Name: time-to-event data and censoring
Uploaded: 2025-01-09T15:14:16.000Z
Duration: 1 min 18 s
Channel: JoVE

生物医学研究から次の3つの例を考えてみましょう。
まず、がん研究では、患者さんが寛解してから再発するまでの時間を解析します。
第二に、歯の健康に関する小児科研究では、子供の誕生から虫歯による最初の歯科充填までの時間を測定しています。
第三に、冠動脈バイパス手術に関する研究では、手術から患者の死亡までの時間を分析します。
このような研究では、所定の開始点から特定のイベントが発生するまでの時間をキャプチャする縦断的データが生成されます。生存時間分析は、このようなデータを分析するためのフレームワークを提供します。
生存分析では、「イベント」とは、病気の再発、死亡、回復など、関心のある経験を指します。
生存分析の「時間」は、研究の開始、介入、または症例の最初の報告から、研究の終了、関心のあるイベントの発生、さらには患者の死亡までの期間を測定します。
生存時間分析では、生存関数、生命表、ハザード分析、および特定の統計モデリングを使用する必要があります。

生存分析の概要

Introduction To Survival Analysis

生存分析は、イベント発生までの時間データを調査するために使用される統計手法です。ここでの「イベント」は、死亡、病気の再発、システム障害、回復などの結果を表します。生存データの一意的な特徴は、調査期間中に一部の個人で関心のあるイベントが観察されなかった場合に発生する打ち切りです。これには、不完全なデータを効果的に処理するための特殊な手法が必要です。

生存分析の主な目的は、特定のイベントが発生するまでの時間である生存時間を推定し、それに影響を与える要因を理解することです。重要な概念には、特定の時間を超えて生存する確率を示す生存関数 (S(t)S(t)) と、任意の時点での瞬間的なイベント率を表すハザード関数 (h(t)h(t)) があります。これらの関数は、時間の経過に伴う生存パターンとリスクに関する洞察を提供します。

一般的な手法には、生存曲線を生成し、グループ間で生存率を比較できるノンパラメトリックアプローチであるKaplan-Meier推定量と、生存時間の特定の分布を想定せずに共変量が生存にどのように影響するかを調べるセミパラメトリック手法であるCox比例ハザードモデルがあります。

生存分析は、治療効果を評価して患者の結果を予測するために医学で広く使用され、製品の寿命を推定するために工学で広く使用され、失業や生涯イベントなどの期間を分析するために社会科学で広く使用されています。検閲されたデータを処理し、時間に依存する現象をモデル化する能力があるため、様々な分野で結果を理解及び予測するための不可欠なツールとなっています。

生物医学研究から次の3つの例を考えてみましょう。
まず、がん研究では、患者が寛解してから再発するまでの時間...

Education

JoVE Core

Statistics

統計

Unit 1

ユニット1

Survival Analysis

生存解析

KEY TERMS AND CONCEPTS

主要用語と概念

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 special methods to handle them correctly.

Two core measures are the survival function and the hazard function. The survival function, written as S(t), gives the probability of surviving beyond a given time. The hazard function, written as h(t), shows the instantaneous event rate at a specific time, which helps describe how risk changes over time.

Common methods include the Kaplan-Meier estimator and the Cox proportional hazards model. Kaplan-Meier is a non-parametric method that creates survival curves and lets researchers compare survival rates between groups. The Cox proportional hazards model is semi-parametric and tests how covariates affect survival without assuming a specific survival-time distribution.

Survival analysis is used in medicine, engineering, and the social sciences. In medicine, it can help assess treatment effects and predict patient outcomes. In engineering, it can estimate product lifespans. In social science studies, it can examine durations such as unemployment or other time-to-life events.

Time-to-Event Data and Censoring

introduction to survival analysis

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

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

Explore time-to-event data, censoring, survival curves, and hazard rates. Learn how survival analysis is used in medicine, engineering, and social science studies.

Time-to-Event Data and Censoring | JoVE K12

statistics

JoVE Core 統計は、データの収集、分析、表示、解釈の概念と応用を学生に紹介します。これらのアニメーション授業は、幅広い分野の学生にとって有益な統計の理解を提供します。さらに、科学者が実際に活動しているビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

Time-to-Event Data and Censoring

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