Cox Proportional Hazards
Cox Proportional Hazards - Related Videos
10:26
Imaging Neurons within Thick Brain Sections Using the Golgi-Cox Method
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Cited by 10 •
2017
We present a protocol for using the Golgi-Cox staining method in thick brain sections, in order to visualize neurons with long dendritic trees contained within single tissue samples. Two variants of this protocol are also presented that involve cresyl violet counterstaining, and the freezing of unprocessed brains for long-term storage.
01:20
Sample Proportion and Population Proportion
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2023
Collecting samples or responses from an entire population takes significant time and effort, so a researcher collects responses from only a sample of that population. Suppose a study needs to collect information about a specific mobile application. After sample collection, the researcher analyzes the data and discovers that most individuals in the sample use that specific mobile application. The sample proportion measures the number of individuals in a sample who either use or don't use the...
06:53
Visualization of Mitochondrial Respiratory Function using Cytochrome C Oxidase / Succinate Dehydrogenase (COX/SDH) Double-labeling Histochemistry
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Cited by 82 •
2011
The cytochrome c oxidase/sodium dehydrogenase (COX/SDH) double-labeling method allows for direct visualization of mitochondrial respiratory enzyme deficiencies in fresh-frozen tissue sections. This is a straightforward histochemical technique and is useful in investigating mitochondrial diseases, aging, and aging-related disorders.
01:12
Hazard Ratio
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2025
The hazard ratio (HR) is a widely used measure in clinical trials to compare the risk of events, such as death or disease recurrence, between two groups over time. It reflects the ratio of hazard rates—the instantaneous risk of the event occurring—between a treatment group and a control group. This measure provides valuable insights into the relative effectiveness of a treatment by assessing how the risk of an event differs between the two groups. For example, in a clinical trial evaluating a...
01:19
Moral Hazard
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2025
Moral hazards arise due to information asymmetry between buyers and sellers in a market. This occurs when one party cannot monitor the actions of the other. The emphasis on actions is important because moral hazard specifically results from the behavior of the party whose actions are not fully observable. In such situations, the party whose actions are not entirely observable may act less cautiously than they otherwise would, knowing their actions are only partially observed. This leaves the...
FAQs
A hazard ratio compares the instantaneous event risk associated with different values of a predictor, while accounting for other variables in the model. A value above one indicates higher estimated hazard, whereas a value below one indicates lower estimated hazard. Interpretation depends on the predictor’s measurement scale and the model’s assumption that the hazard ratio remains constant over time.
Leaving the baseline hazard unspecified makes the model semiparametric rather than fully parametric. The analysis can estimate covariate effects without requiring a particular mathematical form for how baseline event risk changes over time. Partial likelihood then focuses on estimating regression parameters from the observed event ordering and risk comparisons, rather than first specifying the baseline hazard.
The proportional hazards assumption requires the hazard ratio between individuals or groups to remain constant over time. This means a predictor should have a consistent relative association with event risk throughout the observation period. If that relationship changes over time, a single hazard ratio may not adequately summarize the predictor’s effect, limiting the model’s appropriateness for that analysis.
Adding covariates allows the model to estimate associations between predictors and event timing while accounting for other measured factors. This supports comparisons between treatment groups or individuals with differing prognostic characteristics and can help adjust for confounding variables. The resulting hazard ratios describe each predictor’s association in the context of the other covariates included in the model.
An analysis begins by identifying the event time, recording whether each observation experienced the event or was censored, and selecting relevant predictors. The model is then fitted using partial likelihood to estimate covariate effects, commonly reported as hazard ratios. Researchers interpret those estimates in relation to treatment, prognosis, or other factors affecting the timing of the event.
The method is useful when researchers need to compare how quickly events occur rather than analyze only whether an event occurred. Applications include evaluating treatment groups, studying prognostic factors, adjusting comparisons for confounding variables, and analyzing outcomes such as death or relapse. It can also address time-to-failure questions, including equipment failure, when observations are censored.