This function generates nonlinear bins for probability of survival data based on specified thresholds and divisors as specified in Napoli et al. (2017), Schroeder et al. (2019), and Kassar et al. (2016). This function calculates bin statistics, including mean, standard deviation, total alive, total dead, count, and percentage for each bin.
Usage
nonlinear_bins(
data,
Ps_col,
outcome_col,
group_vars = NULL,
divisor1 = 5,
divisor2 = 5,
threshold_1 = 0.9,
threshold_2 = 0.99
)Arguments
- data
A
data.frameortibblecontaining the probability of survival data for a set of patients.- Ps_col
The name of the column containing the survival probabilities (Ps). Should be numeric on a scale from 0 to 1.
- outcome_col
The name of the column containing the outcome data. It should be binary, with values indicating patient survival. A value of
1should represent "alive" (survived), while0should represent "dead" (did not survive).TRUE/FALSEare accepted as well. Ensure the column contains only these possible values.- group_vars
Optional grouping variables for bin statistics calculations. These should be specified as quoted column names.
- divisor1
A parameter to control the width of the probability of survival range bins. Affects the creation of step sizes for the beginning of each bin range. Defaults to
5.- divisor2
A parameter to control the width of the probability of survival range bins. Affects the creation of step sizes for the beginning of each bin range. Defaults to
5.- threshold_1
A parameter to decide where data indices will begin to create step sizes. Defaults to
0.9.- threshold_2
A parameter to decide where data indices will end to create step sizes. Defaults to
0.99.
Value
A list with two elements:
intervals: A vector defining bin boundaries for probability of survival.bin_stats: Atibblecontaining:bin_number: Bin index.bin_start,bin_end: Bin range.mean,sd: Mean and standard deviation ofPs_colwithin the bin.Pred_Survivors_b,Pred_Deaths_b: Predicted counts of survivors and decedents, respectively.AntiS_b,AntiM_b: Anticipated proportion survived, and deceased, respectively.alive,dead: Count of observed survivors and non-survivors.count: Total records in the bin.percent: Percentage of total records within each bin.
Details
Like other statistical computing functions, nonlinear_bins() is happiest
without missing data. It is best to pass complete probability of survival
and outcome data to the function for optimal performance. With smaller
datasets, this is especially helpful. However, nonlinear_bins() will throw
a warning about missing values, if any exist in Ps_col and/or
outcome_col.
nonlinear_bins() assumes Ps_col contains probabilities derived from
real-world inputs for the Trauma Injury Severity Score (TRISS) model.
Synthetic or low-variability data (especially with small sample sizes) may
not reflect the distribution of TRISS-derived survival probabilities. This
can result in unstable estimates or function failure due to insufficient
dispersion. With small sample sizes, it may be important to use smaller
values with the divisor arguments and adjust the thresholds (based on the
distribution of the Ps_col values) to create bins that better accommodate
the data.
By default, nonlinear_bins() derives bin cut points from the full dataset’s
distribution. This ensures comparability across groups when group_vars is
used. To tailor binning to a specific group (e.g., a single hospital), filter
the dataset to that subgroup before calling nonlinear_bins(). The function
will then compute bins and related statistics using only that subset’s
Ps_col distribution. When group_vars is used, and ff a group lacks
observations within one or more bins, rm_bin_summary() will compute
statistics only for the bins that contain data. Bins with no observations are
excluded from the summary for that group.
Note
This function will produce the most reliable and interpretable results when using a dataset that has one row per patient, with each column being a feature.
The mean and AntiS_b are approximately equivalent in this context. They
are kept in the output for clarity.
References
Kassar, O.M., Eklund, E.A., Barnhardt, W.F., Napoli, N.J., Barnes, L.E., Young, J.S. (2016). Trauma survival margin analysis: A dissection of trauma center performance through initial lactate. The American Surgeon, 82(7), 649-653. doi:10.1177/000313481608200733
Napoli, N. J., Barnhardt, W., Kotoriy, M. E., Young, J. S., & Barnes, L. E. (2017). Relative mortality analysis: A new tool to evaluate clinical performance in trauma centers. IISE Transactions on Healthcare Systems Engineering, 7(3), 181–191. doi:10.1080/24725579.2017.1325948
Schroeder, P. H., Napoli, N. J., Barnhardt, W. F., Barnes, L. E., & Young, J. S. (2018). Relative mortality analysis of the “golden hour”: A comprehensive acuity stratification approach to address disagreement in current literature. Prehospital Emergency Care, 23(2), 254–262. doi:10.1080/10903127.2018.1489021
Examples
# Generate example data
set.seed(123)
# Parameters
# Total number of patients
n_patients <- 5000
# Arbitrary group labels
groups <- sample(x = LETTERS[1:2], size = n_patients, replace = TRUE)
# Trauma types
trauma_type_values <- sample(
x = c("Blunt", "Penetrating"),
size = n_patients,
replace = TRUE
)
# RTS values
rts_values <- sample(
x = seq(from = 0, to = 7.8408, by = 0.005),
size = n_patients,
replace = TRUE
)
# patient ages
ages <- sample(
x = seq(from = 0, to = 100, by = 1),
size = n_patients,
replace = TRUE
)
# ISS scores
iss_scores <- sample(
x = seq(from = 0, to = 75, by = 1),
size = n_patients,
replace = TRUE
)
# Generate survival probabilities (Ps)
Ps <- traumar::probability_of_survival(
trauma_type = trauma_type_values,
age = ages,
rts = rts_values,
iss = iss_scores
)
# Simulate survival outcomes based on Ps
survival_outcomes <- rbinom(n_patients, size = 1, prob = Ps)
# Create data frame
data <- data.frame(Ps = Ps, survival = survival_outcomes, groups = groups) |>
dplyr::mutate(death = dplyr::if_else(survival == 1, 0, 1))
# Apply the nonlinear_bins function
results <- nonlinear_bins(
data = data,
Ps_col = Ps,
outcome_col = survival,
divisor1 = 4,
divisor2 = 4,
threshold_1 = 0.9,
threshold_2 = 0.99
)
# View results
results$intervals
#> [1] 0.0002015449 0.0256191282 0.1455317587 0.4842820556 0.9003870455
#> [6] 0.9285354475 0.9518925450 0.9722272703 0.9968989233
results$bin_stats
#> # A tibble: 8 × 13
#> bin_number bin_start bin_end mean sd Pred_Survivors_b Pred_Deaths_b
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 0.000202 0.0256 0.00935 0.00722 10.4 1106.
#> 2 2 0.0256 0.146 0.0732 0.0345 81.7 1033.
#> 3 3 0.146 0.484 0.293 0.0959 327. 788.
#> 4 4 0.484 0.900 0.697 0.124 777. 337.
#> 5 5 0.900 0.929 0.916 0.00790 114. 10.5
#> 6 6 0.929 0.952 0.940 0.00680 117. 7.50
#> 7 7 0.952 0.972 0.963 0.00564 120. 4.65
#> 8 8 0.972 0.997 0.984 0.00686 162. 2.67
#> # ℹ 6 more variables: AntiS_b <dbl>, AntiM_b <dbl>, alive <int>, dead <int>,
#> # count <int>, percent <dbl>
# Example with grouping by a categorical variable
# Run the function using a single grouping variable
results_grouped <- nonlinear_bins(
data,
Ps_col = Ps,
outcome_col = survival,
group_vars = "groups"
)
# View grouped results
results_grouped$bin_stats
#> # A tibble: 20 × 14
#> groups bin_number bin_start bin_end mean sd Pred_Survivors_b
#> <chr> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 A 1 0.000202 0.0165 0.00636 0.00465 2.94
#> 2 A 2 0.0165 0.0794 0.0418 0.0183 19.1
#> 3 A 3 0.0794 0.252 0.155 0.0516 68.5
#> 4 A 4 0.252 0.570 0.393 0.0953 172.
#> 5 A 5 0.570 0.900 0.734 0.0976 320.
#> 6 A 6 0.900 0.923 0.912 0.00660 39.2
#> 7 A 7 0.923 0.941 0.933 0.00541 47.6
#> 8 A 8 0.941 0.962 0.952 0.00587 44.7
#> 9 A 9 0.962 0.976 0.968 0.00426 54.2
#> 10 A 10 0.976 0.997 0.986 0.00610 64.1
#> 11 B 1 0.000202 0.0165 0.00657 0.00466 2.83
#> 12 B 2 0.0165 0.0794 0.0417 0.0180 18.1
#> 13 B 3 0.0794 0.252 0.153 0.0496 68.7
#> 14 B 4 0.252 0.570 0.405 0.0920 184.
#> 15 B 5 0.570 0.900 0.746 0.100 340.
#> 16 B 6 0.900 0.923 0.914 0.00659 52.1
#> 17 B 7 0.923 0.941 0.933 0.00510 45.7
#> 18 B 8 0.941 0.962 0.952 0.00553 50.5
#> 19 B 9 0.962 0.976 0.969 0.00371 42.6
#> 20 B 10 0.976 0.997 0.985 0.00550 73.9
#> # ℹ 7 more variables: Pred_Deaths_b <dbl>, AntiS_b <dbl>, AntiM_b <dbl>,
#> # alive <int>, dead <int>, count <int>, percent <dbl>