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Cancer survival analysis focuses on quantifying and interpreting the time from a key starting point, such as diagnosis or the initiation of treatment, to a specific endpoint, such as remission or death. This analysis provides critical insights into treatment effectiveness and factors that influence patient outcomes, helping to shape clinical decisions and guide prognostic evaluations. A cornerstone of oncology research, survival analysis tackles the challenges of skewed, non-normally...
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Comparing the Survival Analysis of Two or More Groups01:20

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Survival analysis is a cornerstone of medical research, used to evaluate the time until an event of interest occurs, such as death, disease recurrence, or recovery. Unlike standard statistical methods, survival analysis is particularly adept at handling censored data—instances where the event has not occurred for some participants by the end of the study or remains unobserved. To address these unique challenges, specialized techniques like the Kaplan-Meier estimator, log-rank test, and...
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Kaplan-Meier Approach

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The Kaplan-Meier estimator is a non-parametric method used to estimate the survival function from time-to-event data. In medical research, it is frequently employed to measure the proportion of patients surviving for a certain period after treatment. This estimator is fundamental in analyzing time-to-event data, making it indispensable in clinical trials, epidemiological studies, and reliability engineering. By estimating survival probabilities, researchers can evaluate treatment effectiveness,...
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Introduction To Survival Analysis01:18

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Survival analysis is a statistical method used to study time-to-event data, where the "event" might represent outcomes like death, disease relapse, system failure, or recovery. A unique feature of survival data is censoring, which occurs when the event of interest has not been observed for some individuals during the study period. This requires specialized techniques to handle incomplete data effectively.
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Survival Tree01:19

Survival Tree

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Survival trees are a non-parametric method used in survival analysis to model the relationship between a set of covariates and the time until an event of interest occurs, often referred to as the "time-to-event" or "survival time." This method is particularly useful when dealing with censored data, where the event has not occurred for some individuals by the end of the study period, or when the exact time of the event is unknown.
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Actuarial Approach01:20

Actuarial Approach

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The actuarial approach, a statistical method originally developed for life insurance risk assessment, is widely used to calculate survival rates in clinical and population studies. This method accounts for participants lost to follow-up or those who die from causes unrelated to the study, ensuring a more accurate representation of survival probabilities.
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Survival Analysis of Breast Cancer Patients in Texas Using Classical and Machine Learning Methods.

Sidketa I Fofana1, Tamer Oraby1, Salique H Shaham2,3

  • 1School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, Edinburg, USA.

Cureus
|December 8, 2025
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Breast cancer survival is significantly influenced by diagnosis stage, with distant-stage cancers showing a much higher risk. Early detection and support for vulnerable populations are crucial for improving patient outcomes.

Keywords:
breast cancercox proportional hazards regressionkaplan‒meier curveslog-rank testmahalanobis matching distanceracial equityrandom survival forest

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Area of Science:

  • Oncology
  • Epidemiology
  • Biostatistics

Background:

  • Breast cancer is a leading global cancer affecting women.
  • Understanding survival determinants is critical for patient care and public health strategies.

Purpose of the Study:

  • To identify key factors influencing long-term survival in breast cancer patients.
  • To analyze an 11-year cohort of malignant breast cancer survival data in Texas.

Main Methods:

  • Kaplan-Meier curves and log-rank tests for survival analysis.
  • Cox proportional hazards regression and Random Survival Forest for factor identification and prediction.
  • Mahalanobis matching distance for estimating average extended lifetime.

Main Results:

  • Stage, laterality, age, grade, subtypes, hormone receptor status, primary site, race, income, and treatment modalities significantly impact survival.
  • Cancer stage is the most critical predictor; distant-stage cancer has a hazard ratio of 15.869 compared to localized stage.
  • Localized-stage patients had ~67.34 months average survival, versus distant-stage patients.

Conclusions:

  • Stage at diagnosis is the most critical factor for breast cancer survival.
  • Policy recommendations include promoting early diagnosis, screening, and support for elderly and disadvantaged patients.