Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Population Growth

Population Growth

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.However, realistic environmental conditions limit the number of...

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

Survival Curves

Survival Curves

Survival curves are graphical representations that depict the survival experience of a population over time, offering an intuitive way to track the proportion of individuals who remain event-free at each time point. These curves are widely used in fields such as medicine, public health, and reliability engineering to visualize and compare survival probabilities across different groups or conditions.
The Kaplan-Meier estimator is the most common method for constructing survival curves. This...

Assumptions of Survival Analysis

Assumptions of Survival Analysis

Survival models analyze the time until one or more events occur, such as death in biological organisms or failure in mechanical systems. These models are widely used across fields like medicine, biology, engineering, and public health to study time-to-event phenomena. To ensure accurate results, survival analysis relies on key assumptions and careful study design.

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...

Modeling with Differential Equations

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Longitudinal study of genome-wide DNA methylation in individuals with and without post-acute symptoms following SARS-CoV-2 infection.

Epigenomics·2026

Same author

Time-Dependent Mediators in Survival Analysis: Graphical Representation of Causal Assumptions.

Biometrical journal. Biometrische Zeitschrift·2026

Same author

Statistical methods to disentangle genetic effects influencing infertility and early fetal viability with a genome-wide application.

PLoS genetics·2025

Same author

Maternal and Fetal SERPINA3 Polymorphisms and Risk of Preeclampsia: A Dyad and Triad Based Case-Control Study.

Current issues in molecular biology·2025

Same author

Genome-Wide Association Analyses in Family Triads and Dyads Following Assisted Reproductive Technology.

Genetic epidemiology·2025

Same author

Telomere length in relation to fecundability and use of assisted reproductive technologies: the Norwegian Mother, Father, and Child Cohort Study.

BMC medicine·2024

Search research articles

Related Experiment Video

Updated: Jul 12, 2026

Measurement of Survival Time in Brachionus Rotifers: Synchronization of Maternal Conditions

Measurement of Survival Time in Brachionus Rotifers: Synchronization of Maternal Conditions

Published on: July 22, 2016

Survival models based on the Ornstein-Uhlenbeck process.

Odd O Aalen¹, Håkon K Gjessing

¹Department of Statistics, Institute of Basic Medical Sciences, University of Oslo, P.O.Box 1122 Blindern, N-0317 Oslo, Norway. o.o.aalen@basalmed.uio.no

Lifetime Data Analysis

|February 5, 2005

Summary

This study models survival data using the Ornstein-Uhlenbeck process, exploring quasi-stationarity and hazard rate shapes. Findings connect biological homeostasis to mortality plateaus and financial modeling.

More Related Videos

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Related Experiment Videos

Last Updated: Jul 12, 2026

Measurement of Survival Time in Brachionus Rotifers: Synchronization of Maternal Conditions

Measurement of Survival Time in Brachionus Rotifers: Synchronization of Maternal Conditions

Published on: July 22, 2016

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Area of Science:

Mathematical Biology
Biostatistics
Stochastic Processes

Background:

Survival data modeling often benefits from understanding underlying processes.
The Ornstein-Uhlenbeck process models systems stabilizing around an equilibrium, akin to biological homeostasis.
This process has applications in biology, social sciences, and finance.

Purpose of the Study:

To investigate the first-passage time distribution of the Ornstein-Uhlenbeck process.
To analyze quasi-stationarity and hazard rate shapes within this framework.
To extend existing models where hazard rates are squared functions of the Ornstein-Uhlenbeck process.

Main Methods:

Analysis of the first-passage time distribution for the Ornstein-Uhlenbeck process.
Examination of quasi-stationary distributions and hazard rate functions.
Extension of theoretical results for a specific hazard rate model.

Main Results:

Characterization of quasi-stationarity and diverse hazard rate shapes.
Extension of known results for models involving squared Ornstein-Uhlenbeck processes.
Demonstration of relevance to mortality plateau discussions and financial interest rate models.

Conclusions:

The Ornstein-Uhlenbeck process provides a valuable framework for survival data analysis, particularly in biological contexts.
Results offer insights into mortality plateaus and have implications for financial modeling.
The study bridges concepts from stochastic processes, biostatistics, and finance.