b_selection_index_optim: Cross validation index parameter selection

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

Cross validation index parameter selection

Description

Implements the index parameter selection for two markers based on K-fold cross validation.

Usage

b_selection_index_optim(in.par, data, marker_name1, marker_name2,  
          event_time_name = 'years', time_name = 'year', event_name = 'status2', I, b)

Arguments

in.par	Vector of candidate values for the index parameters.
data	A data frame of time dependent data points. Missing values are allowed.
marker_name1	The column name of the first marker values in the data frame data.
marker_name2	The column name of the second 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	scalar bandwidth for the HQM estimator.

Details

The function b_selection_index_optim implements the cross validation index parameter selection for the indexing of two markers and given by

\hat \theta = arg min_{\theta_1, \theta_2} \sum_{i = 1}^N \int_0^T \int_s^T Z_i(t)Z_i(s)(\hat{h}_{\theta_0^T X_i(s)}(t-s)- h_{\theta_0^T X_i(s)}(t-s))^2 dt ds,

where \hat h_x(t) is the HQM estimator of h_x(t), see Bagkavos et al. (2025), \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biomet/asaf008")}, 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 parameters 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

# Obtain the indexing parameters for the combination of albumin and bilirubin markers
# These are the values used in the example of function h_xt_vec
# and yielded the values:  (par.alb, par.bil) = ( 0.0702, 0.0856 ) that were used there.  

I = 26
b_list = seq(1.1, 1.2, by=0.1)

for(i in 1:length(b_list))
{
  res<- optim(c(0.5, 0.5), b_selection_index_optim,  data=pbc2, marker_name1='albumin', 
              marker_name2= 'serBilir', event_time_name = 'years', time_name = 'year', 
              event_name = 'status2', I=26, b=b_list[i], method="Nelder-Mead")
  cat("i= ", i, " ", res$par, " ", res$value, "count calls to fn = ", res$counts, " converge? ", 
        res$convergence,   "\n")
  res
}

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