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
)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
1should represent "alive" (survived), while0should 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 withgroup_varsif the grouping variable is of a different class thanrmm()'s outputs, such asfactororcharactergrouping variables.- seed
Optional numeric value to set a random seed for reproducibility. If
NULL(default), no seed is set.
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 indata.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:statandvalue, 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.
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
# 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
)
#> # A tibble: 1 × 8
#> population_RMM_LL population_RMM population_RMM_UL population_CI
#> <dbl> <dbl> <dbl> <dbl>
#> 1 -0.0818 -0.0174 0.0469 0.0643
#> # ℹ 4 more variables: bootstrap_RMM_LL <dbl>, bootstrap_RMM <dbl>,
#> # bootstrap_RMM_UL <dbl>, bootstrap_CI <dbl>
# pivot!
rmm(data = data, Ps_col = Ps,
outcome_col = survival,
Divisor1 = 4,
Divisor2 = 4,
n_samples = 10,
pivot = TRUE
)
#> # A tibble: 8 × 2
#> stat value
#> <chr> <dbl>
#> 1 population_RMM_LL -0.0818
#> 2 population_RMM -0.0174
#> 3 population_RMM_UL 0.0469
#> 4 population_CI 0.0643
#> 5 bootstrap_RMM_LL -0.0226
#> 6 bootstrap_RMM -0.0133
#> 7 bootstrap_RMM_UL -0.00399
#> 8 bootstrap_CI 0.00930
# 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
)
#> # A tibble: 2 × 9
#> hospital population_RMM_LL population_RMM population_RMM_UL population_CI
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 Hospital A -0.0896 0.00106 0.0917 0.0906
#> 2 Hospital B -0.127 -0.0353 0.0561 0.0914
#> # ℹ 4 more variables: bootstrap_RMM_LL <dbl>, bootstrap_RMM <dbl>,
#> # bootstrap_RMM_UL <dbl>, bootstrap_CI <dbl>
# 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
)
#> # A tibble: 16 × 3
#> hospital stat value
#> <chr> <chr> <dbl>
#> 1 Hospital A population_RMM_LL -0.0896
#> 2 Hospital A population_RMM 0.00106
#> 3 Hospital A population_RMM_UL 0.0917
#> 4 Hospital A population_CI 0.0906
#> 5 Hospital A bootstrap_RMM_LL -0.00505
#> 6 Hospital A bootstrap_RMM 0.00933
#> 7 Hospital A bootstrap_RMM_UL 0.0237
#> 8 Hospital A bootstrap_CI 0.0144
#> 9 Hospital B population_RMM_LL -0.127
#> 10 Hospital B population_RMM -0.0353
#> 11 Hospital B population_RMM_UL 0.0561
#> 12 Hospital B population_CI 0.0914
#> 13 Hospital B bootstrap_RMM_LL -0.0473
#> 14 Hospital B bootstrap_RMM -0.0311
#> 15 Hospital B bootstrap_RMM_UL -0.0149
#> 16 Hospital B bootstrap_CI 0.0162