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

Bei der Überlebensanalyse wird die Zeit bis zum Eintritt eines Ereignisses wie Tod oder Behandlungsversagen bewertet. Der versicherungsmathematische oder Sterbetafel-Ansatz, der aus der Versicherungsmathematik adaptiert wurde, analysiert Überlebensdaten.
In einem klinischen Studienszenario werden die Teilnehmer in Gruppen mit unterschiedlicher Nachbeobachtungsdauer eingeteilt, um sich auf kritische Zeiträume zu konzentrieren, wie z. B. das erste Jahr nach einer risikoreichen Operation.
Die versicherungsmathematische Methode berechnet die Überlebensraten in festgelegten Intervallen und nutzt dabei die Daten aller Teilnehmer, einschließlich derjenigen, die bei der Nachsorge verloren gegangen sind oder an anderen Ursachen gestorben sind.
Um die Auswirkungen auf das Überleben im ersten Jahr zu verstehen, werden die Ein-Jahres-Überlebensraten abgeleitet, indem die Anzahl der Todesfälle von der Gesamtzahl der Teilnehmer abgezogen und durch die ursprüngliche Zahl dividiert wird.
Für die Schätzung des Zwei-Jahres-Überlebens wird nur die Untergruppe der Patienten berücksichtigt, die das erste Jahr überlebten und dann das zweite Jahr weiter überlebten.
Diese Methode ist konsistent, hilft dabei, langfristige Trends zu erkennen und die Wirksamkeit von Behandlungen oder Interventionen zu bewerten, was ein robustes Instrument zum Verständnis der Ergebnisse in der medizinischen Forschung darstellt.

aktuarielle methode

Actuarial Approach

Die aktuarielle Methode, eine statistische Methode, die ursprünglich für die Risikobewertung von Lebensversicherungen entwickelt wurde, wird häufig zur Berechnung der Überlebensraten in klinischen und populationsbasierten Studien verwendet. Diese Methode berücksichtigt Teilnehmende, die während der Nachverfolgung ausfallen oder aus nicht studienbezogenen Gründen versterben, und gewährleistet somit eine präzisere Darstellung der Überlebenswahrscheinlichkeiten.

Betrachten wir das Beispiel eines chirurgischen Eingriffs mit hohem Risiko und erheblicher Sterblichkeit im Frühstadium. Es wird eine zweijährige klinische Studie durchgeführt, die sich auf das kritische erste Jahr konzentriert. Die Teilnehmer werden in zwei Gruppen aufgeteilt: eine wird ein Jahr lang beobachtet, die andere zwei Jahre lang. Die Überlebensraten werden mithilfe der aktuariellen (oder Sterbetafel-)Methode geschätzt, die den Untersuchungszeitraum in Intervalle unterteilt – normalerweise ein Jahr.

Zur Veranschaulichung nehmen wir an, dass die erste Gruppe mit 1.000 Patienten beginnt, von denen 240 innerhalb des ersten Jahres sterben. Die zweite Gruppe beginnt ebenfalls mit 1.000 Patienten, wobei im ersten Jahr 200 und im zweiten Jahr 16 Todesfälle auftreten. Die Einjahresüberlebensrate wird berechnet, indem die Gesamtzahl der Todesfälle von der anfänglichen Kohortengröße abgezogen und das Ergebnis durch die Ausgangspopulation geteilt wird:

Einjahresüberlebensrate = (2000−240−200)/2000=0,78 oder 78 %

Dieser Ansatz kann auch auf Studien zu langfristigen Ergebnissen angewendet werden, wie etwa die Bewertung der Wirksamkeit einer Krebsbehandlung über Jahre hinweg. Die versicherungsmathematische Methode berücksichtigt Patienten, die nicht mehr weiterverfolgt werden können oder aus anderen Gründen sterben, und ermöglicht so eine robuste Analyse der langfristigen Auswirkungen.

Für zweijährige Überlebensraten wird die Berechnung differenzierter. Dabei wird eine bedingte Wahrscheinlichkeit verwendet, wobei nur diejenigen Personen berücksichtigt werden, die die gesamten zwei Jahre beobachtet wurden und das erste Jahr überlebt haben. Die Überlebensrate nach zwei Jahren darf die Überlebensrate nach einem Jahr nicht überschreiten und wird ermittelt, indem die Wahrscheinlichkeit, das erste Jahr zu überleben, mit der Wahrscheinlichkeit, das zweite Jahr zu überleben, multipliziert wird, vorausgesetzt, dass das erste Jahr überlebt wird:

Überlebensrate nach zwei Jahren = 0,78 × 0,98 = 0,7644 oder 76,44 %

Diese anspruchsvolle Methode ist zwar leistungsstark, steht aber vor Herausforderungen wie unvollständigen Nachverfolgungsdaten und einer genauen Aufzeichnung von Todesfällen. Trotz dieser Einschränkungen bleibt sie besonders effektiv bei groß angelegten Bevölkerungsstudien, bei denen die Nachverfolgung einzelner Teilnehmer unpraktisch ist. Durch die Berücksichtigung von Zensur und intervallbasierten Überlebenswahrscheinlichkeiten bietet der versicherungsmathematische Ansatz einen zuverlässigen Rahmen für die Überlebensanalyse in verschiedenen Forschungskontexten.

Aktuarielle Methode

Bei der Überlebensanalyse wird die Zeit bis zum Eintritt eines Ereignisses wie Tod oder Behandlungsversagen bewertet. Der versicherungsmathematische oder Sterbetafel-Ansatz, adaptiert von der versicherungsmathematischen ...

Education

Lehre

JoVE Core

Statistics

Statistik

Unit 1

Einheit 1

Survival Analysis

Überlebensanalyse

KEY TERMS AND CONCEPTS

SCHLÜSSELBEGRIFFE UND KONZEPTE

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

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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

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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

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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 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

Life Table Method for Survival Rates

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