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

Un albero di sopravvivenza viene utilizzato per modellare e visualizzare la relazione tra un insieme di covariate e il tempo fino al verificarsi di un evento di interesse. In genere viene compilato utilizzando un processo di partizionamento ricorsivo.
I rami dell'albero rappresentano le divisioni nei valori di una variabile. I nodi rappresentano sottoinsiemi di dati e i nodi terminali indicano il numero di soggetti nel nodo e potrebbero fornire previsioni finali dell'analisi.
La costruzione di un albero di sopravvivenza richiede principalmente covariate, criteri di divisione, dimensione minima del nodo e soglie di potatura.
Le covariate o variabili predittive possono essere continue, ordinali o categoriali.
Un criterio di divisione è un metodo per scegliere la divisione migliore in ogni nodo. Viene applicato per ridurre al minimo il rischio all'interno del nodo o per massimizzare il grado di separazione tra i nodi.
La dimensione minima del nodo è il numero minimo di osservazioni necessarie per suddividere ulteriormente un nodo. Questo aiuta a controllare le dimensioni dell'albero e previene l'overfitting.
Infine, la soglia di potatura è una misura per decidere quando interrompere la potatura dell'albero.

alberi di sopravvivenza

Survival Tree

Gli alberi di sopravvivenza sono un metodo non parametrico utilizzato nell'analisi della sopravvivenza per modellare la relazione tra un set di covariate e il tempo fino al verificarsi di un evento di interesse, spesso definito "tempo all'evento" (time-to-event) o "tempo di sopravvivenza". Questo metodo è particolarmente utile quando si ha a che fare con dati censurati, in cui l'evento non si è verificato per alcuni individui entro la fine del periodo di studio o quando l'ora esatta dell'evento è sconosciuta.

Creazione di un albero di sopravvivenza

La creazione di un albero di sopravvivenza inizia con un set di dati che include covariate (variabili predittive) e il tempo di sopravvivenza, insieme a un indicatore di censura per ciascun soggetto. Il processo prevede i seguenti passaggi:

<ol>
	<li>Preparazione dei dati: il set di dati viene preparato assicurandosi che tutte le covariate necessarie siano incluse e formattate in modo appropriato. I valori mancanti possono essere gestiti utilizzando metodi come l'imputazione o trattandoli come una categoria separata.</li>
	<li>Costruzione dell'albero: l'albero di sopravvivenza viene creato utilizzando un processo di partizionamento ricorsivo. A ogni passaggio, il set di dati viene suddiviso in due sottoinsiemi in base a una covariata che differenzia al meglio i risultati di sopravvivenza. Ciò avviene, in genere, utilizzando un criterio di suddivisione come il test dei ranghi logaritmici, che confronta le distribuzioni di sopravvivenza tra i gruppi.</li>
	<li>Valutazione dei nodi: ogni nodo nell'albero rappresenta un sottoinsieme dei dati e i nodi terminali (foglie) vengono valutati in base alla stima di Kaplan-Meier della funzione di sopravvivenza. Ciò fornisce una stima della probabilità di sopravvivenza per i soggetti che rientrano in quel nodo.</li>
	<li>Potatura: per evitare l'overfitting, l'albero viene potato rimuovendo i nodi che non forniscono un miglioramento significativo nell'accuratezza del modello. Questo passaggio garantisce che l'albero sia generalizzabile a nuovi dati.</li>
</ol>

Vantaggi e svantaggi

Vantaggi:

<ol style="list-style-type: circle;">
	<li>Flessibilità: gli alberi di sopravvivenza possono gestire un'ampia gamma di tipi di dati e sono resistenti ai valori anomali e dati mancanti.</li>
	<li>Interpretabilità: la struttura ad albero è facile da interpretare, consentendo una visualizzazione diretta della relazione tra covariate e tempo di sopravvivenza.</li>
	<li>Natura non parametrica: non richiedono ipotesi sulla distribuzione dei tempi di sopravvivenza o sulla forma funzionale della relazione tra covariate e sopravvivenza.</li>
</ol>

Svantaggi:

<ol style="list-style-type: circle;">
	<li>Overfitting: senza una potatura adeguata, gli alberi di sopravvivenza possono adattarsi eccessivamente ai dati di training, causando una scarsa generalizzazione.</li>
	<li>Instabilità: piccole modifiche nei dati possono portare a modifiche significative nella struttura ad albero, rendendoli meno stabili rispetto ad altri metodi come le foreste di sopravvivenza</li>
</ol>

Alberi di Sopravvivenza

Un albero di sopravvivenza viene utilizzato per modellare e visualizzare la relazione tra un insieme di covariate e il tempo fino al verificarsi di un evento di interesse. Lo è...

Education

Didattica

JoVE Core

Statistics

Statistica

Unit 1

Unità 1

Survival Analysis

Analisi della sopravvivenza

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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

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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 Statistica introduce agli studenti i concetti e i metodi di raccolta, analisi, presentazione e interpretazione dei dati. Queste video lezioni animate forniscono una comprensione della statistica che è di beneficio agli studenti di molte discipline. Inoltre, i video degli "Scienziati in azione" mostrano l'applicazione dei concetti teorici in esperimenti di ricerca tradizionali e innovativi eseguiti in laboratori internazionali.

Survival Tree in Time-to-Event Analysis

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