How to Talk About Odds Ratios: Scott Long - A Comprehensive Guide

"How to Talk About Odds Ratios" by Scott Long is an invaluable resource for anyone seeking a clear understanding of odds ratios and how to effectively communicate about them. Whether you're a student, researcher, or professional in the field, this guide offers a practical and straightforward approach to grasping this important statistical concept.

Positive Aspects:

Clear and Concise Explanation: Scott Long provides a step-by-step breakdown of odds ratios, ensuring that even those with limited statistical knowledge can comprehend the topic. The guide is written in simple language, making it accessible to a wide range of readers.

Comprehensive Coverage: The guide covers all essential aspects of odds ratios, including their definition, interpretation, calculation, and presentation. It explores various scenarios and provides examples to illustrate real-life applications.

Practical Application: Scott Long emphasizes the practical use of odds ratios, enabling readers to apply their knowledge in their research, academic assignments, or professional work. The guide equips readers with the necessary tools to effectively communicate odds ratios in a clear and understandable manner.

Benefits:

- Enhanced Understanding: By reading this guide, individuals will gain a firm grasp of odds ratios, enabling them to interpret statistical results

## What is a log odds ratio

## How to interpret odds ratios with continuous predictors

## What is the relationship between frequency and probability?

## What is the relationship between odds and probability?

**The odds are defined as the probability that the event will occur divided by the probability that the event will not occur**.

## What is the difference between frequency and likelihood?

**Frequency expresses the number of events in a given time frame.**

**Likelihood means the probability of one (or more) event(s) in a given time frame**.

## What is the relationship between frequency?

**inversely proportional to each other**. Because all light waves move at the same speed in a vacuum, the number of wave crests passing at a given spot in one second is determined by the wavelength.

## Frequently Asked Questions

#### How do you explain odds ratio to a lay person?

#### What is the main question the odds ratio answers?

**how many times higher were the odds of the outcome, in people exposed to the risk factor?**As you can see, the denominator is different from the risk ratio. Rather than calculating the proportion of people who died, it compares the number of people died to those who didn't.

#### How do you find the odds ratio from a regression coefficient?

#### What is the relationship between the coefficient estimates and the odds ratios?

**odd ratio r = exp(coefficient)**. Hope it helps.

#### How do you convert coefficient to odds ratio in Excel?

**=exp(<coef>)**.

#### How do you calculate odds ratio in linear regression?

**odds = P/(1-P)**. In linear regression, you can think of the regression coefficient as the difference between two marginal means when you've chosen values of X that are one unit apart.

#### What is the formula for univariate linear regression?

**Y = b0 + b1 * X**Where, b0 and b1 are the coefficients of regression.

#### Can linear regression be univariate?

**univariate linear regression**is when you want to predict the values of one variable from the values of another.

#### Can you get odds ratio from logistic regression?

**Logistic regression is used to obtain odds ratio in the presence of more than one explanatory variable**. The procedure is quite similar to multiple linear regression, with the exception that the response variable is binomial. The result is the impact of each variable on the odds ratio of the observed event of interest.

#### Does linear regression give you odds ratio?

**relative risk are not possible with linear regression**as in case of the logistic regression where we can calculate the odds ratio by: exp(Beta).

#### What does odds ratio of 1 mean in logistic regression?

**the event is more likely to occur as the predictor increases**. Odds ratios that are less than 1 indicate that the event is less likely to occur as the predictor increases.

#### Is an odds ratio of 1 significant?

**If an odds ratio (OR) is 1, it means there is no association between the exposure and outcome**. So, if the 95% confidence interval for an OR includes 1, it means the results are not statistically significant.

#### What does an odds ratio less than 1 indicate?

**the condition or event is less likely to occur in the first group**. The odds ratio must be nonnegative if it is defined.

#### What does it mean when the odds ratio is greater than 1?

#### How to interpret odds ratio greater than 1 in logistic regression?

**an odds ratio greater than 1 is a positive association**(i.e., higher number for the predictor means group 1 in the outcome), and an odds ratio less than 1 is negative association (i.e., higher number for the predictor means group 0 in the outcome

#### What is the odds ratio between exposure and outcome?

**a measure of association between an exposure and an outcome**. The OR represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure.

#### How do you interpret the odds ratio for a binary variable?

**Odds ratios that are greater than 1 indicate that the event is more likely to occur as the predictor increases**. Odds ratios that are less than 1 indicate that the event is less likely to occur as the predictor increases.

#### How do you interpret the odds ratio?

**>1 indicates increased occurrence of an event**.

**OR <1 indicates decreased occurrence of an event (protective exposure)**Look at CI and P-value for statistical significance of value (Learn more about p values and confidence intervals here) In rare outcomes OR = RR (RR = Relative Risk)

#### Is odds ratio dichotomous?

**the outcome is dichotomous**and the data arise from a case-control study design.

## FAQ

- What do the odds of exposure mean?
- The odds ratio is
**commonly used to report the strength of association between exposure and an event**. The larger the odds ratio, the more likely the event is to be found with exposure. The smaller the odds ratio is than 1, the less likely the event is to be found with exposure. - How do you interpret a negative odds ratio less than 1?
- Important points about Odds ratio:
OR >1 indicates increased occurrence of an event. OR <1 indicates
**decreased occurrence of an event**(protective exposure) Look at CI and P-value for statistical significance of value (Learn more about p values and confidence intervals here) - Can an odds ratio be negative?
**The odds ratio is always positive, although the estimated log odds can be positive or negative**(log odds of −0.2 equals odds ratio of 0.82 = exp(−0.2)).- What is 1 minus odds ratio?
**An OR of 1 implies no association**. For an OR > 1, 100% × (OR – 1) represents the % greater odds for X=x+1 X = x + 1 compared to X=x for a continuous predictor, or for a level compared to the reference level for a categorical predictor. For an OR < 1, 100% × (1 – OR) represents the % lower odds.- How do you interpret odds ratio?
- An odds ratio estimate of, say, 2 means that the odds of the event for the group in the numerator is twice the event odds for the group in the denominator. If you want to interpret it as a percent change from the denominator group,
**use the odds ratio minus 1 and then multiply by 100**. - What does an odds ratio of 0.33 mean?
- It is
**the ratio of the probability a thing will happen over the probability it won't**. In the spades example, the probability of drawing a spade is 0.25. The probability of not drawing a spade is 1 – 0.25. So the odds is 0.25/0.75 or 1:3 (or 0.33 or 1/3 pronounced 1 to 3 odds). - What does it mean when the odds ratio is 0?
- The odds ratio is asymmetrical and can range from 0 to infinity; the odds ratio cannot be negative. Odds ratios
**between 0 and 0.99 indicate a lower risk**, between 1 and infinity indicate a higher risk, and equal to 1 indicate no relationship between two variables. - What are the 4 types of probability?
- What are the types of probability? Probability is the branch of mathematics concerning the occurrence of a random event, and four main types of probability exist:
**classical, empirical, subjective and axiomatic**. - What does a probability of 0 mean?
- Probability as a number lies between 0 and 1 .
A probability of 0 means that
**the event will not happen**. For example, if the chance of being involved in a road traffic accident was 0 this would mean it would never happen. You would be perfectly safe. A probability of 1 means that the event will happen. - What is the inverse of odds?
- An odds ratio larger than one means that group one has a larger proportion than group two, if the opposite is true the odds ratio will be smaller than one. If you swap the two proportions, the odds ratio will take on its inverse (
**1/OR**). - What if log odds is 0?
- If the probability of success is less than 50%, the log odds are negative and the odds are less than 1;
**if the probability of success = 50%, the log odds are 0**and the odds = 1; if the probability of success is greater than 50%, the log odds are positive and the odds are greater than 1. - What is the reciprocal of odds ratio?
- If we switch the order of the categories in the rows and the columns, we get the same odds ratio. If we switch the order for the rows only or for the columns only, we get the reciprocal of the odds ratio,
**1/4.89=0.204**. These properties make the odds ratio a useful indicator of the strength of the relationship. - How do you flip odds ratio and confidence interval?
- To calculate the odds ratio for the reverse group comparison, take the reciprocal of the odds ratio. To calculate the confidence limits for the reverse group comparison,
**take the reciprocals of the limits and swap them**. - How do you interpret odds ratios less than 1?
- Important points about Odds ratio:
OR >1 indicates increased occurrence of an event. OR <1 indicates
**decreased occurrence of an event**(protective exposure) Look at CI and P-value for statistical significance of value (Learn more about p values and confidence intervals here) - What is the formula for odds ratio?
- In a 2-by-2 table with cells a, b, c, and d (see figure), the odds ratio is odds of the event in the exposure group (a/b) divided by the odds of the event in the control or non-exposure group (c/d). Thus the odds ratio is
**(a/b) / (c/d)**which simplifies to ad/bc. - What is an example of a reciprocal ratio?
- The reciprocal of a number is 1 divided by that number. So, for example,
**the reciprocal of 3 is 1 divided by 3, which is 1/3**. - How do you know if an odds ratio is significant?
- Odds ratios typically are reported in a table with 95% CIs.
**If the 95% CI for an odds ratio does not include 1.0, then the odds ratio is considered to be statistically significant at the 5% level**. - How to interpret odds ratio in SAS?
**An odds ratio greater than 1 indicates that the odds of a positive response are higher in row 1 than in row 2**. An odds ratio less than 1 indicates that the odds of a positive response are higher in row 2. The strength of association increases as the deviation from 1 increases.

## How to talk about odds ratios scott long

How do you interpret odds ratio and adjusted odds ratio? | Odds of an event happening is defined as the likelihood that an event will occur, expressed as a proportion of the likelihood that the event will not occur. Therefore, if A is the probability of subjects affected and B is the probability of subjects not affected, then odds = A /B. |

How do you interpret odds ratio 95% CI? | The 95% confidence interval (CI) is used to estimate the precision of the OR. A large CI indicates a low level of precision of the OR, whereas a small CI indicates a higher precision of the OR. It is important to note however, that unlike the p value, the 95% CI does not report a measure's statistical significance. |

What does an odds ratio of 0.5 mean? | As an example, an odds ratio of 0.5 means that there is a 50% decrease in the odds of disease if you have the exposure. An example of an exposure with a protective factor would be brushing your teeth twice a day. |

Is the beta coefficient the odds ratio? | Odds ratios and beta coefficients both estimate the effect of an exposure on the outcome, the later one being the natural logarithm of the former one. For illustrative purposes, here we use beta coefficients instead of odds ratios but conclusions drawn stands for odds ratios as for beta coefficients. |

How do you convert coefficients to odds ratios? | To calculate the odds ratio, exponentiate the coefficient for a level. The result is the odds ratio for the level compared to the reference level. For example, a categorical variable has the levels Hard and Soft, and Soft is the reference level. |

What is the relationship between odds ratio and coefficient? | Odds ratio tells the changes produced in output variable per unit change in that particular input variable. For the relation between both, odd ratio r = exp(coefficient). |

How do you interpret the beta coefficient? | A positive beta coefficient means that an increase in the predictor variable is associated with an increase in the dependent variable, while a negative beta coefficient means that an increase in the predictor variable is associated with a decrease in the dependent variable. |

How do you calculate the odds ratio? | In a 2-by-2 table with cells a, b, c, and d (see figure), the odds ratio is odds of the event in the exposure group (a/b) divided by the odds of the event in the control or non-exposure group (c/d). Thus the odds ratio is (a/b) / (c/d) which simplifies to ad/bc. |

Can odds ratio be more than 100? | Odds represent the probability of an event occurring divided by the probability of an event not occurring. Although related, probability and odds are not the same. Probability values can only range from 0 to 1 (0% to 100%), whereas odds can take on any value. |

What is the maximum likelihood estimate of the odds ratio? | The usual maximum likelihood estimator of odds ratio is defined as Odds ratio is nonnegative real value. When successes are similar in both groups, the odds ratio is equal to 1, meaning that groups are independent of response. |

What are large odds ratios? | • An odds ratio of 4 or more is pretty strong and not likely to be able to be explained away by some unmeasured variables. • An odds ratio bigger than 2 and less than 4 is possibly important and should be looked at very carefully. |

When an odds ratio calculated is more than 1 it means that? | Important points about Odds ratio:
OR >1 indicates increased occurrence of an event. OR <1 indicates decreased occurrence of an event (protective exposure) Look at CI and P-value for statistical significance of value (Learn more about p values and confidence intervals here) |

Can odds ratio be infinite? | An odds ratio of infinity means that the lists are highly dependent (not independent), as one is contained in other. |

How to convert coefficient to odds ratio in R? | The coefficient returned by a logistic regression in r is a logit, or the log of the odds. To convert logits to odds ratio, you can exponentiate it, as you've done above. To convert logits to probabilities, you can use the function exp(logit)/(1+exp(logit)) . |

Is beta the same as odds ratio? | I'm assuming with "Beta" you are referring to the logistic regression slope coefficient estimates and that "SE" refers to their standard error estimates. An odds ratio (OR) in logistic regression is equal to exp(Beta). |

How do you calculate beta from odds ratio? | Assuming that you mean β = regression coefficient on the logit scale and OR = odds ratio, then the following works: take the inverse logit (exp(x)/(1+exp(x))) of the estimate and confidence limits to get the β with 95% CI. The standard error is then approximately the CI width divided by 2×1.95996. |

What is the formula for the odds ratio? | In a 2-by-2 table with cells a, b, c, and d (see figure), the odds ratio is odds of the event in the exposure group (a/b) divided by the odds of the event in the control or non-exposure group (c/d). Thus the odds ratio is (a/b) / (c/d) which simplifies to ad/bc. |

What is the exp beta odds ratio? | “Exp(B),” or the odds ratio, is the predicted change in odds for a unit increase in the predictor. The “exp” refers to the exponential value of B. When Exp(B) is less than 1, increasing values of the variable correspond to decreasing odds of the event's occurrence. |

- What does a beta of 1.5 mean?
- A beta value of 1.5 indicates that
**the price of the stock is more volatile than the market**. In fact, it is assumed to be 50% more volatile than the market. Tech stocks and small caps tend to have high betas.

- A beta value of 1.5 indicates that
- How do you interpret reporting odds ratio?
- The Reporting Odds Ratio (ROR) the odds of a certain event occurring with your medicinal product, compared to the odds of the same event occurring with all other medicinal products in the database.
**A signal is considered when the lower limit of the 95% confidence interval (CI) of the ROR is greater than one**.

- The Reporting Odds Ratio (ROR) the odds of a certain event occurring with your medicinal product, compared to the odds of the same event occurring with all other medicinal products in the database.
- What is the interpretation of GEE?
- Generalized estimating equations, or GEE, is
**a method for modeling longitudinal or clustered data**. It is usually used with non-normal data such as binary or count data. The name refers to a set of equations that are solved to obtain parameter estimates (i.e., model coefficients).

- Generalized estimating equations, or GEE, is
- What does odds ratio of 1.5 mean?
- If something has a 25% chance of happening, the odds are 1:3. You interpret an odds ratio the same way you interpret a risk ratio. An odds ratio of 1.5 means
**the odds of the outcome in group A happening are one and a half times the odds of the outcome happening in group B**.

- If something has a 25% chance of happening, the odds are 1:3. You interpret an odds ratio the same way you interpret a risk ratio. An odds ratio of 1.5 means
- What does an odds ratio of 2.5 mean?
- For example, OR = 2.50 could be interpreted as
**the first group having “150% greater odds than” or “2.5 times the odds of” the second group**.

- For example, OR = 2.50 could be interpreted as
- How do you find the odds ratio in linear regression?
- The formula is easy:
**odds = P/(1-P)**. In linear regression, you can think of the regression coefficient as the difference between two marginal means when you've chosen values of X that are one unit apart.

- The formula is easy:
- How do you convert a regression coefficient to an odds ratio?
- To calculate the odds ratio,
**exponentiate the coefficient for a level**. The result is the odds ratio for the level compared to the reference level. For example, a categorical variable has the levels Hard and Soft, and Soft is the reference level.

- To calculate the odds ratio,
- What is the adjusted odds ratio in linear regression?
- An adjusted odds ratio (AOR) is
**an odds ratio that controls for other predictor variables in a model**. It gives you an idea of the dynamics between the predictors. Multiple regression, which works with several independent variables, produces AORs. AOR is sometimes called a conditional odds ratio.

- An adjusted odds ratio (AOR) is
- Is regression coefficient the same as odds ratio?
- In epidemiology,
**the odds ratio and regression coefficient are both measures of association between an exposure and an outcome**. However, they are calculated using different methods and have different interpretations. The odds ratio (OR) is commonly used in case-control studies and cross-sectional studies.

- In epidemiology,
- What does the odds ratio represent in logistic regression?
- For example, in logistic regression the odds ratio represents
**the constant effect of a predictor X, on the likelihood that one outcome will occur**. The key phrase here is constant effect. In regression models, we often want a measure of the unique effect of each X on Y.

- For example, in logistic regression the odds ratio represents
- What is the power calculation for logistic regression?
- The main application of power calculations is to estimate the number of observations necessary to properly conduct an experiment. In the general framework of logistic regression model, the goal is to explain and predict the probability P that an event appends (usually Y=1). P is equal to:
**P = exp(β0 + β1X1 +**…

- The main application of power calculations is to estimate the number of observations necessary to properly conduct an experiment. In the general framework of logistic regression model, the goal is to explain and predict the probability P that an event appends (usually Y=1). P is equal to:
- What does odds ratio tell you?
- An odds ratio (OR) is
**a measure of association between an exposure and an outcome**. The OR represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure.

- An odds ratio (OR) is
- How to interpret odds ratio in logistic regression continuous variable?
**When an OR is:**- Greater than 1: As the continuous variable increases, the event is more likely to occur.
- Less than 1: As the variable increases, the event is less likely to occur.
- Equals 1: As the variable increases, the likelihood of the event does not change.

- How do you interpret odds ratio for categorical variables?
- The interpretation of the odds ratio depends on whether the predictor is categorical or continuous.
**Odds ratios that are greater than 1 indicate that the event is more likely to occur as the predictor increases**. Odds ratios that are less than 1 indicate that the event is less likely to occur as the predictor increases.

- The interpretation of the odds ratio depends on whether the predictor is categorical or continuous.
- How do you write the interpretation of the odds ratio?
- The odds ratio is a way of comparing whether the odds of a certain outcome is the same for two different groups (9). (17 × 248) = (15656/4216) = 3.71. The result of an odds ratio is interpreted as follows:
**The patients who received standard care died 3.71 times more often than patients treated with the new drug**.

- The odds ratio is a way of comparing whether the odds of a certain outcome is the same for two different groups (9). (17 × 248) = (15656/4216) = 3.71. The result of an odds ratio is interpreted as follows:
- How do you know if an odds ratio is statistically significant?
**If the 95% CI for an odds ratio does not include 1.0**, then the odds ratio is considered to be statistically significant at the 5% level.

- How do you interpret odds ratio with confidence interval?
- Odds Ratio Confidence Interval
In order to calculate the confidence interval, the alpha, or our level of significance, is specified.
**An alpha of 0.05 means the confidence interval is 95% (1 – alpha)**the true odds ratio of the overall population is within range.

- Odds Ratio Confidence Interval
In order to calculate the confidence interval, the alpha, or our level of significance, is specified.
- What is the odds ratio for a continuous predictor?
- When a predictor variable is a continuous variable, the odds ratio is
**the increase or decrease in odds for a change in the predictor variable**. The default is for a 1 unit change in the predictor, although it may be more appropriate to use a larger unit, such as for a change of 10 units of the predictor variable.

- When a predictor variable is a continuous variable, the odds ratio is