In epidemiology, risk ratio (RR) or relative risk is the ratio of the probability of an outcome in an exposed group to the probability of an outcome in an unexposed group. It is computed as , where is the incidence in the exposed group, and is the incidence in the unexposed group.^{[1]} Together with risk difference and odds ratio, risk ratio measures the association between the exposure and the outcome.^{[2]}
Risk ratio is used in the statistical analysis of the data of experimental, cohort and crosssectional studies, to estimate the strength of the association between treatments or risk factors, and outcome.^{[2]}^{[3]} For example, it is used to compare the risk of an adverse outcome when receiving a medical treatment versus no treatment (or placebo), or when exposed to an environmental risk factor versus not exposed.
Assuming the causal effect between the exposure and the outcome, values of RR can be interpreted as follows:
Risk ratio is commonly used to present the results of randomized controlled trials.^{[4]} This can be problematic, if risk ratio is presented without the absolute measures, such as absolute risk, or risk difference.^{[5]} In the case when the base rate of the outcome is low, large or small values of risk ratio may not translate to significant effect, and the importance of the effect to the public health can be overestimated. Equivalently, in the case when the base rate of the outcome is high, values of the risk ratio close to 1 may still result in a significant effect and can be underestimated. Thus, presentation of both absolute and relative measures is recommended.^{[6]}
Risk ratio can be estimated from a 2x2 contingency table:
Group  

Experimental (E)  Control (C)  
Events (E)  EE  CE 
Nonevents (N)  EN  CN 
The point estimate of the risk ratio is
The sampling distribution of the is approximately normal,^{[7]} with standard error
The confidence interval for the is then
where is the standard score for the chosen level of significance^{[8]}^{[9]}. To find the confidence interval around the RR itself, the two bounds of the above confidence interval can be exponentiated.^{[8]}
In regression models, the exposure is typically included as an indicator variable along with other factors that may affect risk. The risk ratio is usually reported as calculated for the mean of the sample values of the explanatory variables.
Risk ratio is different from the odds ratio, although it asymptotically approaches it for small probabilities of outcomes. If EE is substantially smaller than EN, then EE/(EE + EN) EE/EN. Similarly, if CE is much smaller than CN, then CE/(CN + CE) CE/CN. Thus, under the rare disease assumption
In epidemiological research, the odds ratio is commonly used for casecontrol studies, as the risk ratio cannot be estimated.^{[2]}
In fact, the odds ratio has much broader use in statistics, since logistic regression, often associated with clinical trials, works with the log of the odds ratio, not risk ratio. Because the (natural log of the) odds of a record is estimated as a linear function of the explanatory variables, the estimated odds ratio for 70yearolds and 60yearolds associated with the type of treatment would be the same in logistic regression models where the outcome is associated with drug and age, although the risk ratio might be significantly different. In cases like this, statistical models of the odds ratio often reflect the underlying mechanisms more efficiently.
Since risk ratio is a more intuitive measure of effectiveness, the distinction is important especially in cases of medium to high probabilities. If action A carries a risk of 99.9% and action B a risk of 99.0% then the risk ratio is just over 1, while the odds associated with action A are more than 10 times higher than the odds with B.
In statistical modelling, approaches like poisson regression (for counts of events per unit exposure) have risk ratio interpretations: the estimated effect of an explanatory variable is multiplicative on the rate and thus leads to a risk ratio. Logistic regression (for binary outcomes, or counts of successes out of a number of trials) must be interpreted in oddsratio terms: the effect of an explanatory variable is multiplicative on the odds and thus leads to an odds ratio.
We could assume a disease noted by , and no disease noted by , exposure noted by , and no exposure noted by . Risk ratio can be written as
This way the risk ratio can be interpreted in Bayesian terms as the posterior ratio of the exposure (i.e. after seeing the disease) normalized by the prior ratio of exposure.^{[10]} If the posterior ratio of exposure is similar to that of the prior, the effect is approximately 1, indicating no association with the disease, since it didn't change beliefs of the exposure. If on the other hand, the posterior ratio of exposure is smaller or higher than that of the prior ratio, then the disease has changed the view of the exposure danger, and the magnitude of this change is the risk ratio.
Example of risk reduction  

Experimental group (E)  Control group (C)  Total  
Events (E)  EE = 15  CE = 100  115 
Nonevents (N)  EN = 135  CN = 150  285 
Total subjects (S)  ES = EE + EN = 150  CS = CE + CN = 250  400 
Event rate (ER)  EER = EE / ES = 0.1, or 10%  CER = CE / CS = 0.4, or 40% 
Equation  Variable  Abbr.  Value 

CER  EER  absolute risk reduction  ARR  0.3, or 30% 
(CER  EER) / CER  relative risk reduction  RRR  0.75, or 75% 
1 / (CER − EER)  number needed to treat  NNT  3.33 
EER / CER  risk ratio  RR  0.25 
(EE / EN) / (CE / CN)  odds ratio  OR  0.167 
(CER  EER) / CER  preventable fraction among the unexposed  PFu  0.75 
In epidemiology, attributable fraction among the exposed (AF_{e}) is the proportion of incidents in the exposed group that are attributable to the risk factor. Term attributable risk percent among exposed is used if the fraction is expressed as a percentage. It is calculated as , where is the incidence in the exposed group, is the incidence in the unexposed group, and is the relative risk.
It is used when an exposure increases the risk, as opposed to reducing it, in which case its symmetrical notion is preventable fraction among the unexposed.
Big betA big bet (BB) is the larger of two fixed bet amounts in a fixedlimit poker game. A big bet is used in the final rounds of a game to increase the pot amount and thereby enable the possibility of a bluff. Big bets are generally double the wager of the initial or small bet. Any multiround poker game can use big bets to standardize wagers while maintaining a sufficient riskratio to encourage bluffing. Casino poker tables use big bets to set a limit to the amount of money a patron can lose in each wager.
Capital asset pricing modelIn finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a welldiversified portfolio.
Crosssectional studyIn medical research and social science, a crosssectional study (also known as a crosssectional analysis, transverse study, prevalence study) is a type of observational study that analyzes data from a population, or a representative subset, at a specific point in time—that is, crosssectional data.
In economics, crosssectional studies typically involve the use of crosssectional regression, in order to sort out the existence and magnitude of causal effects of one or more independent variables upon a dependent variable of interest at a given point in time. They differ from time series analysis, in which the behavior of one or more economic aggregates is traced through time.
In medical research, crosssectional studies differ from casecontrol studies in that they aim to provide data on the entire population under study, whereas casecontrol studies typically include only individuals with a specific characteristic, with a sample, often a tiny minority, of the rest of the population. Crosssectional studies are descriptive studies (neither longitudinal nor experimental). Unlike casecontrol studies, they can be used to describe, not only the odds ratio, but also absolute risks and relative risks from prevalences (sometimes called prevalence risk ratio, or PRR). They may be used to describe some feature of the population, such as prevalence of an illness, or they may support inferences of cause and effect. Longitudinal studies differ from both in making a series of observations more than once on members of the study population over a period of time.
Forensic epidemiologyThe discipline of forensic epidemiology (FE) is a hybrid of principles and practices common to both forensic medicine and epidemiology. FE is directed at filling the gap between clinical judgment and epidemiologic data for determinations of causality in civil lawsuits and criminal prosecution and defense.Forensic epidemiologists formulate evidencebased probabilistic conclusions about the type and quantity of causal association between an antecedent harmful exposure and an injury or disease outcome in both populations and individuals. The conclusions resulting from an FE analysis can support legal decisionmaking regarding guilt or innocence in criminal actions, and provide an evidentiary support for findings of causal association in civil actions.
Applications of forensic epidemiologic principles are found in a wide variety of types of civil litigation, including cases of medical negligence, toxic or mass tort, pharmaceutical adverse events, medical device and consumer product failures, traffic crashrelated injury and death, person identification and life expectancy.
Monika SchäferKortingMonika SchäferKorting (born 7 May 1952 in Gießen) is a German Pharmacologist and Toxicologist.
NimesulideNimesulide is a nonsteroidal antiinflammatory drug (NSAID) with pain medication and fever reducing properties. Its approved indications are the treatment of acute pain, the symptomatic treatment of osteoarthritis, and primary dysmenorrhoea in adolescents and adults above 12 years old.
Side effects may include liver problems. It has a multifactorial mode of action and is characterized by a fast onset of action. It works by blocking the production of prostaglandins (a chemical associated with pain), thereby relieving pain and inflammation.
Number needed to harmThe number needed to harm (NNH) is an epidemiological measure that indicates how many persons on average need to be exposed to a risk factor over a specific period to cause harm in an average of one person who would not otherwise have been harmed. It is defined as the inverse of the absolute risk increase, and computed as , where is the incidence in the treated (exposed) group, and is the incidence in the control (unexposed) group. Intuitively, the lower the number needed to harm, the worse the risk factor, with 1 meaning that every exposed person is harmed.
NNH is similar to number needed to treat (NNT), where NNT usually refers to a therapeutic intervention and NNH to a detrimental effect or a risk factor.
Odds ratioAn 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 A in the presence of B and the odds of A in the absence of B, or equivalently (due to symmetry), the ratio of the odds of B 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: 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. The OR plays an important role in the logistic model, which generalizes beyond two events.
Note that the odds ratio is symmetric in the two events, and there is no causal direction implied (correlation does not imply causation): a positive OR does not establish that B causes A, nor that A causes B. However, often the odds ratio is used asymmetrically to infer causality by comparing the occurrence of some outcome (A) in the presence of some exposure (B), with the occurrence of the outcome (A) in the absence of a particular exposure (absence of B).Two similar statistics that are often used to quantify associations are the risk ratio (RR) and the absolute risk reduction (ARR). Often, the parameter of greatest interest is actually the RR, which is the ratio of the probabilities analogous to the odds used in the OR. However, available data frequently do not allow for the computation of the RR or the ARR but do allow for the computation of the OR, as in casecontrol studies, as explained below. On the other hand, if one of the properties (A or B) is sufficiently rare (in epidemiology this is called the rare disease assumption), then the OR is approximately equal to the corresponding RR.
OpenEpiOpenEpi is a free, webbased, open source, operating systemindependent series of programs for use in epidemiology, biostatistics, public health, and medicine, providing a number of epidemiologic and statistical tools for summary data. OpenEpi was developed in JavaScript and HTML, and can be run in modern web browsers. The program can be run from the OpenEpi website or downloaded and run without a web connection. The source code and documentation is downloadable and freely available for use by other investigators. OpenEpi has been reviewed, both by media organizations and in research journals.The OpenEpi developers have had extensive experience in the development and testing of Epi Info, a program developed by the Centers for Disease Control and Prevention (CDC) and widely used around the world for data entry and analysis. OpenEpi was developed to perform analyses found in the DOS version of Epi Info modules StatCalc and EpiTable, to improve upon the types of analyses provided by these modules, and to provide a number of tools and calculations not currently available in Epi Info. It is the first step toward an entirely webbased set of epidemiologic software tools. OpenEpi can be thought of as an important companion to Epi Info and to other programs such as SAS, PSPP, SPSS, Stata, SYSTAT, Minitab, Epidata, and R (see the R programming language). Another functionally similar Windowsbased program is Winpepi. See also list of statistical packages and comparison of statistical packages. Both OpenEpi and Epi Info were developed with the goal of providing tools for low and moderate resource areas of the world. The initial development of OpenEpi was supported by a grant from the Bill and Melinda Gates Foundation to Emory University.The types of calculations currently performed by OpenEpi include:
Various confidence intervals for proportions, rates, standardized mortality ratio, mean, median, percentiles
2x2 crude and stratified tables for count and rate data
Matched casecontrol analysis
Test for trend with count data
Independent ttest and oneway ANOVA
Diagnostic and screening test analyses with receiver operating characteristic (ROC) curves
Sample size for proportions, crosssectional surveys, unmatched casecontrol, cohort, randomized controlled trials, and comparison of two means
Power calculations for proportions (unmatched casecontrol, crosssectional, cohort, randomized controlled trials) and for the comparison of two means
Random number generatorFor epidemiologists and other health researchers, OpenEpi performs a number of calculations based on tables not found in most epidemiologic and statistical packages. For example, for a single 2x2 table, in addition to the results presented in other programs, OpenEpi provides estimates for:
Etiologic or prevented fraction in the population and in exposed with confidence intervals, based on risk, odds, or rate data
The crossproduct and MLE odds ratio estimate
Midp exact pvalues and confidence limits for the odds ratio
Calculations of rate ratios and rate differences with confidence intervals and statistical tests.For stratified 2x2 tables with count data, OpenEpi provides:
MantelHaenszel (MH) and precisionbased estimates of the risk ratio and odds ratio
Precisionbased adjusted risk difference
Tests for interaction for the risk ratio, odds ratio, and risk difference
Four different confidence limit methods for the odds ratio.Similar to Epi Info, in a stratified analysis, both crude and adjusted estimates are provided so that the assessment of confounding can be made. With rate data, OpenEpi provides adjusted rate ratio’s and rate differences, and tests for interaction. Finally, with count data, OpenEpi also performs a test for trend, for both crude data and stratified data.
In addition to being used to analyze data by health researchers, OpenEpi has been used as a training tool for teaching epidemiology to students at: Emory University, University of Massachusetts, University of Michigan, University of Minnesota, Morehouse College, Columbia University, University of Wisconsin, San Jose State University, University of Medicine and Dentistry of New Jersey, University of Washington, and elsewhere. This includes campusbased and distance learning courses. Because OpenEpi is easy to use, requires no programming experience, and can be run on the internet, students can use the program and focus on the interpretation of results. Users can run the program in English, French, Spanish, Portuguese or Italian.
Comments and suggestions for improvements are welcomed and the developers respond to user queries. The developers encourage others to develop modules that could be added to OpenEpi and provide a developer’s tool at the website. Planned future development include improvements to existing modules, development of new modules, translation into other languages, and add the ability to cut and paste data and/or read data files.
Preventable fraction among the unexposedIn epidemiology, preventable fraction among the unexposed (PFu), is the proportion of incidents in the unexposed group that could be prevented by exposure. It is calculated as , where is the incidence in the exposed group, is the incidence in the unexposed group, and is the relative risk. It is a synonym of the relative risk reduction.
It is used when an exposure reduces the risk, as opposed to increasing it, in which case its symmetrical notion is attributable fraction among the exposed.
Rachev ratioThe Rachev Ratio (or RRatio) is a riskreturn performance measure of an investment asset, portfolio, or strategy. It was devised by Dr. Svetlozar Rachev and has been extensively studied in quantitative finance. Unlike the rewardtovariability ratios, such as Sharpe ratio and Sortino ratio, the Rachev ratio is a rewardtorisk ratio, which is designed to measure the right tail reward potential relative to the left tail risk in a nonGaussian setting. Intuitively, it represents the potential for extreme positive returns compared to the risk of extreme losses (negative returns), at a rarity frequency q (quantile level) defined by the user.The ratio is defined as the Expected Tail Return (ETR) in the best q% cases divided by the Expected tail loss (ETL) in the worst q% cases. The ETL is the average loss incurred when losses exceed the Value at Risk at a predefined quantile level. The ETR, defined by symmetry to the ETL, is the average profit gained when profits exceed the Profit at risk at a predefined quantile level.
For more tailored applications, the generalized Rachev Ratio has been defined with different powers and/or different confidence levels of the ETR and ETL.
Relative risk reductionIn epidemiology, the relative risk reduction (RRR) or efficacy is the relative decrease in the risk of an adverse event in the exposed group compared to an 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 adverse event is increased by the exposure rather than decreased, term relative risk increase (RRI) is used, and computed as . If the direction of risk change is not assumed, a term relative effect is used and computed as .
Risk differenceIn epidemiology, 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 .
The inverse of the absolute risk reduction is the number needed to treat, and the inverse of the absolute risk increase is the number needed to harm.
Risk management in Indian banksRisk management in Indian banks is a relatively newer practice, but has already shown to increase efficiency in governing of these banks as such procedures tend to increase the corporate governance of a financial institution. In times of volatility and fluctuations in the market, financial institutions need to prove their mettle by withstanding the market variations and achieve sustainability in terms of growth and well as have a stable share value. Hence, an essential component of risk management framework would be to mitigate all the risks and rewards of the products and service offered by the bank. Thus the need for an efficient risk management framework is paramount in order to factor in internal and external risks.The financial sector in various economies like that of India are undergoing a monumental change factoring into account world events such as the ongoing Banking Crisis across the globe. The 2007–present recession in the United States has highlighted the need for banks to incorporate the concept of Risk Management into their regular procedures. The various aspects of increasing global competition to Indian Banks by Foreign banks, increasing Deregulation, introduction of innovative products, and financial instruments as well as innovation in delivery channels have highlighted the need for Indian Banks to be prepared in terms of risk management.Indian Banks have been making great advancements in terms of technology, quality, as well as stability such that they have started to expand and diversify at a rapid rate. However, such expansion brings these banks into the context of risk especially at the onset of increasing Globalization and Liberalization. In banks and other financial institutions, risk plays a major part in the earnings of a bank. The higher the risk, the higher the return, hence, it is essential to maintain a parity between risk and return. Hence, management of Financial risk incorporating a set systematic and professional methods especially those defined by the Basel II becomes an essential requirement of banks. The more risk averse a bank is, the safer is their Capital base.
SidewalkA sidewalk (American English) or pavement (British English), also known as a footpath or footway, is a path along the side of a road. A sidewalk may accommodate moderate changes in grade (height) and is normally separated from the vehicular section by a curb. There may also be a median strip or road verge (a strip of vegetation, grass or bushes or trees or a combination of these) either between the sidewalk and the roadway or between the sidewalk and the boundary.
In some places, the same term may also be used for a paved path, trail or footpath that is not next to a road, for example, a path through a park.
TipredaneTipredane (developmental code name SQ27239) is a synthetic glucocorticoid corticosteroid which was never marketed.
VerubecestatVerubecestat (MK8931) is an experimental drug for the treatment of Alzheimer's disease. It is an inhibitor of betasecretase 1 (BACE1).In April 2012 phase I clinical results were announced. Phase 1b results have also been reported.As of December 2016 it was in two phase 2/3 clinical trials that have progressed to phase 3. EPOCH, was to complete data collection for the primary outcome measure by June 2017. However, in February 2017 Merck halted its latestage trial of verubecestat for mild to moderate Alzheimer's disease after it was reported as having "virtually no chance of finding a positive clinical effect" according to an independent panel of experts. The results of Merck's trial of verubecestat on patients with prodromal (early stage) Alzheimer's were expected in February 2019. However, the trial was terminated in February 2018, after a data monitoring committee concluded it was unlikely that the drug would show a positive benefit/risk ratio. The final conclusion was that "verubecestat did not reduce cognitive or functional decline in patients with mildtomoderate Alzheimer’s disease and was associated with treatmentrelated adverse events".
Överkalix studyThe Överkalix study (Swedish: Överkalixstudien) was a study conducted on the physiological effects of various environmental factors on transgenerational epigenetic inheritance. The study was conducted utilizing historical records, including harvests and food prices, in Överkalix, a small isolated municipality in northeast Sweden. The study was of 303 probands, 164 men and 139 women, born in 1890, 1905, or 1920, and their 1,818 children and grandchildren. 44 were still alive in 1995 when mortality followup stopped. Mortality risk ratios (RR) on children and grandchildren were determined based on available food supply, as indicated by historical data.
Among the sexspecific effects noted; a greater body mass index (BMI) at 9 years in sons, but not daughters, of fathers who began smoking early. The paternal grandfather's food supply was only linked to the mortality RR of grandsons and not granddaughters. The paternal grandmother's food supply was only associated with the granddaughters' mortality risk ratio. The grandmother having a good food supply was associated with a twofold higher mortality (RR).
This transgenerational inheritance was observed with exposure during the slow growth period (SGP). The SGP is the time before the start of puberty, when environmental factors have a larger impact on the body. The ancestors' SGP in this study, was set between the ages of 912 for boys and 8–10 years for girls. This occurred in the SGP of both grandparents, or during the gestation period/infant life of the grandmothers, but not during either grandparent's puberty. The father's poor food supply and the mother's good food supply were associated with a lower risk of cardiovascular death.Only the female probands experienced a twofold higher mortality RR when the paternal grandmother had good food availability during her SGP, compared to the mortality risk of those whose paternal grandmothers had poor food supply during the SGP.
Using the same data, another investigation highlighted that a sharp change in food availability in paternal grandmothers' resulted in an increased risk of cardiovascular mortality in granddaughters adults' life. Such an effect was not observed in other grandparents. The grandparents were considered exposed if they experienced drastic change in their early life ranging from embryo to 13 years old.
Sexspecific effects can be due to parental imprinting a process that results in allelespecific differences in transcription, DNA methylation, and DNA replication timing. Imprinting is an important process in human development, and its deregulation can cause certain defined disease states of other imprinted human disease loci. The establishment of parental imprints occurs during gametogenesis as homologous DNA passes through sperm or egg; subsequently during embryogenesis and into adulthood, alleles of imprinted genes are maintained in two "conformational"/epigenetic states: paternal or maternal. Thus, genomic imprints template their own replication, are heritable, can be identified by molecular analysis, and serve as markers of the parental origin of genomic regions.
The estimation of percentage of human genes subject to parental imprinting is approximately one to two percent, currently parental imprinting has been identified in fewer than 100 distinct named genes.
Overview  

Controlled study (EBM I to II1; A to B)  
Observational study (EBM II2 to II3; B to C)  
Measures 
 
Trial/test types  
Analysis of clinical trials  
Interpretation of results  

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