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Bootstrap confidence intervals for cumulative incidence functions with two time scales

Source: R/boot_cuminc2ts.R
boot_cuminc2ts.Rd

boot_cuminc2ts() is a wrapper function to perform non-parametric bootstrap in order to obtain uncertainty measures for the cumulative incidence functions (and the overall survival function) over two time scales. It allows parallel computing.

Usage

boot_cuminc2ts(
  data,
  causes,
  cause_names = NULL,
  prepare_data_args = list(),
  fit2ts_args = list(),
  cumhaz2ts_args = list(),
  ds,
  nboot = 200,
  seed = NULL,
  conf_level = 0.95,
  parallel = FALSE,
  ncpus = 2
)

Arguments

data

A data.frame containing the original individual-level data.

causes

A character vector of column names in data, one for each competing cause (binary 0/1 indicators).

cause_names

A character vector of names for the causes, passed to cumhaz2ts() and cuminc2ts(). Defaults to the values in causes.

prepare_data_args

A named list of arguments passed to prepare_data(), excluding data and events.

fit2ts_args

A named list of arguments passed to fit2ts(), excluding data2ts.

cumhaz2ts_args

A named list of arguments passed to cumhaz2ts(), excluding fitted_model and cause.

ds

The bin width in the s direction, passed to cuminc2ts().

nboot

Integer. Number of bootstrap replicates. Default is 200.

seed

Integer or NULL. Random seed for reproducibility. Default is NULL.

conf_level

Numeric. Confidence level for the intervals. Default is 0.95.

parallel

Logical. Whether to use parallel computation. Default is FALSE.

ncpus

Integer. Number of CPU cores to use when parallel = TRUE. Default is 2.

Value

A list of two lists: the first list contains the results of the bootstrap with one element per cause. Each element is itself a list containing:

lower

Matrix of lower confidence bounds.

upper

Matrix of upper confidence bounds.

se

Matrix of pointwise standard errors.

boot_replicates

List of nboot matrices of bootstrap CIF estimates.

The second list is the grid of points in correspondence of which the estimates are obtained. This is returned to facilitate plotting of these quantities.

Details

It may happen that, as a consequence of the resampling, the range of values for both u and s differ across the various bootstrap samples. To avoid problems it is necessary to bin the data, fit the model, and compute the cumulative incidence functions on the same range of values across all the samples. To do so, simply specify min_u, max_u, min_s, and max_s wherever required. This is shown in the example below.

Examples

# --- Fake data -----------------------------------------------------------
set.seed(1234)
n <- 30
fakedata <- data.frame(
  id     = 1:n,
  u      = round(runif(n, min = 24, max = 58), 2),
  s_out  = round(runif(n, min = 0.5, max = 10), 2),
  cause1 = c(rep(1, 8), rep(0, 22)),
  cause2 = c(rep(0, 8), rep(1, 7), rep(0, 15))
)

# \donttest{
# --- prepare_data for each cause -----------------------------------------
rec2ts <- prepare_data(
  data   = fakedata,
  u      = "u",
  s_out  = "s_out",
  events = "cause1",
  min_u  = 24, max_u = 58,
  min_s  = 0,  max_s = 10,
  du     = 1,  ds    = .5
)
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.

death2ts <- prepare_data(
  data   = fakedata,
  u      = "u",
  s_out  = "s_out",
  events = "cause2",
  min_u  = 24, max_u = 58,
  min_s  = 0,  max_s = 10,
  du     = 1,  ds    = .5
)
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.

# --- Fit cause-specific hazard models ------------------------------------
mod_cause1 <- fit2ts(
  rec2ts,
  Bbases_spec = list(
    bdeg   = 3,
    nseg_u = 7, min_u = 24, max_u = 58,
    nseg_s = 3, min_s = 0,  max_s = 10
  ),
  optim_criterion = "bic"
)

mod_cause2 <- fit2ts(
  death2ts,
  Bbases_spec = list(
    bdeg   = 3,
    nseg_u = 7, min_u = 24, max_u = 58,
    nseg_s = 3, min_s = 0,  max_s = 10
  ),
  optim_criterion = "bic"
)
# }
# --- Bootstrap confidence intervals --------------------------------------
boot_cif <- boot_cuminc2ts(
  data     = fakedata,
  causes   = c("cause1", "cause2"),
  cause_names = c("cause1", "cause2"),
  prepare_data_args = list(
    u      = "u",
    s_out  = "s_out",
    min_u  = 24, max_u = 58,
    min_s  = 0,  max_s = 10,
    du     = 1,  ds    = .5
  ),
  fit2ts_args = list(
    Bbases_spec = list(
      bdeg   = 3,
      nseg_u = 7, min_u = 24, max_u = 58,
      nseg_s = 3, min_s = 0,  max_s = 10
    ),
    optim_criterion = "bic"
  ),
  cumhaz2ts_args = list(
    plot_grid = list(
      c(umin = 24, umax = 58, du = .5),
      c(smin = 0,  smax = 10, ds = .2)
    )
  ),
  ds         = .2,
  nboot      = 10,
  seed       = 1234,
  conf_level = 0.95,
  parallel   = FALSE
)
#> 
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#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> 
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#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> 
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#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> Warning: Max number of iterations 20 reached but the algorithm did not converge.
#> Warning: Max number of iterations 20 reached but the algorithm did not converge.
#> Warning: Max number of iterations 20 reached but the algorithm did not converge.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> 
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#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
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#> 
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#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> 
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#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> 
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#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> 
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#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> 
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#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> 
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#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> 
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#> Warning: 2 out of 10 bootstrap replicates failed and were discarded.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> `s_in = NULL`. I will use `s_in = 0` for all observations.
#> Done. 8 successful replicates out of 10 attempted.

# --- Inspect output ------------------------------------------------------
# Names of causes
names(boot_cif)
#> [1] "results_cif"  "results_surv" "grid"        

# Dimensions of the lower confidence bound matrix for cause 1
dim(boot_cif$results_cif[["cause1"]]$lower)
#> [1] 69 51

# Pointwise standard errors for cause 2 (first few rows and columns)
boot_cif$results_cif[["cause2"]]$se[1:5, 1:5]
#>             [,1]        [,2]        [,3]        [,4]        [,5]
#> [1,] 0.002609207 0.005180806 0.007717291 0.010221142 0.012694819
#> [2,] 0.002444048 0.004861595 0.007254613 0.009625085 0.011975006
#> [3,] 0.002287397 0.004557973 0.006813294 0.009054959 0.011284593
#> [4,] 0.002138211 0.004267947 0.006390467 0.008507070 0.010619098
#> [5,] 0.001995467 0.003989552 0.005983281 0.007977729 0.009974023