Multivariate Survival Models
Multivariate Survival Models - Related Videos
06:35
Basics of Multivariate Analysis in Neuroimaging Data
0 Views •
Cited by 37 •
2010
The current article describes the basics of multivariate analysis and contrasts it to the more commonly used voxel-wise univariate analysis. Both types of analysis are applied to a clinical-neuroscience data set. Supplementary split-half simulations show better replication of the multivariate results in independent data sets.
13:51
Cross-Modal Multivariate Pattern Analysis
0 Views •
Cited by 5 •
2011
Classical multivariate pattern analysis predicts sensory stimuli a subject perceives from neural activity in the corresponding cortices (e.g. visual stimuli from activity in visual cortex). Here, we apply pattern analysis cross-modally and show that sound- and touch-implying visual stimuli can be predicted from activity in auditory and somatosensory cortices, respectively.
02:19
Modeling Aeromonas Pathogenesis in C. elegans Using a Survival Assay
0 Views •
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.
01:25
Limits of Multivariable Functions
0 Views •
2026
Limits of multivariable functions describe how a function behaves as its input approaches a particular point in the plane. In single-variable calculus, a limit examines the behavior of a function as the input approaches a number from two directions along a line. For functions of two variables, the situation is more complex because the input can approach a point from infinitely many paths in the xy-plane. A limit exists only when the function approaches the same value along every possible...
01:30
Multivariable Functions and Higher Derivatives
0 Views •
2026
A multivariable function assigns a single output value to each ordered set of independent inputs, thereby defining a surface in three-dimensional space. For a function f(x, y), each point (x, y) corresponds to a height z = f(x, y). This geometric interpretation allows systematic analysis of how the output varies as multiple variables change simultaneously. Such functions frequently arise in physical models and optimization problems, where system behavior depends on several interacting...
FAQs
Shared frailty terms represent unobserved risk factors common to related observations, such as members of a family or paired organs. Outcomes exposed to the same frailty become statistically associated because their event risks shift together. Including this shared component can separate covariate effects from cluster-level risk and provide more appropriate inference than assuming each time-to-event outcome is independent.
Correlated random effects describe dependence through jointly varying latent quantities associated with individuals or clusters. Copulas instead connect the separate distributions of event times into a joint distribution, allowing the dependence structure to be modeled explicitly. The choice affects how researchers represent association among outcomes and how they estimate joint survival probabilities or event-risk relationships.
Separate survival analyses treat outcomes as independent, so they may overlook risk shared across family members, paired organs, recurrent events, or clustered observations. Ignoring that dependence can affect estimated covariate effects, survival probabilities, and uncertainty. A multivariate approach preserves information about how event times are related, potentially revealing risk patterns that separate models do not show.
Researchers first identify the related time-to-event outcomes, relevant covariates, and the source of dependence, such as shared individuals, clusters, or underlying risk factors. They then select a suitable structure, including shared frailty, correlated random effects, a copula, or a hierarchical model. The analysis incorporates censoring and estimates covariate effects, survival probabilities, and relationships among event risks.
They are preferable when several event times are connected rather than independent. Examples include familial disease studies, paired organs, recurrent events, reliability systems, and longitudinal clinical research. Modeling the outcomes jointly is especially relevant when the scientific question concerns shared risk or the association between event times, because the dependence itself may carry important statistical and substantive information.
Depending on the model structure, researchers can estimate covariate effects while accounting for dependence, calculate survival probabilities for related outcomes, and characterize relationships among event risks. These results support interpretation of shared or cluster-level patterns rather than isolated event times. In clinical and longitudinal research, the joint analysis can therefore expose associations that remain hidden in separate survival models.