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). Ensure the column contains only these two 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 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
handle NA values and throw a warning about missing probability of survival
values, if any exist in Ps_col.
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
See also
rmm(), and rm_bin_summary()
Examples
# Generate example data with high negative skewness
set.seed(123)
# Parameters
n_patients <- 10000 # Total number of patients
# Skewed towards higher values
Ps <- plogis(rnorm(n_patients, mean = 2, sd = 1.5))
# 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) |>
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 = 5,
divisor2 = 5,
threshold_1 = 0.9,
threshold_2 = 0.99)
# View results
results$intervals
#> [1] 0.02257717 0.54234698 0.70154257 0.79581165 0.85714527 0.90005763
#> [7] 0.92518915 0.94603830 0.96266743 0.97623957 0.99957866
results$bin_stats
#> # A tibble: 10 × 13
#> bin_number bin_start bin_end mean sd Pred_Survivors_b Pred_Deaths_b
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 0.0226 0.542 0.378 0.122 420. 692.
#> 2 2 0.542 0.702 0.628 0.0458 698. 413.
#> 3 3 0.702 0.796 0.753 0.0270 836. 275.
#> 4 4 0.796 0.857 0.829 0.0173 921. 190.
#> 5 5 0.857 0.900 0.879 0.0126 976. 134.
#> 6 6 0.900 0.925 0.913 0.00723 735. 70.0
#> 7 7 0.925 0.946 0.936 0.00596 753. 51.8
#> 8 8 0.946 0.963 0.954 0.00473 768. 36.7
#> 9 9 0.963 0.976 0.970 0.00405 781. 24.4
#> 10 10 0.976 1.00 0.987 0.00621 1209. 16.2
#> # 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
# Add random group variable
data$group <- sample(c("A", "B"), size = n_patients, replace = TRUE)
# Run the function using a single grouping variable
results_grouped <- nonlinear_bins(data,
Ps_col = Ps,
outcome_col = survival,
group_vars = "group"
)
# View grouped results
results_grouped$bin_stats
#> # A tibble: 20 × 14
#> group bin_number bin_start bin_end mean sd Pred_Survivors_b
#> <chr> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 A 1 0.0226 0.542 0.385 0.120 213.
#> 2 A 2 0.542 0.702 0.629 0.0459 361.
#> 3 A 3 0.702 0.796 0.753 0.0266 419.
#> 4 A 4 0.796 0.857 0.829 0.0178 460.
#> 5 A 5 0.857 0.900 0.880 0.0124 499.
#> 6 A 6 0.900 0.925 0.913 0.00724 367.
#> 7 A 7 0.925 0.946 0.936 0.00600 366.
#> 8 A 8 0.946 0.963 0.954 0.00473 392.
#> 9 A 9 0.963 0.976 0.970 0.00413 390.
#> 10 A 10 0.976 1.00 0.987 0.00619 569.
#> 11 B 1 0.0226 0.542 0.370 0.125 207.
#> 12 B 2 0.542 0.702 0.628 0.0458 337.
#> 13 B 3 0.702 0.796 0.752 0.0275 417.
#> 14 B 4 0.796 0.857 0.828 0.0168 461.
#> 15 B 5 0.857 0.900 0.879 0.0129 477.
#> 16 B 6 0.900 0.925 0.913 0.00723 368.
#> 17 B 7 0.925 0.946 0.935 0.00592 387.
#> 18 B 8 0.946 0.963 0.955 0.00472 376.
#> 19 B 9 0.963 0.976 0.970 0.00398 391.
#> 20 B 10 0.976 1.00 0.987 0.00622 640.
#> # ℹ 7 more variables: Pred_Deaths_b <dbl>, AntiS_b <dbl>, AntiM_b <dbl>,
#> # alive <int>, dead <int>, count <int>, percent <dbl>