Name: life table method for survival rates
Uploaded: 2025-01-09T15:14:16.000Z
Duration: 1 min 20 s
Channel: JoVE

L'analisi della sopravvivenza valuta il tempo che intercorre prima che si verifichi un evento come la morte o il fallimento del trattamento. L'approccio attuariale o tabella di vita, adattato dalla scienza attuariale, analizza i dati di sopravvivenza.
In uno scenario di studio clinico, i partecipanti sono divisi in gruppi con diverse durate di follow-up per concentrarsi sui periodi critici, come il primo anno dopo un intervento chirurgico ad alto rischio.
Il metodo attuariale calcola i tassi di sopravvivenza a intervalli predeterminati, utilizzando appieno i dati di tutti i partecipanti, compresi quelli persi al follow-up o che sono morti per altre cause.
Per comprendere l'impatto sulla sopravvivenza al primo anno, i tassi di sopravvivenza a un anno sono derivati sottraendo il numero di decessi dal totale dei partecipanti e dividendo per il numero originale.
Solo il sottogruppo di pazienti osservati per tutti i due anni viene considerato per stimare la sopravvivenza a due anni, concentrandosi su coloro che sono sopravvissuti il primo anno e poi hanno continuato a sopravvivere il secondo anno.
Questo metodo è coerente, aiuta a identificare le tendenze a lungo termine e valuta l'efficacia dei trattamenti o degli interventi, fornendo uno strumento robusto per comprendere i risultati della ricerca medica.

l’approccio attuariale

Actuarial Approach

L'approccio attuariale, un metodo statistico originariamente sviluppato per la valutazione del rischio assicurativo sulla vita, è ampiamente utilizzato per calcolare i tassi di sopravvivenza negli studi clinici e di popolazione. Questo metodo tiene conto dei partecipanti persi durante il monitoraggio, o di coloro che muoiono per cause non correlate allo studio, garantendo una rappresentazione più accurata delle probabilità di sopravvivenza.

Si consideri l'esempio di una procedura chirurgica ad alto rischio con significativa mortalità in fase iniziale. Viene condotto uno studio clinico di due anni, incentrato sul primo anno critico. I partecipanti vengono divisi in due gruppi: uno seguito per un anno e un altro per due anni. I tassi di sopravvivenza vengono stimati utilizzando il metodo attuariale (o della tavola di sopravvivenza), che divide il periodo di studio in intervalli, in genere un anno.

A scopo illustrativo, supponiamo che il primo gruppo inizi con 1.000 pazienti, di cui 240 muoiono entro il primo anno. Anche il secondo gruppo inizia con 1.000 pazienti, con 200 decessi nel primo anno e 16 nel secondo anno. Il tasso di sopravvivenza a un anno si calcola sottraendo il numero totale di decessi dalla dimensione iniziale della coorte e dividendo il risultato per la popolazione iniziale:

Tasso di sopravvivenza a un anno = (2000−240−200)/2000=0,78 o 78%

Questo approccio può essere applicato anche a studi di esiti a lungo termine, come la valutazione dell'efficacia di un trattamento contro il cancro nel corso degli anni. Il metodo attuariale tiene conto dei pazienti persi al follow-up o che muoiono per cause non correlate, consentendo un'analisi solida degli effetti a lungo termine.

Per i tassi di sopravvivenza a due anni, il calcolo diventa più sfumato. Si utilizza la probabilità condizionale, considerando solo gli individui osservati per i due anni interi e sopravvissuti al primo anno. Il tasso di sopravvivenza a due anni non deve superare il tasso a un anno e si determina moltiplicando la probabilità di sopravvivere al primo anno per la probabilità di sopravvivere al secondo anno, subordinatamente alla sopravvivenza al primo anno:

Tasso di sopravvivenza a due anni = 0,78×0,98 = 0,7644 o 76,44%

Questo metodo sofisticato, sebbene potente, deve affrontare problematiche quali dati di follow-up incompleti e registrazione accurata dei decessi. Nonostante queste limitazioni, tale metodo rimane particolarmente efficace negli studi di popolazione su larga scala, in cui il monitoraggio dei singoli partecipanti è impraticabile. Tenendo conto della censura e delle probabilità di sopravvivenza basate sugli intervalli, l'approccio attuariale fornisce un quadro affidabile per l'analisi della sopravvivenza in diversi contesti di ricerca.

L’Approccio Attuariale

L'analisi della sopravvivenza valuta il tempo che intercorre prima che si verifichi un evento come la morte o il fallimento del trattamento. L'approccio attuariale o tabella di vita, adattato da quello attuariale ...

Education

Didattica

JoVE Core

Statistics

Statistica

Unit 1

Unità 1

Survival Analysis

Analisi della sopravvivenza

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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, especially in studies with early deaths after a high-risk surgical procedure. In one example, a two-year study follows two groups. One group is observed for one year, and the other is observed for two years.

The one-year survival rate is found from the starting group size and the number of deaths during that year. In the example, 1,000 patients begin in each group. The first group has 240 deaths in the first year, and the second group has 200 deaths in the first year. Using the actuarial calculation, the one-year survival rate is 78%.

The same method can also be used for long-term studies, such as testing how well a cancer treatment works over several years. It accounts for patients who are not followed for the full study or who die from unrelated causes. That makes the survival estimate more realistic when individual tracking is difficult.

Two-year survival uses conditional probability, which means the second year is calculated only for people who survived the first year and were observed for the full two years. In the example, the second-year survival probability is multiplied by the first-year survival probability. The result is 0.78 times 0.98, or 76.44%.

A two-year survival rate should not be higher than the one-year rate. The method is powerful, but it depends on complete follow-up and accurate death records. Even with those limits, it is especially useful in large population studies where following each person closely is not practical.

Life Table Method for Survival Rates

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

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 the life table method, or actuarial approach, estimates one-year and two-year survival rates while accounting for follow-up losses and unrelated deaths.

Life Table Method for Survival Rates | 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.

Life Table Method for Survival Rates

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