The hazard rate, also known as the hazard function or failure rate, is a statistical measure used to describe the instantaneous rate at which an event occurs, given that the event has not yet happened. From a probabilistic perspective, it represents the likelihood that a subject will experience the event in a very small time interval, conditional on surviving up to the beginning of that interval. In terms of frequency, the hazard rate can be viewed as the ratio of the number of events to the...

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...

When a ligand binds to a cell-surface receptor, the receptor's intracellular domain changes shape, which may either activate its enzyme function or allow its binding to other molecules. The initial signal is amplified by most signal transduction pathways. This means that a single ligand molecule can activate multiple molecules of a downstream target. Proteins that relay a signal are most commonly phosphorylated at one or more sites, activating or inactivating the protein. Kinases catalyze...

Mitogen-activated protein kinase, or MAPK pathway, activates three sequential kinases to regulate cellular responses such as proliferation, differentiation, survival, and apoptosis. The canonical MAPK pathway starts with a mitogen or growth factor binding to an RTK. The activated RTKs stimulate Ras, which recruits Raf or MAP3 Kinase (MAPKKK), the first kinase of the MAPK signaling cascade. Raf further phosphorylates and activates MEK or MAP2 Kinases (MAPKK), which in turn phosphorylates MAP...