Name: survival tree in time-to-event analysis
Uploaded: 2025-01-09T15:14:17.000Z
Duration: 1 min 19 s
Channel: JoVE

생존 트리는 공변량 집합과 관심 있는 이벤트가 발생할 때까지의 시간 사이의 관계를 모델링하고 시각화하는 데 사용됩니다. 일반적으로 재귀 분할 프로세스를 사용하여 구축됩니다.
트리의 가지는 변수 값의 분할을 나타냅니다. 노드는 데이터의 하위 집합을 나타내고 터미널 노드는 노드의 개체 수를 나타내며 분석의 최종 예측을 제공할 수 있습니다.
생존 트리를 구성하려면 주로 공변량, 분할 기준, 최소 노드 크기 및 가지치기 임계값이 필요합니다.
공변량 또는 예측 변수는 계량형, 순서형 또는 범주형일 수 있습니다.
분할 기준은 각 노드에서 최상의 분할을 선택하는 방법입니다. 노드 내의 위험을 최소화하거나 노드 간의 분리 정도를 최대화하기 위해 적용됩니다.
최소 노드 크기는 노드를 더 분할하는 데 필요한 최소 관측치 수입니다. 이렇게 하면 트리의 크기를 제어하고 과적합을 방지하는 데 도움이 됩니다.
마지막으로, 가지치기 임계값은 나무 가지치기를 중지할 시기를 결정하는 척도입니다.

생존 트리

Survival Tree

생존 트리는 생존 분석에서 공변량 집합과 관심 이벤트가 발생할 때까지의 시간(종종 "이벤트 발생 시간" 또는 "생존 시간"이라고 함) 간의 관계를 모델링하는 데 사용되는 비모수적 방법입니다. 이 방법은 특히 검열된 자료를 처리할 때 유용합니다. 검열된 자료는 연구 기간이 끝날 때까지 일부 개인에게 이벤트가 발생하지 않았거나 이벤트의 정확한 시간을 알 수 없는 경우에 유용합니다.

생존 트리 구축

생존 트리 구축은 공변량(예측 변수)과 생존 시간, 각 피험자에 대한 검열 지표를 포함하는 자료 집합으로 시작합니다. 이 과정에는 다음 단계가 포함됩니다.

<ol>
	<li>자료 준비: 모든 필수 공변량이 포함되고 적절한 형식이 지정되었는지 확인하여 자료 집합을 준비합니다. 누락된 값은 임퓨테이션과 같은 방법을 사용하거나 별도의 범주로 처리할 수 있습니다.</li>
	<li>트리 구축: 생존 트리는 재귀적 분할 과정을 사용하여 구축됩니다. 각 단계에서 자료 집합은 생존 결과를 가장 잘 구분하는 공변량을 기준으로 두 개의 하위 집합으로 분할됩니다. 이는 일반적으로 그룹 간 생존 분포를 비교하는 로그 순위 검정과 같은 분할 기준을 사용하여 수행됩니다.</li>
	<li>노드 평가: 트리의 각 노드는 자료의 하위 집합을 나타내며, 최종 노드(잎)는 생존 함수의 Kaplan-Meier 추정치를 기준으로 평가됩니다. 이는 해당 노드에 속하는 피험자의 생존 확률을 추정합니다.</li>
	<li>가지치기: 과적합을 방지하기 위해 모델 정확도를 크게 개선하지 않는 노드를 제거하여 트리를 가지칩니다. 이 단계는 트리가 새 자료로 일반화될 수 있도록 보장합니다.</li>
</ol>

장단점

장점:

<ol style="list-style-type: circle;">
	<li>유연성: 생존 트리는 광범위한 자료 유형을 처리할 수 있으며 이상치와 누락된 값에 강합니다.</li>
	<li>해석 가능성: 트리 구조는 해석하기 쉽고, 공변량과 생존 시간 간의 관계를 간단하게 시각화할 수 있습니다.</li>
	<li>비모수적 특성: 생존 시간 분포나 공변량과 생존 간의 관계의 함수 형태에 대한 가정이 필요하지 않습니다.</li>
</ol>

단점:

<ol style="list-style-type: circle;">
	<li>과적합: 적절한 가지치기 없이 생존 트리는 훈련 자료에 과적합되어 일반화가 제대로 이루어지지 않을 수 있습니다.</li>
	<li>불안정성: 자료의 작은 변화로 인해 트리 구조가 크게 변할 수 있어 생존 숲과 같은 다른 방법에 비해 안정성이 떨어집니다.</li>
</ol>

생존 트리는 공변량 집합과 관심 있는 이벤트가 발생할 때까지의 시간 사이의 관계를 모델링하고 시각화하는 데 사용됩니다. 그것이...

Education

교육

JoVE Core

Statistics

통계학

Unit 1

제1단원

Survival Analysis

생존 분석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

survival tree in time-to-event analysis

A survival tree is a non-parametric tool in survival analysis that links predictor variables, or covariates, to survival time. Survival time is the time until an event of interest occurs. It is useful when some data are censored, which means the event has not happened for some people by the end of the study or the exact event time is unknown.

Building a survival tree starts with a dataset that includes covariates, survival time, and a censoring indicator for each subject. The data must be prepared so the needed covariates are included and formatted correctly. Missing values can be handled by imputation or by treating them as a separate category.

The tree is built through recursive partitioning. At each step, the data are split into two groups based on the covariate that best separates the survival outcomes. A common splitting rule is the log-rank test, which compares survival distributions between groups.

Each node in the tree represents a subset of the data. The terminal nodes, or leaves, are evaluated with the Kaplan-Meier estimate of the survival function. This gives a survival probability estimate for subjects in that node. The tree is then pruned by removing nodes that do not improve model accuracy enough, which helps reduce overfitting and makes the model more useful for new data.

Survival trees have several strengths. They can handle many data types and are robust to outliers and missing values. They are also easy to interpret because the tree structure clearly shows how covariates relate to survival time. As a non-parametric method, they do not require assumptions about the distribution of survival times or the exact form of the relationship between covariates and survival.

They also have limits. Without pruning, survival trees can overfit the training data and perform poorly on new data. They can also be unstable, because small changes in the data may produce a very different tree. This makes them less stable than methods such as survival forests.

Survival Tree in Time-to-Event Analysis

introduction to survival analysis

Time-to-Event Data and Censoring

Survival analysis is a statistical method for time-to-event data. The event can be death, disease relapse, system failure, or recovery. It helps estimate survival time, which is the time until a specific event occurs, and it also shows what factors may affect that time. A key idea in survival analysis is censoring. Censoring happens when the event of interest has not been observed for some people during the study period. Because the data are incomplete in those cases, survival analysis uses...

life tables

Life Tables and Survival Patterns

A life table is a statistical tool that shows mortality and survival patterns in a population. It organizes data across age intervals so students can see how likely a group is to survive or die at each stage of life. The table gives a clear snapshot of population dynamics over time. Life tables are used in demography, public health, actuarial science, and ecology. They help scientists study life expectancy, plan health interventions, estimate insurance risk, and compare how species survive in...

survival curves

Kaplan-Meier Survival Curve Basics

Kaplan-Meier survival curves show how the chance of staying event-free changes over time. They are used to track survival in a population and to compare groups in medicine, public health, and reliability engineering. The Kaplan-Meier estimator is the most common way to build these curves. It is a non-parametric method, which means it does not assume a fixed pattern for the data. The result is a stepwise line that drops each time an event happens, such as death, disease recurrence, or...

actuarial approach

Life Table Method for Survival Rates

The life table method, also called the actuarial approach, is used to estimate survival rates in clinical and population studies. It began in life insurance, where risk over time must be measured carefully. In health research, it gives a clearer picture of survival when some participants are lost to follow-up or die from causes unrelated to the study. This method works by dividing the study period into set intervals, usually one year. That makes it useful for tracking outcomes over time,...

kaplan-meier approach

Survival Curves with Kaplan-Meier Data

The Kaplan-Meier estimator is a non-parametric method for estimating a survival function from time-to-event data. It is commonly used in medical research to track how many patients survive for a set time after treatment. It is also important in clinical trials, epidemiological studies, and reliability engineering. This method helps researchers study survival probabilities over time, even when some data are incomplete. That incomplete data is called censored data, which means the exact event...

assumptions of survival analysis

Survival Analysis Assumptions in Studies

Survival analysis studies the time until an event happens. The event may be death in a living organism or failure in a mechanical system. These models are used in medicine, biology, engineering, and public health to study time-to-event data. Careful study design matters because the method depends on several key assumptions. One common feature of survival times is positive skewness. This means events often happen early, while fewer cases occur later. Survival data also often include censoring,...

comparing the survival analysis of two or more groups

comparing-the-survival-analysis-of-two-or-more-groups

Kaplan-Meier Curves and Hazard Ratios

Kaplan-Meier curves and hazard ratios help researchers compare survival time between groups. Survival analysis looks at the time until an event happens, such as death, disease recurrence, or recovery. It is a key tool in medical research. A major strength of survival analysis is that it can handle censored data. Censored data means the event has not happened for some participants by the end of the study, or it has not been observed. This makes survival analysis different from standard...

the mantel-cox log-rank test

Log-Rank Test for Comparing Survival Curves

The Mantel-Cox log-rank test compares survival curves from two groups. It checks whether the groups have a statistically significant difference in survival time. This makes it useful when the timing of an event matters, such as death or disease recurrence. The log-rank test is non-parametric. That means it does not assume a specific distribution for the survival data. It is also useful in medical research, where it often helps compare a new treatment with a control or standard treatment in...

applications of life tables

Life Tables in Public Policy and Science

Life tables are used in many fields to study mortality and survival rates. They give a numerical way to examine how long people or living things are likely to survive. This makes them useful for public health, business planning, and scientific research. In demography and public health, life tables help experts study population changes and predict future trends. They can show patterns such as an aging population or the effect of a health policy. In Nigeria, health officials used survival rates...

cancer survival analysis

Cancer Survival Curves and Risk Factors

Cancer survival analysis measures how long it takes from diagnosis or the start of treatment to a specific outcome, such as remission or death. It helps researchers judge treatment effectiveness and understand what affects patient outcomes. These results also support clinical decisions and prognostic evaluations. Survival data are often skewed and not normally distributed. They also include censored cases, where the full survival time is unknown because the study ends, a patient is lost to...

hazard rate

Modeling Event Risk Over Time

Hazard rate is a statistical measure that describes how event risk changes over time. It is also called the hazard function or failure rate. In survival analysis, it shows the instantaneous rate at which an event occurs, but only after the subject has not had the event yet. From a probability view, hazard rate gives the chance that a subject will have the event in a very small time interval. That chance is conditional on surviving to the start of that interval. From a frequency view, it can...

hazard ratio

Hazard Ratio in Clinical Trials

The hazard ratio is a way to compare event risk in clinical trials. It is often used to study events such as death or disease recurrence in two groups over time. The two groups are usually a treatment group and a control group. A hazard ratio compares hazard rates, which are the instantaneous risk of an event happening at a given moment. It shows how the risk in one group relates to the risk in the other group. In a cancer drug study, for example, the hazard ratio can show how a new treatment...

truncation in survival analysis

Left and Right Truncation in Survival Data

Truncation in survival analysis describes data loss caused by the timing of an event or by when a subject can enter a study. It can happen in two forms: left truncation and right truncation. In both cases, some individuals are left out of the dataset before analysis begins. Left truncation happens when people who had the event before a set time are not included in the study. This often occurs with delayed entry, which means a person is only observed if they survive until the entry point. For...

censoring survival data

Types of Censoring in Survival Analysis

Survival analysis studies time-to-event data, which tracks how long it takes for an outcome to happen. It is used in medicine, engineering, and social science. A common problem in this type of data is censoring, which means the full event time is not observed for every person or item. Censoring can happen for several reasons and in different patterns. The most common kind is right censoring. This happens when the event has not occurred by the end of the study or when a participant is lost to...

survival tree

A survival tree is a non-parametric tool in survival analysis that links predictor variables, or covariates, to survival time. Survival time is the time until an event of interest occurs. It is useful when some data are censored, which means the event has not happened for some people by the end of the study or the exact event time is unknown. Building a survival tree starts with a dataset that includes covariates, survival time, and a censoring indicator for each subject. The data must be...

parametric survival analysis: weibull and exponential methods

parametric-survival-analysis-weibull-and-exponential-methods

Modeling Survival Time with Weibull and Exponential

Parametric survival analysis models survival time by assuming a specific probability distribution for when an event occurs. The Weibull and exponential distributions are two common choices because they are flexible and relatively straightforward to use. The Weibull distribution is a flexible model in parametric survival analysis. It can describe both increasing and decreasing hazard rates, depending on its shape parameter beta. When beta is greater than 1, the hazard rate rises over time. That...

key terms and concepts

Learn how survival trees use covariates, censoring, and recursive partitioning to model time-to-event data, estimate survival, and manage overfitting.

Survival Tree in Time-to-Event Analysis | JoVE K12

statistics

JoVE Core Statistics introduces the concepts and application of the collection, analysis, presentation, and interpretation of data to students. These animated lessons provide an understanding of statistics beneficial to students from a wide range of disciplines. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide

Survival Tree in Time-to-Event Analysis

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