some rephrasing

doc/index.rst

@@ -17,24 +17,22 @@ Gradient-boosting Survival Analysis and Competing Risks
 
    * scalable gradient boosting
 
-**hazardous** is a Python library for **survival analysis - i.e. time-to-event prediction - 
-and competing risks** predictions. The model proposed in this library is
-a **scalable** gradient-boosting called **SurvivalBoost**.
-
-With a **scikit-learn compatible API**, we also provide different useful
-metrics for the evaluation of the model such as the **Integrated Brier Score**
-or the **C-index** adapted for competing risks setting.
-
+**hazardous** is a Python library for **survival analysis** -i.e. time-to-event prediction- 
+and **competing risks** modeling. It introduces **SurvivalBoost**, a **scalable**
+gradient-boosting model designed for this task.
 
+With a scikit-learn-compatible API, the library also offers various metrics
+for model evaluation, including the **Integrated Brier Score** and the **C-index**,
+both adapted for the competing risks setting.
 
 What is the difference between Survival Analysis and the Competing risks setting?
--------------------------------------
-Compared to the Survival Analysis setting, the Competing Risks setting
-considers that the event of interest is not the only event of interest 
-that may happen.
-Predicting which event will happen first, and when, from data where some
-events have not yet been observed:
+---------------------------------------------------------------------------------
+In contrast to the Survival Analysis setting, the Competing Risks setting accounts
+for the possibility that multiple types of events of interest may occur,
+not just a single event.
 
+It focuses on predicting which event will occur first and when, based on data where
+some events have not yet been observed.
 .. image:: competing_risk_diagram.svg
 
 What is SurvivalBoost?
@@ -49,23 +47,23 @@ cumulative incidence function and the survival function at any horizon.
 SurvivalBoost puts a focus on predictive the accuracy -defined as the ability to predict 
 the observed event- rather than on inference. 
 
-More information about the theory behind the model is described in `Survival Models:
+Additional theoretical details about the model can be found in `Survival Models:
 Proper Scoring Rule and Stochastic Optimization with Competing Risks
 <https://arxiv.org/pdf/2410.16765>`_.
 
 .. seealso::
 
-   The library depends on `lifelines <https://lifelines.readthedocs.io/en/latest/>`_ 
-   for the Kaplan-Meier estimator used in SurvivalBoost. We thank the authors of 
-   lifelines for their work and their contribution to the community of survival analysis
-   with the implementation of models -e.g. Kaplan-Meier, Cox model, Aalen-Johansen- and
-   metrics -e.g. C-index, Brier Score-.
-
+   The library relies on `lifelines <https://lifelines.readthedocs.io/en/latest/>`_ 
+   for the Kaplan-Meier estimator used in SurvivalBoost. We extend our gratitude to
+   the authors of lifelines for their significant contributions to the survival
+   analysis community, including the implementation of models such as
+   the Kaplan-Meier, Cox model, and Aalen-Johansen, as well as metrics
+   like the C-index and Brier Score.
 
 .. note::
-   Quantifying the statistical association or causal effect of covariates with/on
-   the cumulated event incidence or instantaneous hazard rate is not in the scope
-   of this library at this time.
+   Quantifying the statistical association or causal effect of covariates on the
+   cumulative event incidence or instantaneous hazard rate is currently beyond
+   the scope of this library.
 
 - License: MIT
 - GitHub repository: https://github.com/soda-inria/hazardous