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

考虑绘制一幅图，以横轴（X轴）表示年龄，纵轴（Y轴）表示某一年内死亡比例，展示死亡累积概率随年龄变化的曲线。
这可以用一个方程来表示，其中累积分布函数 F(t) 是指在时间 t 之前死亡人数与观察总人数的比值。
由于无法观察所有个体直至死亡，该曲线无法估算生存率。
因此，生存函数或生存曲线——S(t)——是指存活至时间 t 或更长时间的人群比例或百分比。其表达式如下。
然后利用年龄和存活人数的百分比绘制生存曲线。
生存模型有多种类型。指数生存模型描述的是随时间保持恒定的风险，即事件发生的风险与时间无关。
威布尔生存模型可用于危险率随时间单调增加或减少的各种情况。
当风险率非单调时，可使用对数正态模型和对数逻辑模型。

生存曲线<

Survival Curves

生存曲线是一种图形表示，描绘一段时间内人群的生存经历，提供了一种直观的方式来跟踪每个时间点上无事件发生的个体比例。这些曲线广泛应用于医学、公共卫生和可靠性工程等领域，以可视化和比较不同群体或条件下的生存概率。

Kaplan-Meier 估计量是构建生存曲线最常用的方法。这种非参数方法生成一个阶跃函数，其中曲线在每次发生事件（例如死亡、疾病复发或机械故障）时下降。下降之间的水平段表示稳定期，在此期间没有任何事件发生。曲线的 x 轴表示时间，而 y 轴表示生存概率，范围从 0 到 1。生存曲线提供了几个关键见解：

<ol>
	<li>随时间变化的生存概率：

	该曲线说明了个体在特定时间点之后生存的可能性。例如，如果治疗组的生存曲线高于对照组，则表明治疗在延长生命或延迟事件方面是有效的。
	</li>
	<li>中位生存时间：
	中位生存时间是生存概率降至 0.5 的点，表示预计队列的一半经历该事件的时间。该指标在临床研究中尤为重要，是治疗效果的基准。
	</li>
	<li> 组间比较：
	生存曲线是比较不同组生存经历的有力工具，例如接受各种治疗的患者或受到不同压力条件的系统。对数秩检验等统计检验通常与生存曲线一起使用，以确定观察到的组间差异是否是统计学显著的。
	</li>
</ol>

例如，在比较两种癌症疗法的临床试验中，生存曲线可以揭示哪种治疗方法能提供更好的生存结果。曲线下降得越缓慢，表明该组的生存概率越高。同样，在可靠性工程中，生存曲线用于估计组件或系统的使用寿命，从而实现有效的维护规划和故障分析。

通过提供复杂的时间事件数据的清晰易懂的视觉表示，生存曲线在数据分析中发挥着至关重要的作用。它们能够总结生存概率、确定关键指标（如中位生存时间）并有利于组间比较，这使得它们在一系列应用中不可或缺。

考虑绘制一幅图表，以特定年份的死亡累积概率为数据，横轴（X轴）表示年龄，纵轴（Y轴）表示已死亡个体的比例。  
这……

Education

教育

JoVE Core

Statistics

统计学

Unit 1

第一单元

Survival Analysis

生存分析

KEY TERMS AND CONCEPTS

关键术语与概念

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 统计学（Statistics）向学生介绍了数据收集、分析、呈现和解释的概念和应用。 这些生动的课程提供了对来自广泛学科的学生有益的统计学的理解。 此外，"行动中的科学家"视频展示了相关概念在当今世界各地实验室进行的经典和原创研究实验中的应用

Kaplan-Meier Survival Curve Basics

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