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#' @return a function that can be used to calculate metrics (with parameters `y_true`, `risk`, `surv`, and `times`)
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#'
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#' @section References:
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#' - \[1\] Graf, Erika, et al. ["Assessment and comparison of prognostic classification schemes for survival data."](https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0258%2819990915/30%2918%3A17/18%3C2529%3A%3AAID-SIM274%3E3.0.CO%3B2-5) Statistics in Medicine 18.17‐18 (1999): 2529-2545.
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#' - \[1\] Graf, Erika, et al. "Assessment and comparison of prognostic classification schemes for survival data." Statistics in Medicine 18.17‐18 (1999): 2529-2545.
#' @return numeric from 0 to 1, lower scores are better (Brier score of 0.25 represents a model which returns always returns 0.5 as the predicted survival function)
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#'
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#' @section References:
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#' - \[1\] Brier, Glenn W. ["Verification of forecasts expressed in terms of probability."](https://journals.ametsoc.org/view/journals/mwre/78/1/1520-0493_1950_078_0001_vofeit_2_0_co_2.xml) Monthly Weather Review 78.1 (1950): 1-3.
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#' - \[2\] Graf, Erika, et al. ["Assessment and comparison of prognostic classification schemes for survival data."](https://onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0258(19990915/30)18:17/18%3C2529::AID-SIM274%3E3.0.CO;2-5) Statistics in Medicine 18.17‐18 (1999): 2529-2545.
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#' - \[1\] Brier, Glenn W. "Verification of forecasts expressed in terms of probability." Monthly Weather Review 78.1 (1950): 1-3.
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#' - \[2\] Graf, Erika, et al. "Assessment and comparison of prognostic classification schemes for survival data." Statistics in Medicine 18.17‐18 (1999): 2529-2545.
#' @return a numeric vector of length equal to the length of the times vector, each value (from the range from 0 to 1) represents the AUC metric at a specific time point, with higher values indicating better performance.
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#'
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#' @section References:
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#' - \[1\] Uno, Hajime, et al. ["Evaluating prediction rules for t-year survivors with censored regression models."](https://www.jstor.org/stable/27639883) Journal of the American Statistical Association 102.478 (2007): 527-537.
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#' - \[2\] Hung, Hung, and Chin‐Tsang Chiang. ["Optimal composite markers for time dependent receiver operating characteristic curves with censored survival data."](https://www.jstor.org/stable/41000414) Scandinavian Journal of Statistics 37.4 (2010): 664-679.
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#' - \[1\] Uno, Hajime, et al. "Evaluating prediction rules for t-year survivors with censored regression models." Journal of the American Statistical Association 102.478 (2007): 527-537.
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#' - \[2\] Hung, Hung, and Chin‐Tsang Chiang. "Optimal composite markers for time dependent receiver operating characteristic curves with censored survival data." Scandinavian Journal of Statistics 37.4 (2010): 664-679.
#' @return a numeric vector of length equal to the length of the times vector, each value (from the range from 0 to 1) represents 1 - AUC metric at a specific time point, with lower values indicating better performance.
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#'
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#' #' @section References:
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#' - \[1\] Uno, Hajime, et al. ["Evaluating prediction rules for t-year survivors with censored regression models."](https://www.jstor.org/stable/27639883) Journal of the American Statistical Association 102.478 (2007): 527-537.
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#' - \[2\] Hung, Hung, and Chin‐Tsang Chiang. ["Optimal composite markers for time‐dependent receiver operating characteristic curves with censored survival data."](https://www.jstor.org/stable/41000414) Scandinavian Journal of Statistics 37.4 (2010): 664-679.
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#' - \[1\] Uno, Hajime, et al. "Evaluating prediction rules for t-year survivors with censored regression models." Journal of the American Statistical Association 102.478 (2007): 527-537.
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#' - \[2\] Hung, Hung, and Chin‐Tsang Chiang. "Optimal composite markers for time‐dependent receiver operating characteristic curves with censored survival data." Scandinavian Journal of Statistics 37.4 (2010): 664-679.
#' @return numeric from 0 to 1, higher values indicate better performance
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#'
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#' #' @section References:
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#' - \[1\] Uno, Hajime, et al. ["Evaluating prediction rules for t-year survivors with censored regression models."](https://www.jstor.org/stable/27639883) Journal of the American Statistical Association 102.478 (2007): 527-537.
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#' - \[2\] Hung, Hung, and Chin‐Tsang Chiang. ["Optimal composite markers for time‐dependent receiver operating characteristic curves with censored survival data."](https://www.jstor.org/stable/41000414) Scandinavian Journal of Statistics 37.4 (2010): 664-679.
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#' - \[1\] Uno, Hajime, et al. "Evaluating prediction rules for t-year survivors with censored regression models." Journal of the American Statistical Association 102.478 (2007): 527-537.
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#' - \[2\] Hung, Hung, and Chin‐Tsang Chiang. "Optimal composite markers for time‐dependent receiver operating characteristic curves with censored survival data." Scandinavian Journal of Statistics 37.4 (2010): 664-679.
#' @return numeric from 0 to 1, lower values indicate better performance
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#'
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#' #' @section References:
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#' - \[1\] Uno, Hajime, et al. ["Evaluating prediction rules for t-year survivors with censored regression models."](https://www.jstor.org/stable/27639883) Journal of the American Statistical Association 102.478 (2007): 527-537.
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#' - \[2\] Hung, Hung, and Chin‐Tsang Chiang. ["Optimal composite markers for time‐dependent receiver operating characteristic curves with censored survival data."](https://www.jstor.org/stable/41000414) Scandinavian Journal of Statistics 37.4 (2010): 664-679.
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#' - \[1\] Uno, Hajime, et al. "Evaluating prediction rules for t-year survivors with censored regression models." Journal of the American Statistical Association 102.478 (2007): 527-537.
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#' - \[2\] Hung, Hung, and Chin‐Tsang Chiang. "Optimal composite markers for time‐dependent receiver operating characteristic curves with censored survival data." Scandinavian Journal of Statistics 37.4 (2010): 664-679.
#' @return numeric from 0 to 1, lower values indicate better performance
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#' @section References:
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#' - \[1\] Brier, Glenn W. ["Verification of forecasts expressed in terms of probability."](https://journals.ametsoc.org/view/journals/mwre/78/1/1520-0493_1950_078_0001_vofeit_2_0_co_2.xml) Monthly Weather Review 78.1 (1950): 1-3.
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#' - \[2\] Graf, Erika, et al. ["Assessment and comparison of prognostic classification schemes for survival data."](https://onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0258(19990915/30)18:17/18%3C2529::AID-SIM274%3E3.0.CO;2-5) Statistics in Medicine 18.17‐18 (1999): 2529-2545.
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#' - \[1\] Brier, Glenn W. "Verification of forecasts expressed in terms of probability." Monthly Weather Review 78.1 (1950): 1-3.
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#' - \[2\] Graf, Erika, et al. "Assessment and comparison of prognostic classification schemes for survival data." Statistics in Medicine 18.17‐18 (1999): 2529-2545.
Copy file name to clipboardExpand all lines: R/model_performance.R
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#' @param times a numeric vector of times. If `type == "metrics"` then the survival function is evaluated at these times, if `type == "roc"` then the ROC curves are calculated at these times.
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#'
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#' @return An object of class `"model_performance_survival"`. It's a list of metric values calculated for the model. It contains:
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#' - Harrell's concordance index \[[1](https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.4780030207)\]
#' - C/D AUC using the estimator proposed by Uno et. al \[[4](https://www.jstor.org/stable/27639883#metadata_info_tab_contents)\]
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#' - Harrell's concordance index \[1\]
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#' - Brier score \[2, 3\]
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#' - C/D AUC using the estimator proposed by Uno et. al \[4\]
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#' - integral of the Brier score
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#' - integral of the C/D AUC
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#'
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#' @section References:
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#' - \[1\] Harrell, F.E., Jr., et al. ["Regression modelling strategies for improved prognostic prediction."](https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.4780030207) Statistics in Medicine 3.2 (1984): 143-152.
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#' - \[2\] Brier, Glenn W. ["Verification of forecasts expressed in terms of probability."](https://journals.ametsoc.org/view/journals/mwre/78/1/1520-0493_1950_078_0001_vofeit_2_0_co_2.xml) Monthly Weather Review 78.1 (1950): 1-3.
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#' - \[3\] Graf, Erika, et al. ["Assessment and comparison of prognostic classification schemes for survival data."](https://onlinelibrary.wiley.com/doi/abs/10.1002/%28SICI%291097-0258%2819990915/30%2918%3A17/18%3C2529%3A%3AAID-SIM274%3E3.0.CO%3B2-5) Statistics in Medicine 18.17‐18 (1999): 2529-2545.
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#' - \[4\] Uno, Hajime, et al. ["Evaluating prediction rules for t-year survivors with censored regression models."](https://www.jstor.org/stable/27639883#metadata_info_tab_contents) Journal of the American Statistical Association 102.478 (2007): 527-537.
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#' - \[1\] Harrell, F.E., Jr., et al. "Regression modelling strategies for improved prognostic prediction." Statistics in Medicine 3.2 (1984): 143-152.
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#' - \[2\] Brier, Glenn W. "Verification of forecasts expressed in terms of probability." Monthly Weather Review 78.1 (1950): 1-3.
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#' - \[3\] Graf, Erika, et al. "Assessment and comparison of prognostic classification schemes for survival data." Statistics in Medicine 18.17‐18 (1999): 2529-2545.
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#' - \[4\] Uno, Hajime, et al. "Evaluating prediction rules for t-year survivors with censored regression models." Journal of the American Statistical Association 102.478 (2007): 527-537.
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