Name: kaplan-meier survival curve basics
Uploaded: 2025-01-09T15:14:16.000Z
Duration: 1 min 18 s
Channel: JoVE

Si consideri un grafico della probabilità cumulativa di morte tracciata come età sull'asse X rispetto alla proporzione di morti sull'asse Y per un anno specifico.
Questo può essere espresso come un'equazione, dove la funzione di distribuzione cumulativa F(t) è il rapporto tra il numero di persone morte per tempo t e il numero totale osservato.
Poiché tutti i membri della popolazione non vengono osservati fino alla morte, questa curva non può stimare la sopravvivenza.
Quindi, la funzione di sopravvivenza o curva di sopravvivenza – S(t) – è la proporzione o la percentuale di persone che vivono fino a t o oltre. Esso è espresso come segue.
La curva di sopravvivenza viene quindi tracciata utilizzando l'età e la percentuale di persone sopravvissute.
Esistono vari tipi di modelli di sopravvivenza. Il modello di sopravvivenza esponenziale caratterizza un pericolo costante nel tempo, il che significa che il rischio che l'evento si verifichi è indipendente dal tempo.
Il modello di sopravvivenza di Weibull può essere utilizzato in varie situazioni in cui il tasso di rischio aumenta o diminuisce monotonicamente nel tempo.
I modelli Log-normale e log-logistico possono essere utilizzati in scenari in cui il tasso di rischio non è monotono.

curve di sopravvivenza

Survival Curves

Le curve di sopravvivenza sono rappresentazioni grafiche che descrivono la probabilità di sopravvivenza di una popolazione nel tempo, offrendo un modo intuitivo per tracciare la percentuale di individui che rimangono privi di eventi in ogni momento. Queste curve sono ampiamente utilizzate in campi come la medicina, la sanità pubblica e l'ingegneria dell'affidabilità per visualizzare e confrontare le probabilità di sopravvivenza tra diversi gruppi o condizioni.

Lo stimatore di Kaplan-Meier è il metodo più comune per costruire curve di sopravvivenza. Questo approccio non parametrico genera una funzione graduale, in cui la curva scende ogni volta che si verifica un evento (come morte, recidiva di malattia o guasto meccanico). I segmenti orizzontali tra le cadute indicano periodi di stabilità, durante i quali non si verificano eventi. L'asse x della curva rappresenta il tempo, mentre l'asse y mostra la probabilità di sopravvivenza, che va da 0 a 1. Le curve di sopravvivenza forniscono diverse informazioni chiave:

<ol>
	<li>Probabilità di sopravvivenza nel tempo:

	la curva illustra la probabilità che gli individui sopravvivano oltre specifici punti temporali. Ad esempio, se una curva di sopravvivenza per un gruppo di trattamento rimane più alta di quella di un gruppo di controllo, indica l'efficacia del trattamento nel prolungare la vita o ritardare l'evento.
	</li>
	<li>Tempo di sopravvivenza mediano:
	il tempo di sopravvivenza mediano è il punto in cui la probabilità di sopravvivenza scende a 0,5, indicando il tempo entro il quale si prevede che metà della coorte abbia sperimentato l'evento. Questa metrica è particolarmente importante negli studi clinici come parametro di riferimento per l'efficacia del trattamento.
	</li>
	<li>Confronti di gruppo:
	le curve di sopravvivenza sono strumenti efficaci e utili a confrontare le esperienze di sopravvivenza di gruppi diversi, come pazienti sottoposti a vari trattamenti o sistemi sottoposti a diverse condizioni di stress. Test statistici come il test dei ranghi logaritmici sono spesso utilizzati insieme alle curve di sopravvivenza per determinare se le differenze osservate tra i gruppi sono statisticamente significative.
	</li>
</ol>

Ad esempio, in uno studio clinico che confronta due terapie contro il cancro, le curve di sopravvivenza possono rivelare quale trattamento offre migliori risultati di sopravvivenza. Una curva che declina più gradualmente indica un gruppo con migliori probabilità di sopravvivenza. Allo stesso modo, nell'ingegneria dell'affidabilità, le curve di sopravvivenza vengono impiegate per stimare la durata di vita di componenti o sistemi, consentendo un'efficace pianificazione della manutenzione e un'analisi dei guasti.

Fornendo una chiara e accessibile rappresentazione visiva di dati complessi, relativi ad un certo periodo di tempo e per l’osservazione di eventi specifici, le curve di sopravvivenza svolgono un ruolo cruciale nell'analisi dei dati. La loro capacità di riassumere le probabilità di sopravvivenza, identificare parametri chiave come il tempo di sopravvivenza mediano e facilitare i confronti di gruppo le rende indispensabili in una vasta gamma di applicazioni.

Curve di sopravvivenza

Si consideri un grafico della probabilità cumulativa di morte tracciata come età sull'asse X rispetto alla proporzione di morti sull'asse Y per un anno specifico.
Questo...

Education

Didattica

JoVE Core

Statistics

Statistica

Unit 1

Unità 1

Survival Analysis

Analisi della sopravvivenza

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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 mechanical failure.

The flat parts of the curve matter too. They show time periods when no events occur. On the graph, the x-axis shows time and the y-axis shows survival probability, which ranges from 0 to 1.

These curves help show survival probability over time. If one treatment group stays higher than a control group, it suggests better survival or a longer delay before the event. The median survival time is the point where the curve reaches 0.5, meaning half the group has had the event by that time.

Survival curves are also useful for group comparisons. Researchers may compare patients receiving different treatments or systems under different stress conditions. A log-rank test is often used to check whether the difference between curves is statistically significant. In a cancer trial, for example, a curve that falls more slowly can show better survival outcomes.

In reliability engineering, survival curves help estimate how long a component or system may last. That information supports maintenance planning and failure analysis. Because they turn time-to-event data into a clear graph, survival curves are an important tool for data analysis.

Kaplan-Meier Survival Curve Basics

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 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

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...

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 Kaplan-Meier survival curves track event-free survival over time, show median survival time, and compare groups in medicine and engineering.

Kaplan-Meier Survival Curve Basics | 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.

Kaplan-Meier Survival Curve Basics

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