Survival analysisSurvival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysis in engineering, duration analysis or duration modelling in economics, and event history analysis in sociology.
Survival functionThe survival function is a function that gives the probability that a patient, device, or other object of interest will survive past a certain time. The survival function is also known as the survivor function or reliability function. The term reliability function is common in engineering while the term survival function is used in a broader range of applications, including human mortality. The survival function is the complementary cumulative distribution function of the lifetime.
Special functionsSpecial functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by consensus, and thus lacks a general formal definition, but the list of mathematical functions contains functions that are commonly accepted as special. Many special functions appear as solutions of differential equations or integrals of elementary functions.
Mathematical analysisAnalysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).
Functional analysisFunctional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, inner product, norm, or topology) and the linear functions defined on these spaces and suitably respecting these structures. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining, for example, continuous or unitary operators between function spaces.
Proportional hazards modelProportional hazards models are a class of survival models in statistics. Survival models relate the time that passes, before some event occurs, to one or more covariates that may be associated with that quantity of time. In a proportional hazards model, the unique effect of a unit increase in a covariate is multiplicative with respect to the hazard rate. For example, taking a drug may halve one's hazard rate for a stroke occurring, or, changing the material from which a manufactured component is constructed may double its hazard rate for failure.
Cause of deathIn law, medicine, and statistics, cause of death is an official determination of the conditions resulting in a human's death, which may be recorded on a death certificate. A cause of death is determined by a medical examiner. In rare cases, an autopsy needs to be performed by a pathologist. The cause of death is a specific disease or injury, in contrast to the manner of death, which is a small number of categories like "natural", "accident", "suicide", and "homicide", each with different legal implications.
Manner of deathIn many legal jurisdictions, the manner of death is a determination, typically made by the coroner, medical examiner, police, or similar officials, and recorded as a vital statistic. Within the United States and the United Kingdom, a distinction is made between the cause of death, which is a specific disease or injury, versus manner of death, which is primarily a legal determination versus the mechanism of death (also called the mode of death) which does not explain why the person died or the underlying cause of death and can include cardiac arrest or exsanguination.
Cell deathCell death is the event of a biological cell ceasing to carry out its functions. This may be the result of the natural process of old cells dying and being replaced by new ones, as in programmed cell death, or may result from factors such as diseases, localized injury, or the death of the organism of which the cells are part. Apoptosis or Type I cell-death, and autophagy or Type II cell-death are both forms of programmed cell death, while necrosis is a non-physiological process that occurs as a result of infection or injury.
Irritable bowel syndromeIrritable bowel syndrome (IBS) is a "disorder of gut-brain interaction" characterized by a group of symptoms that commonly include abdominal pain, abdominal bloating and changes in the consistency of bowel movements. These symptoms may occur over a long time, sometimes for years. IBS can negatively affect quality of life and may result in missed school or work or reduced productivity at work. Disorders such as anxiety, major depression, and chronic fatigue syndrome are common among people with IBS.
