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

Uma árvore de sobrevivência é usada para modelar e visualizar a relação entre um conjunto de covariáveis e o tempo até que ocorra um evento de interesse. Normalmente, ele é criado usando um processo de particionamento recursivo.
As ramificações da árvore representam as divisões nos valores de uma variável. Os nós representam subconjuntos dos dados e os nós terminais indicam o número de sujeitos no nó e podem fornecer previsões finais da análise.
A construção de uma árvore de sobrevivência requer principalmente covariáveis, critérios de divisão, tamanho mínimo do nó e limites de poda.
As covariáveis ou variáveis preditoras podem ser contínuas, ordinais ou categóricas.
Um critério de divisão é um método para escolher a melhor divisão em cada nó. É aplicado para minimizar o risco dentro do nó ou para maximizar o grau de separação entre os nós.
O tamanho mínimo do nó é o menor número de observações necessárias para que um nó seja dividido ainda mais. Isso ajuda a controlar o tamanho da árvore e evita o sobreajuste.
Finalmente, o limite de poda é uma medida para decidir quando parar de podar a árvore.

Árvores de sobrevivência

Survival Tree

Árvores de sobrevivência são um método não paramétrico usado em análise de sobrevivência para modelar a relação entre um conjunto de covariáveis ​​e o tempo até que um evento de interesse ocorra, frequentemente chamado de "tempo para o evento" ou "tempo de sobrevivência". Este método é particularmente útil ao lidar com dados censurados, onde o evento não ocorreu para alguns indivíduos até o final do período de estudo, ou quando o tempo exato do evento é desconhecido.  Construindo uma Árvore de Sobrevivência A construção de uma árvore de sobrevivência começa com um conjunto de dados que inclui covariáveis ​​(variáveis ​​preditoras) e o tempo de sobrevivência, juntamente com um indicador de censura para cada sujeito. O processo envolve as seguintes etapas: <ol> <li>Preparação dos Dados: O conjunto de dados é preparado garantindo que todas as covariáveis ​​necessárias sejam incluídas e formatadas adequadamente. Valores ausentes podem ser manipulados usando métodos como imputação, ou tratando-os como uma categoria separada.</li> <li>Construção da Árvore: A árvore de sobrevivência é construída usando um processo de particionamento recursivo. Em cada etapa, o conjunto de dados é dividido em dois subconjuntos com base em uma covariável que melhor diferencia os resultados de sobrevivência. Isso normalmente é feito usando um critério de divisão, como o teste log-rank, que compara as distribuições de sobrevivência entre os grupos.</li> <li>Avaliação de Nó: cada nó na árvore representa um subconjunto dos dados, e os nós terminais (folhas) são avaliados com base na estimativa de Kaplan-Meier da função de sobrevivência. Isso fornece uma estimativa da probabilidade de sobrevivência para os indivíduos que se enquadram nesse nó.</li> <li>Poda: Para evitar o overfitting, a árvore é podada, removendo nós que não fornecem melhoria significativa na precisão do modelo. Esta etapa garante que a árvore seja generalizável para novos dados.</li> </ol>  Vantagens e desvantagens Vantagens: <ol style="list-style-type: circle;"> <li>Flexibilidade: as árvores de sobrevivência podem lidar com uma ampla gama de tipos de dados e são robustas para outliers e valores ausentes.</li> <li>Interpretabilidade: A estrutura da árvore é fácil de interpretar, permitindo uma visualização direta da relação entre covariáveis ​​e o tempo de sobrevivência.</li> <li>Natureza não paramétrica: Elas não exigem suposições sobre a distribuição dos tempos de sobrevivência ou a forma funcional da relação entre covariáveis ​​e sobrevivência.</li> </ol> Desvantagens: <ol style="list-style-type: circle;"> <li>Overfitting: Sem uma poda adequada, as árvores de sobrevivência podem fazer um overfit dos dados de treinamento, levando a uma generalização ruim.</li> <li>Instabilidade: Pequenas mudanças nos dados podem levar a mudanças significativas na estrutura da árvore, tornando-as menos estáveis ​​em comparação a outros métodos, como florestas de sobrevivência</li> </ol>

Uma árvore de sobrevivência é usada para modelar e visualizar a relação entre um conjunto de covariáveis e o tempo até que ocorra um evento de interesse. É ...

Education

JoVE Core

Statistics

Estatísticas

Unit 1

Unidade 1

Survival Analysis

Análise de Sobrevivência

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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 Estatística apresenta os conceitos e aplicação da coleta, análise, apresentação e interpretação de dados para os alunos. Esses vídeos de animação fornecem uma compreensão de estatística beneficial para alunos de uma ampla gama de disciplinas. Além disso, os vídeos do cientista em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássicos e originais realizados nos laboratórios atuais em todo o mundo.

Survival Tree in Time-to-Event Analysis

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