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Individual Data Pre-Processing

Source: R/IndividualDataPP.R
IndividualDataPP.Rd

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

data

data.frame, for the individual reserving. The number of development periods can be larger than the number of accident periods.

id

character, data column that contains the policy identifier. If NULL (default), we assume that each row is an observation. We assume that each observation can only have one reporting time, if not null we take the reporting time of the first row for each id.

continuous_features

character, continuous features columns to be scaled.

categorical_features

character, categorical features columns to be one-hot encoded.

accident_period

character, it contains the name of the column in data corresponding to the accident period.

calendar_period

character, it contains the name of the column in data corresponding to the calendar period.

input_time_granularity

character, time unit of the input data. Granularity supported:

  • "days": the input data are daily.

  • "months": the input data are monthly.

  • "quarters": the input data are quarterly

  • "semesters": six-month periods.

  • "years": the input data are yearly.

Default to months.

output_time_granularity

character, time unit of the output data. The granularity supported is the same as for the input data:

  • "days": the output data will be on a daily scale.

  • "months": the output data will be on a monthly scale.

  • "quarters": the output data will be on a quarterly scale.

  • "semesters": six-month periods.

  • "years": the output data will be on yearly scale.

The output granularity must be equal to or coarser than the input granularity. Also, the output granularity must be consistent with the input granularity, meaning that the time conversion must be possible. E.g., it is possible to group quarters to years. Quarters can also be grouped to semesters. Default to quarters.

years

numeric, number of development years in the study.

calendar_period_extrapolation

logical, whether a spline for calendar extrapolation should be considered in the cox model fit. Default is `FALSE`.

continuous_features_spline

character, names of continuous features to model with splines; NULL uses linear terms. Use "AP_i" for a remapped accident-period feature.

degrees_cf

numeric, degrees of the spline for smoothing continuous features.

degrees_of_freedom_cf

numeric, degrees of freedom of the splines for smoothing continuous features.

degrees_cp

numeric, degrees of the spline for smoothing the calendar period effect.

degrees_of_freedom_cp

numeric, degrees of freedom of the splines for smoothing the calendar period effect.

Value

An IndividualDataPP list containing training.data (observed rows), full.data (all encoded rows), and data_information (conversion factor, input/output formulas, feature names, time units, horizon, and original column names).

After pre-processing, we provide a standard encoding for the time components. This regards the output in training.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.

Details

Accident and reporting periods are indexed from one. Development time is DP_i = RP_i - AP_i + 1; reverse development time is DP_rev_i = DP_max - DP_i + 1, and truncation time is TR_i = AP_i - 1. Training retains observed rows with DP_rev_i > TR_i.

The conversion factor is the input time unit divided by the output time unit (for example, 1/3 for months to quarters). Accident and calendar periods are grouped using ceiling; development periods also account for the position of the accident period within each output period. Days use a 360-day year for the development horizon.

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.

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)