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Probability is the branch of mathematics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.
The word probability has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure the real, physical, tendency of something to occur, or is it a measure of how strongly one believes it will occur, or does it draw on both these elements? In answering such questions, mathematicians interpret the probability values of probability theory.
Uncertainty or incertitude refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or stochastic environments, as well as due to ignorance, indolence, or both. It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, finance, medicine, psychology, sociology, engineering, metrology, meteorology, ecology and information science.
In probability theory, odds provide a measure of the probability of a particular outcome. Odds are commonly used in gambling and statistics. For example for an event that is 40% probable, one could say that the odds are "2 in 5","2 to 3 in favor", or "3 to 2 against".
Risk assessment determines possible mishaps, their likelihood and consequences, and the tolerances for such events. The results of this process may be expressed in a quantitative or qualitative fashion. Risk assessment is an inherent part of a broader risk management strategy to help reduce any potential risk-related consequences.
In survival analysis, the hazard ratio (HR) is the ratio of the hazard rates corresponding to the conditions characterised by two distinct levels of a treatment variable of interest. For example, in a clinical study of a drug, the treated population may die at twice the rate of the control population. The hazard ratio would be 2, indicating a higher hazard of death from the treatment.
An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B. The odds ratio is defined as the ratio of the odds of event A taking place in the presence of B, and the odds of A in the absence of B. Due to symmetry, odds ratio reciprocally calculates the ratio of the odds of B occurring in the presence of A, and the odds of B in the absence of A. Two events are independent if and only if the OR equals 1, i.e., the odds of one event are the same in either the presence or absence of the other event. If the OR is greater than 1, then A and B are associated (correlated) in the sense that, compared to the absence of B, the presence of B raises the odds of A, and symmetrically the presence of A raises the odds of B. Conversely, if the OR is less than 1, then A and B are negatively correlated, and the presence of one event reduces the odds of the other event occurring.
The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Rational choice theory, a cornerstone of microeconomics, builds this postulate to model aggregate social behaviour.
A case–control study is a type of observational study in which two existing groups differing in outcome are identified and compared on the basis of some supposed causal attribute. Case–control studies are often used to identify factors that may contribute to a medical condition by comparing subjects who have the condition with patients who do not have the condition but are otherwise similar. They require fewer resources but provide less evidence for causal inference than a randomized controlled trial. A case–control study is often used to produce an odds ratio. Some statistical methods make it possible to use a case–control study to also estimate relative risk, risk differences, and other quantities.
In epidemiology, a risk factor or determinant is a variable associated with an increased risk of disease or infection.
The number needed to treat (NNT) or number needed to treat for an additional beneficial outcome (NNTB) is an epidemiological measure used in communicating the effectiveness of a health-care intervention, typically a treatment with medication. The NNT is the average number of patients who need to be treated to prevent one additional bad outcome. It is defined as the inverse of the absolute risk reduction, and computed as , where is the incidence in the control (unexposed) group, and is the incidence in the treated (exposed) group. This calculation implicitly assumes monotonicity, that is, no individual can be harmed by treatment. The modern approach, based on counterfactual conditionals, relaxes this assumption and yields bounds on NNT.
The relative risk (RR) or risk ratio is the ratio of the probability of an outcome in an exposed group to the probability of an outcome in an unexposed group. Together with risk difference and odds ratio, relative risk measures the association between the exposure and the outcome.
A hazard analysis is one of many methods that may be used to assess risk. At its core, the process entails describing a system object that intends to conduct some activity. During the performance of that activity, an adverse event may be encountered that could cause or contribute to an occurrence. Finally, that occurrence will result in some outcome that may be measured in terms of the degree of loss or harm. This outcome may be measured on a continuous scale, such as an amount of monetary loss, or the outcomes may be categorized into various levels of severity.
The risk difference (RD), excess risk, or attributable risk is the difference between the risk of an outcome in the exposed group and the unexposed group. It is computed as , where is the incidence in the exposed group, and is the incidence in the unexposed group. If the risk of an outcome is increased by the exposure, the term absolute risk increase (ARI) is used, and computed as . Equivalently, if the risk of an outcome is decreased by the exposure, the term absolute risk reduction (ARR) is used, and computed as .
Medical statistics deals with applications of statistics to medicine and the health sciences, including epidemiology, public health, forensic medicine, and clinical research. Medical statistics has been a recognized branch of statistics in the United Kingdom for more than 40 years, but the term has not come into general use in North America, where the wider term 'biostatistics' is more commonly used. However, "biostatistics" more commonly connotes all applications of statistics to biology. Medical statistics is a subdiscipline of statistics.
It is the science of summarizing, collecting, presenting and interpreting data in medical practice, and using them to estimate the magnitude of associations and test hypotheses. It has a central role in medical investigations. It not only provides a way of organizing information on a wider and more formal basis than relying on the exchange of anecdotes and personal experience, but also takes into account the intrinsic variation inherent in most biological processes.
In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value, often focusing on negative, undesirable consequences. Many different definitions have been proposed. One international standard definition of risk is the "effect of uncertainty on objectives".
Population impact measures (PIMs) are biostatistical measures of risk and benefit used in epidemiological and public health research. They are used to describe the impact of health risks and benefits in a population, to inform health policy.
Pre-test probability and post-test probability are the probabilities of the presence of a condition before and after a diagnostic test, respectively. Post-test probability, in turn, can be positive or negative, depending on whether the test falls out as a positive test or a negative test, respectively. In some cases, it is used for the probability of developing the condition of interest in the future.
The Effect Model law states that a natural relationship exists for each individual between the frequency (observation) or the probability (prediction) of a morbid event without any treatment and the frequency or probability of the same event with a treatment . This relationship applies to a single individual, individuals within a population, or groups. This law enables the prediction of the (absolute) benefit of a treatment for a given patient. It has wide-reaching implications in R&D for new pharmaceutical products as well as personalized medicine. The law was serendipitously discovered in the 1990s by Jean-Pierre Boissel. While studying the effectiveness of class-I antiarrhythmic drugs in the prevention of death after myocardial infarction, he stumbled upon a situation which contradicts one of the basic premises of meta-analysis theory, i.e. that the heterogeneity test was significant at the same time for the assumption “the relative risk is a constant” and “ is a constant”.
Risk aversion is a preference for a sure outcome over a gamble with higher or equal expected value. Conversely, rejection of a sure thing in favor of a gamble of lower or equal expected value is known as risk-seeking behavior.
References
- ↑ Porta, Miquel, ed. (2014). A dictionary of epidemiology (PDF) (Six ed.). Oxford: Oxford University Press. ISBN 9780199976720 . Retrieved 11 November 2017.
- ↑ Trevena, LJ; Davey, HM; Barratt, A; Butow, P; Caldwell, P (February 2006). "A systematic review on communicating with patients about evidence". Journal of Evaluation in Clinical Practice. 12 (1): 13–23. doi: 10.1111/j.1365-2753.2005.00596.x . PMID 16422776.