From f40f28ce7969a607a44ab50e229fff6fda618fef Mon Sep 17 00:00:00 2001 From: corolth1 Date: Mon, 1 Jul 2024 11:42:35 -0400 Subject: [PATCH] edits --- docs/AUTHORS.md | 1 - docs/conf.py | 1 + docs/index.rst | 1 + ...ion_metrics_survival_model.md => survival.md} | 16 ++++++++-------- 4 files changed, 10 insertions(+), 9 deletions(-) rename docs/notebooks/{evaluation_metrics_survival_model.md => survival.md} (96%) diff --git a/docs/AUTHORS.md b/docs/AUTHORS.md index 98b27bb..51327c4 100644 --- a/docs/AUTHORS.md +++ b/docs/AUTHORS.md @@ -8,4 +8,3 @@ Contributors * David Ohlssen `(contributor)` * Berkman Sahiner `(contributor)` * Nicholas Petrick `(contributor)` - diff --git a/docs/conf.py b/docs/conf.py index 350f69c..cc398f9 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -30,6 +30,7 @@ "sphinxcontrib.bibtex", ] + # templates_path = ['_templates'] exclude_patterns = ["_build", "Thumbs.db", ".DS_Store"] diff --git a/docs/index.rst b/docs/index.rst index 20c62a9..155613b 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -16,6 +16,7 @@ Welcome to TorchSurv's documentation! :maxdepth: 2 :caption: Tutorials: + notebooks/survival notebooks/introduction notebooks/momentum diff --git a/docs/notebooks/evaluation_metrics_survival_model.md b/docs/notebooks/survival.md similarity index 96% rename from docs/notebooks/evaluation_metrics_survival_model.md rename to docs/notebooks/survival.md index 09cf67e..9c63833 100644 --- a/docs/notebooks/evaluation_metrics_survival_model.md +++ b/docs/notebooks/survival.md @@ -1,7 +1,8 @@ -# Predictive accuracy evaluation metrics for survival model -Author: Mélodie Monod
-Date: 28th June 2024 +# A statistical introduction + + +* **Author**: Mélodie Monod ## Introduction @@ -11,9 +12,9 @@ The evaluation metrics for assessing the predictive performance of a model depen To understand the evaluation metrics for time-to-event data, it is helpful to start with a review of the evaluation metrics used for binary outcomes, as the former are extensions of the latter. -Assume we have a binary response $Y_i \in \{0,1\}$, for any individual $i$. The model is a probabilistic classifier that outputs a score $\pi_i \in [0,1]$, which is an estimate of the probability $p(Y_i = 1)$. +Assume we have a binary response $Y_i \in \{0,1\}$, for any individual $i$. The model is a probabilistic classifier that outputs a score $\pi_i \in [0,1]$, which is an estimate of the probability $p(Y_i = 1)$. -The predicted response for individual $i$, denoted $\hat{Y}_i$, is obtained by comparing the score to a threshold $c$, +The predicted response for individual $i$, denoted $\hat{Y}_i$, is obtained by comparing the score to a threshold $c$, $$ \hat{Y}_i = @@ -38,7 +39,7 @@ $$ \text{AUC} = \int_0^1 TPR(FPR(c)) dFPR(c). $$ -It can be shown that the AUC is equal to $p(\pi_i > \pi_j|Y_i = 1, Y_j = 0)$. This is the probability that, for a comparable pair, the individual without the event has a lower score than the individual with the event. This probability is also referred to as the C-index (denoted by C). In the binary context, the AUC is equal to the C-index. +It can be shown that the AUC is equal to $p(\pi_i > \pi_j|Y_i = 1, Y_j = 0)$. This is the probability that, for a comparable pair, the individual without the event has a lower score than the individual with the event. This probability is also referred to as the C-index (denoted by C). In the binary context, the AUC is equal to the C-index.
Proof of the AUC's probabilistic interpretation @@ -253,8 +254,7 @@ The Brier score assesses both calibration and discrimination and serves as an al A meta-analysis by Zhou et al. (2022) recorded the proportion of evaluation metrics for survival models used from 2010 to 2021 in prominent journals such as "Annals of Statistics," "Biometrika," "Journal of the American Statistical Association," "Journal of the Royal Statistical Society, Series B," "Statistics in Medicine," "Artificial Intelligence in Medicine," and "Lifetime Data Analysis." This analysis indicates that the use of the C-index has been steadily increasing and has recently become a dominant predictive measure. In 2021, the C-index was used in more than 75% of the readings. - - + ## Reference * Heagerty, P. J., & Zheng, Y. (2005). Survival Model Predictive Accuracy and ROC Curves. In Biometrics (Vol. 61, Issue 1, pp. 92–105). Oxford University Press (OUP). https://doi.org/10.1111/j.0006-341x.2005.030814.x * Lambert, J., & Chevret, S. (2016). Summary measure of discrimination in survival models based on cumulative/dynamic time-dependent ROC curves. In Statistical Methods in Medical Research (Vol. 25, Issue 5, pp. 2088–2102). SAGE Publications