Parametric Survival Models
Parametric Survival Models - Related Videos
01:14
Parametric Survival Analysis: Weibull and Exponential Methods
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2025
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...
02:19
Modeling Aeromonas Pathogenesis in C. elegans Using a Survival Assay
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2026
Source: Chen, Y., et al. Evaluating Virulence and Pathogenesis of Aeromonas Infection in a Caenorhabditis elegans Model. J. Vis. Exp. (2018)This video demonstrates a survival assay using C. elegans to model Aeromonas pathogenesis, where oral ingestion of the bacteria leads to intestinal infection and mortality, enabling quantitative assessment of bacterial virulence in a live host system.
11:04
Quantification of Global Diastolic Function by Kinematic Modeling-based Analysis of Transmitral Flow via the Parametrized Diastolic Filling Formalism
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Cited by 8 •
2014
Accurate, causality-based quantification of global diastolic function has been achieved by kinematic modeling-based analysis of transmitral flow via the Parametrized Diastolic Filling (PDF) formalism. PDF generates unique stiffness, relaxation, and load parameters and elucidates 'new' physiology while providing sensitive and specific indexes of dysfunction.
00:10
Precision Measurements and Parametric Models of Vertebral Endplates
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Cited by 1 •
2019
A reverse engineering system is employed to record and obtain detailed and comprehensive geometry data of vertebral endplates. Parametric models of vertebral endplate are then developed, which are beneficial to designing personalized spinal implants, making clinical diagnoses, and developing accurate finite element models.
01:30
Parametric Surfaces
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2026
A parametric surface in three-dimensional space is defined through a vector-valued function\begin{equation*}\mathbf{r}(u, v) = x(u, v)\mathbf{i} + y(u, v)\mathbf{j} + z(u, v)\mathbf{k}\end{equation*}where u and v are parameters within a specified domain D in the uv-plane. The functions x(u, v), y(u, v), and z(u, v) define the coordinates of points on the surface. As u and v vary over D, the position vector r(u, v) traces a continuous surface in space. This parametric representation is essential...
FAQs
Right censoring contributes partial information rather than a completed event time. The likelihood uses the observed follow-up time and indicates that the event had not occurred by that point, while observed events contribute their event-time information. This allows model parameters and covariate effects to be estimated without treating censored observations as if the event occurred at censoring.
The selected distribution determines how event times are represented and influences estimates of survival probabilities, hazards, and median event times. Exponential, Weibull, log-normal, and log-logistic specifications make different distributional assumptions. Choosing a distribution whose assumptions are appropriate for the data is especially important when the model is used to extrapolate beyond the observed follow-up period.
Covariates are included to estimate how measured characteristics relate to the time-to-event outcome. Their effects are fitted alongside the distribution parameters, allowing the model to produce risk estimates that differ between individuals. In applied research, this supports individualized prognosis and helps quantify how observed characteristics are associated with survival or event timing.
A fitted model can provide survival probabilities, hazard functions, median event times, and individual risk estimates. These outputs describe both the chance of remaining event-free over time and the event rate represented by the hazard. Together, they support interpretation of prognosis, comparison of expected event timing, and communication of model-based outcomes.
A typical workflow identifies event times, records which observations are right-censored, selects a candidate distribution such as Weibull or log-normal, and estimates distribution parameters through the likelihood. Researchers can then include covariates, obtain survival or risk estimates, and use the fitted model for the intended prognosis, treatment, reliability, or extrapolation task.
They are useful when researchers need estimates beyond the period directly covered by the data, such as longer-term survival or failure patterns. The fitted distribution supplies the continuation of the event-time model after follow-up ends. This extrapolation is informative only when the chosen distributional assumptions are appropriate, so the resulting predictions depend on that modeling choice.