rmm: Relative Mortality Metric (RMM) Calculation

Description

Calculates the Relative Mortality Metric (RMM) from Napoli et al. (2017) based on patient survival probabilities (Ps) and actual outcomes. The function groups patients into bins based on their survival probability scores (Ps) and computes a weighted mortality metric along with confidence intervals. For more information on the methods used in this function, see as well Schroeder et al. (2019), and Kassar et al. (2016).

The Relative Mortality Metric (RMM) quantifies the performance of a center in comparison to the anticipated mortality based on the TRISS national benchmark. The RMM measures the difference between observed and expected mortality, with a range from -1 to 1.

An RMM of 0 indicates that the observed mortality aligns with the expected national benchmark across all acuity levels.
An RMM greater than 0 indicates better-than-expected performance, where the center is outperforming the national benchmark.
An RMM less than 0 indicates under-performance, where the center’s observed mortality is higher than the expected benchmark.

This metric helps assess how a center's mortality compares to the national standards, guiding quality improvement efforts. rmm() utilizes bootstrap sampling to calculate the confidence intervals via the standard error method.

Usage

rmm(
  data,
  Ps_col,
  outcome_col,
  group_vars = NULL,
  n_samples = 100,
  Divisor1 = 5,
  Divisor2 = 5,
  Threshold_1 = 0.9,
  Threshold_2 = 0.99,
  pivot = FALSE,
  seed = NULL
)

Value

A tibble containing the Relative Mortality Metric (RMM) and related statistics:

population_RMM_LL: The lower bound of the 95% confidence interval for the population RMM.
population_RMM: The final calculated Relative Mortality Metric for the population existing in data.
population_RMM_UL: The upper bound of the 95% confidence interval for the population RMM.
population_CI: The confidence interval width for the population RMM.
bootstrap_RMM_LL: The lower bound of the 95% confidence interval for the bootstrap RMM.
bootstrap_RMM: The average RMM value calculated for the bootstrap sample.
bootstrap_RMM_UL: The upper bound of the 95% confidence interval for the bootstrap RMM.
bootstrap_CI: The width of the 95% confidence interval for the bootstrap RMM.
If pivot = TRUE, the results will be in long format with two columns: stat and value, where each row corresponds to one of the calculated statistics.
If pivot = FALSE (default), the results will be returned in wide format, with each statistic as a separate column.

Arguments

data: A data frame or tibble containing the data.
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 1 should represent "alive" (survived), while 0 should represent "dead" (did not survive). Ensure the column contains only these two possible values.
group_vars: Optional character vector specifying grouping variables for stratified analysis. If NULL, the calculation is performed on the entire dataset.
n_samples: A numeric value indicating the number of bootstrap samples to take from the data source.
Divisor1: A divisor used for binning the survival probabilities (default is 5).
Divisor2: A second divisor used for binning the survival probabilities (default is 5).
Threshold_1: The first threshold for dividing the survival probabilities (default is 0.9).
Threshold_2: The second threshold for dividing the survival probabilities (default is 0.99).
pivot: A logical indicating whether to return the results in a long format (pivot = TRUE) or wide format (pivot = FALSE, default). Use with caution in tandem with group_vars if the grouping variable is of a different class than rmm()'s outputs, such as factor or character grouping variables.
seed: Optional numeric value to set a random seed for reproducibility. If NULL (default), no seed is set.

Author

Nicolas Foss, Ed.D, MS, original implementation in MATLAB by Nicholas J. Napoli, Ph.D., MS

Details

Like other statistical computing functions, rmm() 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, rmm() will handle NA values and throw a warning about missing probability of survival values, if any exist in Ps_col.

Due to the use of bootstrap sampling within the function, users should consider setting the random number seed within rmm() for reproducibility.

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

Run this code

# Generate example data with high negative skewness
set.seed(10232015)

# 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))

# Example usage of the `rmm` function
rmm(data = data, Ps_col = Ps,
    outcome_col = survival,
    Divisor1 = 4,
    Divisor2 = 4,
    n_samples = 10
    )

# pivot!
rmm(data = data, Ps_col = Ps,
    outcome_col = survival,
    Divisor1 = 4,
    Divisor2 = 4,
    n_samples = 10,
    pivot = TRUE
    )

# Create example grouping variable (e.g., hospital)
hospital <- sample(c("Hospital A", "Hospital B"), n_patients, replace = TRUE)

# Create data frame
data <- data.frame(
  Ps = Ps,
  survival = survival_outcomes,
  hospital = hospital
) |>
  dplyr::mutate(death = dplyr::if_else(survival == 1, 0, 1))

# Example usage of the `rmm` function with grouping by hospital
rmm(
  data = data,
  Ps_col = Ps,
  outcome_col = survival,
  group_vars = "hospital",
  Divisor1 = 4,
  Divisor2 = 4,
  n_samples = 10
)

# Pivoted output for easier visualization
rmm(
  data = data,
  Ps_col = Ps,
  outcome_col = survival,
  group_vars = "hospital",
  Divisor1 = 4,
  Divisor2 = 4,
  n_samples = 10,
  pivot = TRUE
)

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