# Ratio Calculator

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However, this cannot be done if we start with the outcome and try to work back to the risk factor, as in a case-control study. Calculating a confidence interval provides you with an indication of how reliable your odds ratio is the wider the interval, the greater the uncertainty associated with your estimate. By changing the inputs the contingency table and confidence level in the Alternative Scenarios you can see how each input is related to the confidence interval.

The larger your sample size, the more certain you can be that the estimates reflect the population, so the narrower the confidence interval. However, the relationship is not linear, e. Choosing a sample size is an important aspect when designing your study or survey. The odds of an event occurring is calculated as the ratio of the probability of a property being present compared to the probability of it being absent; this is simply the number of times that the property is absent divided by the number of times it is absent.

The odds ratio is calculated by dividing the odds of the first group by the odds in the second group. In the case of the worked example, it is the ratio of the odds of lung cancer in smokers divided by the odds of lung cancer in non-smokers: If the odds ratio is greater than 1, then being a smoker is considered to be associated with having lung cancer since smoking raises the odds of having lung cancer.

The contingency table summarises the outcomes of each individual sampled in terms of whether Properties A and B are absent or present. It represents the joint frequency distribution of the two properties. The confidence level is the probability that the confidence interval contains the true odds ratio.

The higher the confidence level the more certain you can be that the interval contains the true odds ratio. Formula This calculator uses the following formulae to calculate the odds ratio or and its confidence interval ci. Discussion When the prevalence of the outcome is low, the odds ratio can be used to estimate the relative risk in a case-control study.

Definitions Odds and odds ratio The odds of an event occurring is calculated as the ratio of the probability of a property being present compared to the probability of it being absent; this is simply the number of times that the property is absent divided by the number of times it is absent. Contingency table The contingency table summarises the outcomes of each individual sampled in terms of whether Properties A and B are absent or present.

Confidence level The confidence level is the probability that the confidence interval contains the true odds ratio. One common use of the OR is in determination of the effect size of a difference in two drug interventions. As an example, consider the treatment of patients with endocarditis caused by Staphylococcus aureus SA. The question is this: What are the odds of dying with the new drug as opposed to the standard antibiotic therapy protocol?

The odds ratio is a way of comparing whether the odds of a certain outcome is the same for two different groups 9. The odds ratio is simply the ratio between the following two ratios: The ratio between standard treatment and the new drug for those who died, and the ratio between standard treatment and the new drug for those who survived.

From the data in the table 1, it is calculated as follows: The result is the same: The result of an odds ratio is interpreted as follows: The patients who received standard care died 3. Based on these results the researcher would recommend that all males aged 30 to 60 diagnosed with bacterial endocarditis caused by SA be prescribed the new drug. This recommendation assumes, of course, that the experience of side effects with the two categories of drugs is similar.

Severe side effects or development of allergic reactions to the new drug could change that recommendation. Results from fictional SA endocarditis treatment study. How other odds ratio results are interpreted: An OR of 1. An OR higher than 1 means that the first group in this case, standard care group was more likely to experience the event death than the second group.

An OR of less than 1 means that the first group was less likely to experience the event. However, an OR value below 1. The degree to which the first group is less likely to experience the event is not the OR result. It is important to put the group expected to have higher odds of the event in the first column. When the odds of the first group experiencing the event is less than the odds of the second group, one must reverse the two columns so that the second group becomes the first and the first group becomes the second.

Then it will be possible to interpret the difference because that reversal will calculate how many more times the second group experienced the event than the first. If we reverse the columns in the example above, the odds ratio is: Odds ratio in epidemiology studies.

In epidemiology studies, the researchers often use the odds ratio to determine post hoc if different groups had different outcomes on a particular measure. For example, Friese et al. Through use of the odds ratio, they discovered that use of the needle biopsy was associated with a reduced probability of multiple surgeries.

The odds ratio table for this study would have the following structure Table 2: Table format for epidemiology study. In this study, Friese et al. This table should have been changed because an OR value of 0. All that can be said is that the women who had an initial needle biopsy had fewer surgeries than women who did not have the biopsy.

The great value of the odds ratio is that it is simple to calculate, very easy to interpret, and provides results upon which clinical decisions can be made. Furthermore, it is sometimes helpful in clinical situations to be able to provide the patient with information on the odds of one outcome versus another. Patients may decide to accept or forego painful or expensive treatments if they understand what their odds are for obtaining a desired result from the treatment.

Many patients want to be involved in decisions about their treatment, but to be able to participate effectively, they must have information about their likely results in terms they can understand. At least in the industrialized world, most patients have received enough schooling to understand basic percentages and the meaning of probabilities.

The odds ratio provides information that both clinicians and their patients can use for decision-making. Odds ratios are one of a category of statistics clinicians often use to make treatment decisions.

Other statistics commonly used to make treatment decisions include risk assessment statistics such as absolute risk reduction and relative risk reduction statistics. The odds ratio supports clinical decisions by providing information on the odds of a particular outcome relative to the odds of another outcome. In the endocarditis example, the risk or odds of dying if treated with the new drug is relative to the risk odds of dying if treated with the standard treatment antibiotic protocol.

Relative risk assessment statistics are particularly suited to diagnostic and treatment decision-making and will be addressed in a future paper. Prevalence and factors associated with aflatoxin contamination of peanuts from Western Kenya. International Journal of Food Microbiology ; Dependence on the nicotine gum in former smokers. Effect of treatment and adherence on ethnic differences in blood pressure control among adults with hypertension.

Annals of Epidemiology ; Infective endocarditis in adults. New England Journal of Medicine ; Binomial distribution sample confidence intervals estimation: Downloaded on April 14, from:

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