Understanding relative risk, odds ratio, and related terms. Interpretation of odds and risk ratios, journal of. This work is licensed under a creative commons attribution. We propose a simple method to approximate a risk ratio from the adjusted odds ratio and derive an estimate of an association or treatment effect that better represents the true relative risk. Even when used appropriately, odds ratios are often difficult to interpret. Odds ratio and proportions calculator introduction the odds ratio tab of this procedure calculates any one of three parameters, odds ratio, p 1, or p 2, from the other two parameters. Which of the following would be the correct interpretation of this odds ratio. Chapter 525 mantelhaenszel test statistical software. Odds ratioscurrent best practice and use feinberg school of. When a logistic regression is calculated, the regression coefficient b1 is the estimated increase in the log odds of the outcome per unit increase in the value of the exposure. The ratio of two odds, the interpretation of the odds ratio may vary according to definition of odds and the situation under discussion. Creative commons attributionnoncommercialsharealike license.
What is an intuitive explanation of how log odds should be. The ratio of the probability of occurrence of an event to that of nonoccurrence. This video demonstrates how to calculate odds ratio and relative risk values using the statistical software program spss. In a cohort study, the odds ratio is expressed as the ratio of the number of. The more frequent the outcome, the more the odds ratio overestimates the risk ratio when it is more than 1 or underestimates it when it is less than 1.
Analysts often prefer to interpret the results of logistic regression using the odds and odds ratios rather than the logits or log odds themselves. Biometry, data interpretation, epidemiologic methods, risk difference, risk ratio. This article illustrates this problem using an example from the recent dermatology literature. The variables in the equation table only includes a constant so each person has the same chance of survival. The relative risks of using odds ratios dermatology. Effect of changing incidence on or problem let us consider the relationship between smoking and lung cancer. However, only under certain conditions does the odds ratio approximate the risk ratio. The odds ratio is the only parameter that can be used to compare two groups of binary responses from retrospective studies.
Dear professor mean, i know you told me that when one of the row probabilities in a two by two table is 0% or if one of the row probabilities is 100%, then the odds ratio is either 0 or infinity. That is fine english, but this can quickly lead to confusion. The comparison of odds extends nicely to regression analysis e. Common uses of or include medical research and crosssectional studies. Problems arise for clinicians or authors when they interpret the odds ratio as a risk ratio. Block 0 assesses the usefulness of having a null model, which is a model with no explanatory variables. Maths and statistics help centre university of sheffield. Using predictive margins to make clearer explanations. In these casecontrol studies, the odds ratio estimates the rate ratio only if the health outcome is rare, i. We knew that logistic regression gives log odd values. If however the odds differ then the or will depart from 1. Probability and odds build the foundation of the or calculation. The odds ratio is one of a range of statistics used to assess the risk of a particular outcome or.
To use or not to use the odds ratio in epidemiologic studies. Among ba earners, having a parent whose highest degree is a ba degree versus a 2year degree or less increases the log odds by 0. This odds ratio can be computed by raising the base of the natural log to the bth power, where b is the slope from our logistic regression equation. However, we can easily transform this into odds ratios by exponentiating the coefficients. Pdf how odd is odds ratio to understand and how risky is risk. The odds ratio can also be used to determine whether a particular exposure is a risk factor for a particular outcome, and to compare the magnitude of various risk factors for that outcome. Dec 19, 2018 the or provides effect size information on the relative odds of two groups. One common mistake with logits is the interpretation of.
The oddsratio must be used cautiously and interpreted in a manner that properly represents research findings in order to avoid potentially false inference. The odds ratio is the measure of association for a casecontrol study. However what we hope this section has done is show you how probabilities, odds, and odds ratios are all related, how we can model the proportions in a binary outcome through a linear prediction of the log odds or logits, and how these can be converted back into odds ratios for easier interpretation. Unit 1 ratios and interpretation as we learnt in our earlier studies, accounting information is used to answer two key questions about a business. When odds were used as the measure of disease frequency and the summary odds ratio was 0. Odds ratios are a measure of difference in rate between two groups.
Sample odds ratio this is the odds ratio calculated for the 2by2 table listed on this row. Interpretation of odds and risk ratios interpretation of odds and risk ratios oconnor, a. Odds ratios are commonly presented in the medical literature, including dermatology journals. A very high current ratio may mean there is excess cash that should possibly be invested elsewhere in the business or that there is too much inventory. It does not alter the type of analysis done at all, only the terms. Understanding odds ratios in binary logistic regression. The interpretation of each is presented in plain english rather than in technical language. Note that p 1 pand 2 are the proportions in groups one and two, respectively. Types of cases used in case control studies prevalent cases are all persons who were existing cases of the health outcome or disease during the observation period. An odds ratio or is a measure of association between an exposure and an. Nov 26, 2016 this video demonstrates how to interpret the odds ratio exponentiated beta in a binary logistic regression using spss with two independent variables. Take the quiz to check you are comfortable with what you have learnt so far. How do i interpret odds ratios in logistic regression.
This reports odds ratios which give multiplicative effects on the odds rather than additive effects on the log odds or logits. Odds ratio, hazard ratio and relative risk 67 8 nurminen, m. Interpretation of odds and risk ratios, journal of veterinary. The aim of this analysis was to provide an alternative derivation of the odds ratio or to provide an intuitive meaning, freeing it from. Analysts often prefer to interpret the results of logistic regression using the odds and odds ratios rather than the logits or logodds themselves. Nevertheless, it would be inappropriate to interpret an or with 95% ci that spans. For example, consider table 1 showing the outcome variable dependent or independent feeding for those who eat more or less than of served food data. Interpreting results of casecontrol studies if the pvalue is equal to or less than a predetermined cutoff usually 0. An odds ratio or is a measure of association between an. Some people call the odds the odds ratio because the odds itself is a ratio.
Clinically useful notes are provided, wherever necessary. Load the odds ratio and proportions calculator procedure by selecting it from the tools menu. The low pvalues is taken to be evidence against the hypothesis that the odds ratio is 1, which might therefore be rejected. Ad bc the sample odds ratio is not calculated when any of the four cell counts is zero. Interpreting odds ratio with two independent variables in. An odds ratio is interpreted as if it were a relative risk. Note that this value is different from the corrected odds ratio report in the strata detail section. Discriminant analysis is computationally simpler than the. Interpretation logistic regression log odds interpretation. A guide for teachers and students despite the frequent use of logistic regression in the social sciences, considerable confusion exists about its use and interpretation.
The or provides effect size information on the relative odds of two groups. Applying an exponential exp transformation to the regression coefficient gives the odds ratio. If the odds were the same for boys and for girls then we would have an odds ratio of 1. Predictive margins for interpretation predictive margins for nonlinear models wecanstillvisualizethis wecanstillmakeapicture. Spss can be used to determine odds ratio and relative risk values for. An introduction to logistic and probit regression models. Casecontrol studies are quite common in medical studies. Relative risks, odds ratios and cluster randomised trials michael j campbell, suzanne mason, jon nicholl abstract it is well known in cluster randomised trials with a binary outcome and a logistic link that the population average model and cluster specific model estimate different population parameters for. So, it doesnt make sense to talk about just the odds ratio for a single group, you have to say what youre comparing that group with. Interpreting results of casecontrol studies centers for disease. May 01, 20 interpretation of odds and risk ratios interpretation of odds and risk ratios oconnor, a. One common mistake with logits is the interpretation of the odds ratios you can calculate the actual odds ratio from your proc freq not controlling for the effects of other variables e. The interpretation of the odds ratio is that the odds for the development of severe. Relative risks, odds ratios and cluster randomised trials michael j campbell, suzanne mason, jon nicholl abstract it is well known in cluster randomised trials with a binary outcome and a logistic link that the population average model and cluster specific model estimate different population parameters for the odds ratio.
Pdf odds ratios and risk ratios are one of the most widely used statistical data interpretation tool while reporting the data from any clinical trial. The following examples are mainly taken from idre ucle faq page and they are recreated with r. Interpreting the logistic regressions coefficients is somehow tricky. The odds are the ratio of the probability that an outcome occurs to the probability that the outcome does not occur. Case control studies unc gillings school of global. Among ba earners, having a parent whose highest degree is a ba degree versus a 2yr degree or less increases the log odds of entering a stem job by 0. Both the odds ratio and the risk ratio are valid measures of. We have also considered the form in which different types of businesses prepare their final accounts. If then odds ratio 1 the event is equally likely in both groups odds ratio 1 the event is more likely in group 1 odds ratio odds ratio 36 students are much more likely to drink beer than teachers.
This confusion is attributed to a lack of adequate teaching materials and to unfamiliarity with logistic regression by many. In other words, the exponential function of the regression coefficient e b1 is the odds ratio associated with a oneunit increase in the exposure. The incidence of hepatitis among people who ate food from the bakery was 3. The answer is not obvious and it is best explained via an example nurminen, 1995.
Or1 exposure associated with higher odds of outcome. In case control study since the incidence is not available so relative risk can not be calculated directly. Convert log odd ratio in to odd ratio to get a nice interp. Odds ratios that are greater than 1 indicate that the event is more likely to occur as the predictor increases. Proportions tab this window lets you calculate p 1, 2, the difference, ratio, odds ratio, or lnor from various. Feb 24, 20 odds ratio an odds ratio is the odds of the event in one group, for example, those exposed to a drug, divided by the odds of the event in another group not exposed odd ratio in epidemiology.
Below we have a data file with information about families containing the husbands income in thousands of dollars ranging from 10,000 to 12,000, and whether the wife works, 1 if the wife does work, and 0 if the wife does not work. Many research papers present findings as odds ratios ors and relative risks. 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. Logistic regression is perhaps the most widely used method for adjustment of confounding in epidemiologic studies. The estimate and its ci suggest to assume an odds ratio smaller than 1.
Looking at some examples beside doing the math helps getting the concept of odds, odds ratios and consequently getting more familiar with the meaning of the regression coefficients. When the risk ratio cannot be obtained directly such as in a casecontrol study, the odds ratio is calculated and often interpreted as if it were the risk ratio. Thus the odds ratio should, in general, give way to the incidence ratio and difference as the measures of choice for exposure effect in epidemiology. The ratio is easy to calculate and easy to interpret when written appropriately. Subsequently, the term relative risk commonly refers to either the risk ratio or the odds ratio. You might find it easier to start with more fundamental quantity, odds actually this is just another way of expressing probability. One common mistake with logits is the interpretation of the. Odds ratio can be calculated in a cohort study and in a case. If you did that, you would have to call this calculation the. It quantifies the relationship between an exposure such as eating a food or attending an. Relative risks and odds ratios statistics 149 spring 2006. There are four other reasons why the odds ratio is a useful measure for comparing population probabilities 1. Nevertheless, it would be inappropriate to interpret an or with.
Relative risks, odds ratios and cluster randomised trials. Introduction to log odds ratio university of groningen. Maths and statistics help centre 3 interpretation of the output the output is split into two sections, block 0 and block 1. Aug 29, 20 this video demonstrates how to calculate odds ratio and relative risk values using the statistical software program spss. Case control studies unc gillings school of global public. The interpretation of the odds ratio depends on whether the predictor is categorical or continuous. Because many variables in regression analysis are dichotomous or discrete. A major drawback of the probit model is that it lacks nat ural interpretation of regression parameters. Example datasets installed with stata areinstalled. Odds ratio, hazard ratio and relative risk 61 since we already have relative risk, why would we want to calculate the odds ratio. The concept and method of calculation are explained for each of these in simple terms and with the help of examples. Interpreting the odds ratio look at the column labeled expb expb means e to the power b or e.
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