performance_pencox {pencal}

Predictive performance of the penalized Cox model with time-independent covariates

Description

This function computes the naive and optimism-corrected measures of performance (C index, time-dependent AUC and time-dependent Brier score) for a penalized Cox model with time-independent covariates. The optimism correction is computed based on a cluster bootstrap optimism correction procedure (CBOCP, Signorelli et al., 2021)

Usage

performance_pencox(fitted_pencox, metric = c("tdauc", "c", "brier"),
  times = c(2, 3), n.cores = 1, verbose = TRUE)

Arguments

fitted_pencox

the output of pencox

metric

the desired performance measure(s). Options include: 'tdauc', 'c' and 'brier'

times

numeric vector with the time points at which to estimate the time-dependent AUC and time-dependent Brier score

n.cores

number of cores to use to parallelize part of the computations. If ncores = 1 (default), no parallelization is done. Pro tip: you can use parallel::detectCores() to check how many cores are available on your computer

verbose

if TRUE (default and recommended value), information on the ongoing computations is printed in the console

Value

A list containing the following objects:

• call: the function call;

• concordance: a data frame with the naive and optimism-corrected estimates of the concordance (C) index;

• tdAUC: a data frame with the naive and optimism-corrected estimates of the time-dependent AUC at the desired time points.

Author(s)

Mirko Signorelli

References

Signorelli, M. (2023). pencal: an R Package for the Dynamic Prediction of Survival with Many Longitudinal Predictors. arXiv preprint: arXiv:2309.15600

Signorelli, M., Spitali, P., Al-Khalili Szigyarto, C, The MARK-MD Consortium, Tsonaka, R. (2021). Penalized regression calibration: a method for the prediction of survival outcomes using complex longitudinal and high-dimensional data. Statistics in Medicine, 40 (27), 6178-6196. DOI: 10.1002/sim.9178

See Also

pencox

Examples

# generate example data
set.seed(1234)
p = 4 # number of longitudinal predictors
simdata = simulate_prclmm_data(n = 100, p = p, p.relev = 2, 
             seed = 123, t.values = c(0, 0.5, 1, 1.5, 2))
# create dataframe with baseline measurements only
baseline.visits = simdata$long.data[which(!duplicated(simdata$long.data$id)),]
df = merge(simdata$surv.data, baseline.visits, by = 'id')
df = df[ , -c(5:6)]

do.bootstrap = FALSE
# IMPORTANT: set do.bootstrap = TRUE to compute the optimism correction!
n.boots = ifelse(do.bootstrap, 100, 0)
more.cores = FALSE
# IMPORTANT: set more.cores = TRUE to speed computations up!
if (!more.cores) n.cores = 2
if (more.cores) {
   # identify number of available cores on your machine
   n.cores = parallel::detectCores()
   if (is.na(n.cores)) n.cores = 2
}

form = as.formula(~ baseline.age + marker1 + marker2
                     + marker3 + marker4)
base.pcox = pencox(data = df, 
              formula = form, 
              n.boots = n.boots, n.cores = n.cores) 
ls(base.pcox)
                   
# compute the performance measures
perf = performance_pencox(fitted_pencox = base.pcox, 
          metric = 'tdauc', times = 3:5, n.cores = n.cores)
 # use metric = 'brier' for the Brier score and metric = 'c' for the
 # concordance index

# time-dependent AUC estimates:
ls(perf)
perf$tdAUC