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

특정 연도에 대해 X축의 연령과 Y축의 사망 비율로 표시된 누적 사망 확률의 그래프를 생각해 보십시오.
이것은 방정식으로 표현될 수 있으며, 여기서 누적 분포 함수 F(t)는 관찰된 총 수에 대한 시간 t까지 사망한 사람 수의 비율입니다.
모든 개체군 구성원이 죽을 때까지 관찰되지 않기 때문에 이 곡선은 생존을 추정할 수 없습니다.
따라서 생존 함수 또는 생존 곡선(S(t))은 t 시간 또는 그 이상까지 사는 사람들의 비율 또는 백분율입니다. 다음과 같이 표현됩니다.
그런 다음 연령과 생존 인구 비율을 사용하여 생존 곡선을 그립니다.
생존 모델에는 다양한 유형이 있습니다. 지수 생존 모델은 시간이 지남에 따라 지속적인 위험을 특성화하며, 이는 이벤트 발생의 위험이 시간과 무관하다는 것을 의미합니다.
Weibull 생존 모형은 시간이 지남에 따라 위험률이 단조롭게 증가하거나 감소하는 다양한 상황에서 사용할 수 있습니다.
로그 정규 및 로그 로지스틱 모델은 위험률이 단조롭지 않은 시나리오에서 사용할 수 있습니다.

생존 곡선

Survival Curves

생존 곡선은 시간 경과에 따른 인구의 생존 경험을 묘사하는 그래픽 표현으로, 각 시점에서 이벤트 없이 남아 있는 개인의 비율을 추적하는 직관적인 방법을 제공합니다. 이러한 곡선은 의학, 공중 보건 및 신뢰성 엔지니어링과 같은 분야에서 널리 사용되어 다양한 그룹이나 조건에서 생존 확률을 시각화하고 비교합니다.

카플란-마이어 추정치는 생존 곡선을 구성하는 가장 일반적인 방법입니다. 이 비모수적 접근 방식은 단계적 함수를 생성하는데, 여기서 곡선은 사망, 질병 재발 또는 기계적 고장과 같은 이벤트가 발생할 때마다 떨어집니다. 떨어지는 수평 세그먼트는 이벤트가 발생하지 않는 안정 기간을 나타냅니다. 곡선의 x축은 시간을 나타내고 y축은 0~1 범위의 생존 확률을 보여줍니다. 생존 곡선은 몇 가지 주요 통찰력을 제공합니다.

<ol>
	<li>시간 경과에 따른 생존 확률:

	곡선은 개인이 특정 시점을 넘어 생존할 가능성을 보여줍니다. 예를 들어, 치료 그룹의 생존 곡선이 대조군보다 높은 경우, 이는 수명을 연장하거나 사건을 지연시키는 치료의 효과를 나타냅니다.
	</li>
	<li>중간 생존 시간:
	중간 생존 시간은 생존 확률이 0.5로 떨어지는 지점으로, 코호트의 절반이 사건을 경험할 것으로 예상되는 시간을 나타냅니다. 이 지표는 치료 효능의 벤치마크로서 임상 연구에서 특히 중요합니다.
	</li>
	<li>그룹 비교:
	생존 곡선은 다양한 치료를 받는 환자나 다양한 스트레스 조건에 노출된 시스템과 같이 다양한 그룹의 생존 경험을 비교하는 데 강력한 도구입니다. 로그 순위 검정과 같은 통계적 검정은 종종 생존 곡선과 함께 사용되어 그룹 간에 관찰된 차이가 통계적으로 유의미한지 확인합니다.
	</li>
</ol>

예를 들어, 두 가지 암 치료법을 비교하는 임상 시험에서 생존 곡선은 어떤 치료법이 더 나은 생존 결과를 제공하는지 보여줄 수 있습니다. 곡선이 더 점진적으로 감소하면 생존 확률이 더 나은 그룹을 나타냅니다. 마찬가지로 신뢰성 엔지니어링에서 생존 곡선은 구성 요소 또는 시스템의 수명을 추정하는 데 사용되어 효과적인 유지 관리 계획 및 고장 분석을 가능하게 합니다

복잡한 이벤트 발생 시간 자료를 명확하고 접근 가능한 시각적 표현으로 제공함으로써 생존 곡선은 자료 분석에서 중요한 역할을 합니다. 생존 확률을 요약하고, 중간 생존 시간과 같은 주요 지표를 식별하고, 그룹 비교를 용이하게 하는 기능은 다양한 응용 분야에서 없어서는 안 될 요소입니다.

특정 연도에 대해 X축의 연령과 Y축의 사망 비율로 표시된 누적 사망 확률의 그래프를 생각해 보십시오.
이...

Education

교육

JoVE Core

Statistics

통계학

Unit 1

제1단원

Survival Analysis

생존 분석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 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

Kaplan-Meier Survival Curve Basics

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