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If the probabilities of the event in each of the groups are p 1 first group and p 2 second group , then the odds ratio is:.

An odds ratio of 1 indicates that the condition or event under study is equally likely to occur in both groups. An odds ratio greater than 1 indicates that the condition or event is more likely to occur in the first group.

And an odds ratio less than 1 indicates that the condition or event is less likely to occur in the first group. The odds ratio must be nonnegative if it is defined.

It is undefined if p 2 q 1 equals zero, i. The odds ratio can also be defined in terms of the joint probability distribution of two binary random variables.

The joint distribution of binary random variables X and Y can be written. However note that in some applications the labeling of categories as zero and one is arbitrary, so there is nothing special about concordant versus discordant values in these applications.

Other measures of effect size for binary data such as the relative risk do not have this symmetry property. In this case, the odds ratio equals one, and conversely the odds ratio can only equal one if the joint probabilities can be factored in this way.

Thus the odds ratio equals one if and only if X and Y are independent. If the odds ratio R differs from 1, then.

Once we have p 11 , the other three cell probabilities can easily be recovered from the marginal probabilities. Suppose that in a sample of men, 90 drank wine in the previous week, while in a sample of women only 20 drank wine in the same period.

The odds of a man drinking wine are 90 to 10, or 9: The detailed calculation is:. This example also shows how odds ratios are sometimes sensitive in stating relative positions: The logarithm of the odds ratio, the difference of the logits of the probabilities , tempers this effect, and also makes the measure symmetric with respect to the ordering of groups.

One approach to inference uses large sample approximations to the sampling distribution of the log odds ratio the natural logarithm of the odds ratio.

If we use the joint probability notation defined above, the population log odds ratio is. If we observe data in the form of a contingency table.

The sample log odds ratio is. The distribution of the log odds ratio is approximately normal with:. The standard error for the log odds ratio is approximately.

This is an asymptotic approximation, and will not give a meaningful result if any of the cell counts are very small. An alternative approach to inference for odds ratios looks at the distribution of the data conditionally on the marginal frequencies of X and Y.

An advantage of this approach is that the sampling distribution of the odds ratio can be expressed exactly. Logistic regression is one way to generalize the odds ratio beyond two binary variables.

Suppose we have a binary response variable Y and a binary predictor variable X , and in addition we have other predictor variables Z 1 , If we use multiple logistic regression to regress Y on X , Z 1 , Specifically, at the population level.

In many settings it is impractical to obtain a population sample, so a selected sample is used. In this situation, our data would follow the following joint probabilities:.

This shows that the odds ratio and consequently the log odds ratio is invariant to non-random sampling based on one of the variables being studied.

Note however that the standard error of the log odds ratio does depend on the value of f. In both these settings, the odds ratio can be calculated from the selected sample, without biasing the results relative to what would have been obtained for a population sample.

Due to the widespread use of logistic regression , the odds ratio is widely used in many fields of medical and social science research. The odds ratio is commonly used in survey research , in epidemiology , and to express the results of some clinical trials , such as in case-control studies.

It is often abbreviated "OR" in reports. When data from multiple surveys is combined, it will often be expressed as "pooled OR". In clinical studies, as well as in some other settings, the parameter of greatest interest is often the relative risk rather than the odds ratio.

If the absolute risk in the control group is available, conversion between the two is calculated by: Odds ratios have often been confused with relative risk in medical literature.

For non-statisticians, the odds ratio is a difficult concept to comprehend, and it gives a more impressive figure for the effect.

This may reflect the simple process of uncomprehending authors choosing the most impressive-looking and publishable figure.

This is known as the 'invariance of the odds ratio'. In contrast, the relative risk does not possess this mathematical invertible property when studying disease survival vs.

This phenomenon of OR invertibility vs. RR non-invertibility is best illustrated with an example:. As one can see, a RR of 0. In contrast, an OR of 0.

This is again what is called the 'invariance of the odds ratio', and why a RR for survival is not the same as a RR for risk, while the OR has this symmetrical property when analyzing either survival or adverse risk.

The danger to clinical interpretation for the OR comes when the adverse event rate is not rare, thereby exaggerating differences when the OR rare-disease assumption is not met.

On the other hand, when the disease is rare, using a RR for survival e. When one or more of the cells in the contingency table can have a small value, the sample odds ratio can be biased and exhibit high variance.

A number of alternative estimators of the odds ratio have been proposed to address this issue. One alternative estimator is the conditional maximum likelihood estimator, which conditions on the row and column margins when forming the likelihood to maximize as in Fisher's exact test.

The following four contingency tables contain observed cell counts, along with the corresponding sample odds ratio OR and sample log odds ratio LOR:.

The following joint probability distributions contain the population cell probabilities, along with the corresponding population odds ratio OR and population log odds ratio LOR:.

From Wikipedia, the free encyclopedia. A method of correcting the odds ratio in cohort studies of common outcomes".

A method to directly estimate risk ratios in cohort studies of common outcomes". European Journal of Epidemiology. Improving the understanding of risk reporting".

The British Journal of General Practice. Use and misuse of the odds ratio". Researchers looking precisely at the etiological factors linked with ODD are limited.

The literature often examines common risk factors linked with all disruptive behaviours, rather than specifically about ODD. Symptoms of ODD are also often believed to be the same as CD even though the disorders have their own respective set of symptoms.

When looking at disruptive behaviours such as ODD, research has shown that the causes of behaviours are multifactorial. However, disruptive behaviours have been identified as being mostly due either to biological or environmental factors.

Research indicates that parents pass on a tendency for externalizing disorders to their children that may be displayed in multiple ways, such as inattention, hyperactivity, or oppositional and conduct problems.

Research has also shown that there is a genetic overlap between ODD and other externalizing disorders. Heritability can vary by age, age of onset, and other factors.

ODD also tends to occur in families with a history of ADHD , substance use disorders , or mood disorders , suggesting that a vulnerability to develop ODD may be inherited.

A difficult temperament, impulsivity, and a tendency to seek rewards can also increase the risk of developing ODD. New studies into gene variants have also identified possible gene-environment G x E interactions, specifically in the development of conduct problems.

A variant of the gene that encodes the neurotransmitter metabolizing enzyme monoamine oxidase-A MAOA , which relates to neural systems involved in aggression, plays a key role in regulating behavior following threatening events.

Brain imaging studies show patterns of arousal in areas of the brain that are associated with aggression in response to emotion-provoking stimuli.

Many pregnancy and birth problems are related to the development of conduct problems. Malnutrition, specifically protein deficiency, lead poisoning or exposure to lead, [11] and mother's use of alcohol or other substances during pregnancy may increase the risk of developing ODD.

In numerous research, substance abuse prior to birth have also been associated with developing disruptive behaviours such as ODD.

Deficits and injuries to certain areas of the brain can lead to serious behavioral problems in children. Brain imaging studies have suggested that children with ODD may have subtle differences in the part of the brain responsible for reasoning, judgment and impulse control.

The BIS produces anxiety and inhibits ongoing behavior in the presence of novel events, innate fear stimuli, and signals of nonreward or punishment.

Neuroimaging studies have also identified structural and functional brain abnormalities in several brain regions in youths with conduct disorders.

These brain regions are the amygdala, prefrontal cortex, anterior cingulate, and insula, as well as interconnected regions. As many as 40 percent of boys and 25 percent of girls with persistent conduct problems display significant social-cognitive impairments.

Some of these deficits include immature forms of thinking such as egocentrism , failure to use verbal mediators to regulate his or her behavior, and cognitive distortions, such as interpreting a neutral event as an intentional hostile act.

In fact, students with ODD have limited social knowledge that is only based on individual experiences that shapes how they process information and solve problems cognitively.

This information can be linked with the social information processing model SIP that describes how children process information in order to respond appropriately or inappropriately in social settings.

This model explains that children will go through five stages before displaying behaviors: However, children with ODD have cognitive distortions and impaired cognitive processes.

This will therefore directly impact their interactions and relationship negatively. It has been shown that social and cognitive impairments result in negative peer relationships, loss of friendship and an interruption in socially engaging in activities.

Children learn through observational learning and social learning. Therefore, observations of models have a direct impact and greatly influence children's behaviors and decision-making processes.

Children often learn through modeling behavior. Negative parenting practices and parent—child conflict may lead to antisocial behaviour, but they may also be a reaction to the oppositional and aggressive behaviors of children.

Insecure parent—child attachments can also contribute to ODD. Often little internalization of parent and societal standards exists in children with conduct problems.

These weak bonds with their parents may lead children to associate with delinquency and substance abuse. Family instability and stress can also contribute to the development of ODD.

Although the association between family factors and conduct problems is well established, the nature of this association and the possible causal role of family factors continues to be debated.

In a number of studies, low socioeconomic status has also been associated with disruptive behaviours such as ODD. Other social factors such as neglect, abuse, uninvolved parents and lack of supervision can also contribute to ODD.

Externalizing problems are reported to be more frequent among minority-status youth, a finding that is likely related to economic hardship, limited employment opportunities, and living in high-risk urban neighbourhoods.

For a child or adolescent to qualify for a diagnosis of ODD, behaviours must cause considerable distress for the family or interfere significantly with academic or social functioning.

Interference might take the form of preventing the child or adolescent from learning at school or making friends, or placing him or her in harmful situations.

These behaviours must also persist for at least six months. Approaches to the treatment of ODD include parent management training , individual psychotherapy , family therapy , cognitive behavioral therapy , and social skills training.

Psychopharmacological treatment is the use of prescribed medication in managing oppositional defiant disorder. Prescribed medication to control ODD include mood stabilizers , antipsychotics, and stimulants.

In two controlled randomized trials, it was found that between administered lithium and the placebo group, administering lithium decreased aggression in children with conduct disorder in a safe manner.

However, in a third study it found the treatment of lithium over a period of two weeks invalid. Effectiveness of drug and medication treatment is not well established.

Affects that can result in taking these medications include hypotension , extrapyramidal symptoms , tardive dyskinesia , obesity , and increase in weight.

Psychopharmacological treatment is found to be most effective when paired with another treatment plan, such as individual intervention or multimodal intervention.

Individual interventions are focused on child specific individualized plans. Anger control and stress inoculation helps prepare the child for possible upsetting situations or events that may cause anger and stress.

It includes a process of steps they may go through. Assertiveness training educates individuals in keeping balance between passivity and aggression.

It is about creating a response that is controlled, and fair. Child- focused problem solving skills training program aims to teach the child new skills and cognitive processes that teach how deal with negative thoughts, feelings and actions.

According to randomized trials evidence shows that parent management training is most effective.

Parent-child interaction training is intended to coach the parents while involving the child. This training has two phases. The first phase being child-directed interaction, whereby it is focused on teaching the child non directive play skills.

The second phase is parent directed interaction, where the parents are coached on aspects including clear instruction, praise for compliance, and time-out noncompliance.

The parent-child interaction training is best suited for elementary aged children. Parent and family treatment has a low financial cost, that can yield an increase in beneficial results.

Multimodal intervention is an effective treatment that looks at different levels including family, peers, school, and neighbourhood.

It is an intervention that concentrates on multiple risk factors. The focus is on parent training, classroom social skills, and playground behaviour program.

The intervention is intensive and addresses barriers to individuals improvement such as parental substance abuse or parental marital conflict.

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