b_selection: Cross validation bandwidth selection

In HQM: Superefficient Estimation of Future Conditional Hazards Based on Marker Information

Cross validation bandwidth selection

Description

Implements the bandwidth selection for the future conditional hazard rate \hat h_x(t) based on K-fold cross validation.

Usage

b_selection(data,   marker_name, event_time_name = 'years',
            time_name = 'year', event_name = 'status2', I, b_list)

Arguments

data	A data frame of time dependent data points. Missing values are allowed.
marker_name	The column name of the marker values in the data frame data.
event_time_name	The column name of the event times in the data frame data.
time_name	The column name of the times the marker values were observed in the data frame data.
event_name	The column name of the events in the data frame data.
I	Number of observations leave out for a K cross validation.
b_list	Vector of bandwidths that need to be tested.

Details

The function b_selection implements the cross validation bandwidth selection for the future conditional hazard rate \hat h_x(t) given by

b_{CV} = arg min_b \sum_{i = 1}^N \int_0^T \int_s^T Z_i(t)Z_i(s)(\hat{h}_{X_i(s)}(t-s)- h_{X_i(s)}(t-s))^2 dt ds,

where \hat h_x(t) is a smoothed kernel density estimator of h_x(t) and Z_i the exposure process of individual i. Note that \hat h_x(t) is dependent on b.

Value

A list with the tested bandwidths and its cross validation scores.

References

Bagkavos, I., Isakson, R., Mammen, E., Nielsen, J., and Proust–Lima, C. (2025). Biometrika, 112(2), asaf008. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biomet/asaf008")}

See Also

b_selection_prep_g, Q1, R_K, prep_cv, dataset_split

Examples

I = 26
# For Albumin marker:
b_list = seq(0.9, 1.7, 0.1)
 

b_scores_alb = b_selection(pbc2,  'albumin', 'years', 'year', 'status2', I, b_list)
b_scores_alb[[2]][which.min(b_scores_alb[[1]])]

# For Bilirubin marker:
b_list = seq(3, 4, 0.1)
b_scores_bil = b_selection(pbc2, 'serBilir', 'years', 'year', 'status2', I, b_list)
b_scores_bil[[2]][which.min(b_scores_bil[[1]])]
b_scores_bil

HQM documentation built on Jan. 8, 2026, 9:08 a.m.