 1/2, 1 for "days", "months", "quarters", "semesters", "years" respectively. We will have RP_o = AP_o + DP_o.

Value

IndividualDataPP object. A list containing

• full.data: data.frame. The input data after pre-processing.

• starting.data: data.frame. The input data as they were provided from the user.

• training.data: data.frame. The input data pre-processed for training.

• conversion_factor: numeric. The conversion factor for going from input granularity to output granularity. E.g, the conversion factor for going from months to quarters is 1/3.

• string_formula_i: character. The survival formula to model the data in input granularity.

• string_formula_o: character. The survival formula to model the in data output granularity.

• continuous_features: character. The continuous features names as provided from the user.

• categorical_features: character. The categorical features names as provided from the user.

• calendar_period_extrapolation: logical. The value specifying if a calendar period component is extrapolated.

• years: numeric. Total number of development years in the data. Default is NULL and computed automatically from the data.

• accident_period: character. Accident period column name.

• calendar_period: character. Calendar_period column name.

• input_time_granularity: character. Input time granularity.

• output_time_granularity: character. Output time granularity.

After pre-processing, we provide a standard encoding for the time components. This regards the output in training.data and full.data. In the ReSurv notation:

• AP_i: Input granularity accident period.

• AP_o: Output granularity accident period.

• DP_i: Input granularity development period in forward time.

• DP_rev_i: Input granularity development period in reverse time.

• DP_rev_o: Output granularity development period in reverse time.

• TR_i: Input granularity truncation time.

• TR_o: Output granularity truncation time.

• I: event indicator, under this framework is equal to one for each entry.

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.

Examples

input_data_0 <- data_generator(
random_seed = 1964,
scenario = "alpha",
time_unit = 1,
years = 2,
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 = 2)

Fit ReSurv models on the individual data.

Description

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
)

Arguments

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

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.

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.

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")

Fit ReSurv models on the individual data.

Description

This function fits and computes the reserves for the ReSurv models

Usage

## 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
)

Arguments

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

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.

References

Pittarello, G., Hiabu, M., & Villegas, A. M. (2023). Chain Ladder Plus: a versatile approach for claims reserving. arXiv preprint arXiv:2301.03858.

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")

Fit ReSurv models on the individual data.

Description

This function fits and computes the reserves for the ReSurv models

Usage

## 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
)

Arguments

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

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.

References

Pittarello, G., Hiabu, M., & Villegas, A. M. (2023). Chain Ladder Plus: a versatile approach for claims reserving. arXiv preprint arXiv:2301.03858.

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")

K fold cross-validation of a ReSurv model.

Description

This function computes a K fold cross-validation of a pre-specified machine learning model supported from the ReSurv package for a given grid of hyperparameters. The hyperparameters to be tested are provided in a list, namely hparameters_grid. Conversely, the parameters for the models run are provided separately as arguments and they are specific for each machine learning model support from.

Usage

ReSurvCV(
  IndividualDataPP,
  model,
  hparameters_grid,
  folds,
  random_seed,
  continuous_features_scaling_method = "minmax",
  print_every_n = 1L,
  nrounds = NULL,
  early_stopping_rounds = NULL,
  epochs = 1,
  parallel = FALSE,
  ncores = 1,
  num_workers = 0,
  verbose = FALSE,
  verbose.cv = FALSE
)

Arguments

Value

Best ReSurv model fit. The output is different depending on the machine learning approach that is required for cross-validation. A list containing:

• out.cv: data.frame, total output of the cross-validation (all the input parameters combinations).

• out.cv.best.oos: data.frame, combination with the best out of sample likelihood.

For XGB the columns in out.cv and out.cv.best.oos are the hyperparameters booster, eta, max_depth, subsample, alpha, lambda, min_child_weight. They also contain the metrics train.lkh, test.lkh, and the computational time time. For NN the columns in out.cv and out.cv.best.oos are the hyperparameters num_layers, optim, activation, lr, xi, eps, tie, batch_size, early_stopping, patience, node train.lkh test.lkh. They also contain the metrics train.lkh, test.lkh, and the computational time time.

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.

K fold cross-validation of ReSurv model.

Description

This function computes a K fold cross-validation of a pre-specified ReSurv model for a given grid of parameters.

Usage

## S3 method for class 'IndividualDataPP'
ReSurvCV(
  IndividualDataPP,
  model,
  hparameters_grid,
  folds,
  random_seed,
  continuous_features_scaling_method = "minmax",
  print_every_n = 1L,
  nrounds = NULL,
  early_stopping_rounds = NULL,
  epochs = NULL,
  parallel = FALSE,
  ncores = 1,
  num_workers = 0,
  verbose = FALSE,
  verbose.cv = FALSE
)

Arguments

Value

Best ReSurv model fit. The output is different depending on the machine learning approach that is required for cross-validation. A list containing:

• out.cv: data.frame, total output of the cross-validation (all the input parameters combinations).

• out.cv.best.oos: data.frame, combination with the best out of sample likelihood.

For XGB the columns in out.cv and out.cv.best.oos are the hyperparameters booster, eta, max_depth, subsample, alpha, lambda, min_child_weight. They also contain the metrics train.lkh, test.lkh, and the computational time time. For NN the columns in out.cv and out.cv.best.oos are the hyperparameters num_layers, optim, activation, lr, xi, eps, tie, batch_size, early_stopping, patience, node train.lkh test.lkh. They also contain the metrics train.lkh, test.lkh, and the computational time time.

K fold cross-validation of ReSurv model.

Description

This function computes a K fold cross-validation of a pre-specified ReSurv model for a given grid of parameters.

Usage

## Default S3 method:
ReSurvCV(
  IndividualDataPP,
  model,
  hparameters_grid,
  folds,
  random_seed,
  continuous_features_scaling_method = "minmax",
  print_every_n = 1L,
  nrounds = NULL,
  early_stopping_rounds = NULL,
  epochs = 1,
  parallel = FALSE,
  ncores = 1,
  num_workers = 0,
  verbose = FALSE,
  verbose.cv = FALSE
)

Arguments

Value

Best ReSurv model fit. The output is different depending on the machine learning approach that is required for cross-validation. A list containing:

• out.cv: data.frame, total output of the cross-validation (all the input parameters combinations).

• out.cv.best.oos: data.frame, combination with the best out of sample likelihood.

For XGB the columns in out.cv and out.cv.best.oos are the hyperparameters booster, eta, max_depth, subsample, alpha, lambda, min_child_weight. They also contain the metrics train.lkh, test.lkh, and the computational time time. For NN the columns in out.cv and out.cv.best.oos are the hyperparameters num_layers, optim, activation, lr, xi, eps, tie, batch_size, early_stopping, patience, node train.lkh test.lkh. They also contain the metrics train.lkh, test.lkh, and the computational time time.

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.

Individual data generator

Description

This function generates the monthly individual claims data in the accompanying methodological paper using the SynthETIC package. This simple function allows to simulate from a sand-box to test out the ReSurv approach. Some parameters of the simulation can be changed.

Usage

data_generator(
  ref_claim = 2e+05,
  time_unit = 1/360,
  years = 4,
  random_seed = 1964,
  period_exposure = 200,
  period_frequency = 0.2,
  scenario = 1
)

Arguments

Value

Individual claims data. It contains the following columns:

• claim_number: Policy ID.

• claim_type: Type of claim. It can be either 0 or 1.

• AP: Accident period

• RP: Reporting period.

References

Avanzi, B., Taylor, G., Wang, M., & Wong, B. (2021). SynthETIC: an individual insurance claim simulator with feature control. Insurance: Mathematics and Economics, 100, 296-308.

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.

Examples

input_data_0 <- data_generator(
random_seed = 1964,
scenario = "alpha",
time_unit = 1,
years = 2,
period_exposure = 100)

Install Python Environment for ReSurv

Description

Install a Python environment that allows the user to apply the Neural Network (NN) models.

Usage

install_pyresurv(
  ...,
  envname = "pyresurv",
  new_env = identical(envname, "pyresurv")
)

Arguments

Value

No return value.

Compute the out-of-sample likelihood

Description

When the lower triangle data are available, this method computes the likelihood on the lower triangle.

Usage

ooslkh(object, ...)

Arguments

Value

numeric, out-of-sample likelihood.

Compute the out-of-the sample likelihood

Description

When the lower triangle data are available, this method computes the likelihood on the lower triangle.

Usage

## S3 method for class 'ReSurvFit'
ooslkh(object, ...)

Arguments

Value

numeric, out-of-sample likelihood.

Compute the out-of-the sample likelihood

Description

When the lower triangle data are available, this method computes the likelihood on the lower triangle.

Usage

## Default S3 method:
ooslkh(object, ...)

Arguments

Value

numeric, out-of-sample likelihood.

Helper functions

Description

This script contains the utils functions that are used in ReSurv.

Usage

pkg.env

Format

An object of class environment of length 60.

Plot for machine learning models

Description

This function plots the mean absolute SHAP values for the ReSurv fits of machine learning models.

Usage

## S3 method for class 'ReSurvFit'
plot(x, nsamples = NULL, ...)

Arguments

Value

ggplot2 of the SHAP values for an "XGB" model or a "NN" model.

Plot of the development factors

Description

Plots the development factors by group code.

Usage

## S3 method for class 'ReSurvPredict'
plot(
  x,
  granularity = "input",
  group_code = 1,
  color_par = "royalblue",
  linewidth_par = 2.5,
  ylim_par = NULL,
  ticks_by_par = NULL,
  base_size_par = NULL,
  title_par = NULL,
  x_text_par = NULL,
  plot.title.size_par = NULL,
  ...
)

Arguments

Value

ggplot2 of the development factors

Predict IBNR frequency

Description

This function predicts the results from the ReSurv fits.

Usage

## S3 method for class 'ReSurvFit'
predict(
  object,
  newdata = NULL,
  grouping_method = "probability",
  check_value = 1.85,
  ...
)

Arguments

Value

Predictions for the ReSurvFit model. It includes

• ReSurvFit: Fitted ReSurv model.

• long_triangle_format_out: data.frame. Predicted development factors and IBNR claim counts for each feature combination in long format.

  • input_granularity: data.frame. Predictions for each feature combination in long format for input_time_granularity.

    • AP_i: Accident period, input_time_granularity.

    • DP_i: Development period, input_time_granularity.

    • f_i: Predicted development factors, input_time_granularity.

    • group_i: Group code, input_time_granularity. This associates to each feature combination an identifier.

    • expected_counts: Expected counts, input_time_granularity.

    • IBNR: Predicted IBNR claim counts, input_time_granularity.

  • output_granularity: data.frame. Predictions for each feature combination in long format for output_time_granularity.

    • AP_o: Accident period, output_time_granularity.

    • DP_o: Development period, output_time_granularity.

    • f_o: Predicted development factors, output_time_granularity.

    • group_o: Group code, output_time_granularity. This associates to each feature combination an identifier.

    • expected_counts: Expected counts, output_time_granularity.

    • IBNR: Predicted IBNR claim counts, output_time_granularity.

• lower_triangle: Predicted lower triangle.

  • input_granularity: data.frame. Predicted lower triangle for input_time_granularity.

  • output_granularity: data.frame. Predicted lower triangle for output_time_granularity.

• predicted_counts: numeric. Predicted total frequencies.

• grouping_method: character. Chosen grouping method.

Print summary of IBNR predictions

Description

Gives overview of IBNr predictions

Usage

## S3 method for class 'summaryReSurvPredict'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

Value

print of summary of predictions

Summary of IBNR predictions

Description

Gives overview of IBNR predictions

Usage

## S3 method for class 'ReSurvPredict'
summary(object, granularity = "input", ...)

Arguments

Value

Summary of predictions

Survival continuously ranked probability score.

Description

Return the Survival Continuously Ranked Probability Score (SCRPS) of a ReSurv model.

Usage

survival_crps(ReSurvFit, user_data_set = NULL)

Arguments

Details

The model fit uses the theoretical framework of Hiabu et al. (2023), that relies on the

Value

Survival CRPS, data.table that contains the CRPS (crps) for each observation (id).

References

Pittarello, G., Hiabu, M., & Villegas, A. M. (2023). Chain Ladder Plus: a versatile approach for claims reserving. arXiv preprint arXiv:2301.03858.

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.

Survival continuously ranked probability score.

Description

Return the Survival Continuously Ranked Probability Score (SCRPS) of a ReSurv model.

Usage

## S3 method for class 'ReSurvFit'
survival_crps(ReSurvFit, user_data_set = NULL)

Arguments

Details

The model fit uses the theoretical framework of Hiabu et al. (2023), that relies on the

Value

Survival CRPS, data.table that contains the CRPS (crps) for each observation (id).

References

Pittarello, G., Hiabu, M., & Villegas, A. M. (2023). Chain Ladder Plus: a versatile approach for claims reserving. arXiv preprint arXiv:2301.03858.

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.

Survival continuously ranked probability score.

Description

Return the Survival Continuously Ranked Probability Score (SCRPS) of a ReSurv model.

Usage

## Default S3 method:
survival_crps(ReSurvFit, user_data_set = NULL)

Arguments

Details

The model fit uses the theoretical framework of Hiabu et al. (2023), that relies on the

Value

Survival CRPS, data.table that contains the CRPS (crps) for each observation (id).

References

Pittarello, G., Hiabu, M., & Villegas, A. M. (2023). Chain Ladder Plus: a versatile approach for claims reserving. arXiv preprint arXiv:2301.03858.

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.