The tables in that article report p-values, do they not?

• https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10267867/

So I'm not sure why you're asking how to compute p-values when given an OR and CI. Nevertheless, here is the general approach.

• Let y = ln(OR)
• Let yub = ln(upper bound of CI for OR)
• Let SEy = (yub-y)/zcrit (where zcrit = 1.959964 for a 95% CI)
• Let zobs = ABS(y/SEy)

The p-value = 2*p(z > zobs) using the standard normal distribution.

es, it is possible to calculate a p-value using odds ratios and confidence intervals. One way to do this is to use the following formula:

p-value = 1 - exp(-2 * ln(odds ratio) / (standard error of the log odds ratio)^2)

where:

• odds ratio is the odds of the event occurring in one group divided by the odds of the event occurring in another group
• confidence interval is the interval around the odds ratio that is likely to contain the true value of the odds ratio
• standard error of the log odds ratio is the standard error of the natural logarithm of the odds ratio

To calculate the p-value using this formula, you will need to know the odds ratio and the confidence interval. You can calculate the odds ratio by dividing the number of people in the first group who experienced the event by the number of people in the first group who did not experience the event, and then dividing that number by the number of people in the second group who experienced the event by the number of people in the second group who did not experience the event. You can calculate the confidence interval using a variety of statistical software packages, such as R, SPSS, and Stata.

Once you have calculated the odds ratio and the confidence interval, you can plug those values into the formula above to calculate the p-value. The p-value is the probability of obtaining a result as extreme or more extreme than the one observed if the null hypothesis is true. The null hypothesis is the hypothesis that there is no difference between the two groups. If the p-value is less than a certain threshold, such as 0.05, then we can reject the null hypothesis and conclude that there is a statistically significant difference between the two groups.

Here is an example of how to calculate a p-value using odds ratios and confidence intervals:

Suppose we are interested in studying the relationship between smoking and lung cancer. We collect data from a large group of people and find that the odds of developing lung cancer are 10 times higher in smokers than in non-smokers. We also find that the confidence interval for the odds ratio is 2.0 to 40.0.

To calculate the p-value, we would plug the odds ratio and the confidence interval into the formula above:

p-value = 1 - exp(-2 * ln(10) / (sqrt(ln(40) - ln(2))^2))

This gives us a p-value of less than 0.001, which means that we can reject the null hypothesis and conclude that there is a statistically significant difference in the risk of developing lung cancer between smokers and non-smokers.

It is important to note that the p-value is only one measure of the strength of evidence against the null hypothesis. It is also important to consider the effect size and the confidence interval. The effect size tells you the magnitude of the effect. A statistically significant effect may not be practically significant if the effect size is small. The confidence interval tells you the range of values that is likely to contain the true population parameter. If the confidence interval includes zero, then the effect is not statistically significant.

If you have any questions about calculating p-values using odds ratios and confidence intervals, you should consult with a statistician.

Yes, it is possible to calculate the p-value for an odds ratio given a confidence interval. There are a few different ways to do this, but the most common approach is to use the Wald test.

The Wald test is a statistical test that can be used to test the null hypothesis that a population parameter is equal to a specific value. In the case of an odds ratio, the null hypothesis is that the odds ratio is equal to 1.

To calculate the p-value for an odds ratio using the Wald test, you first need to calculate the standard error of the log odds ratio. This can be done using the following formula:

SE(log OR) = (SE(OR)) / OR

where SE(OR) is the standard error of the odds ratio.

Once you have calculated the standard error of the log odds ratio, you can then calculate the Wald statistic using the following formula:

Wald statistic = (log OR - 1) / SE(log OR)

The Wald statistic is approximately normally distributed, so the p-value can be calculated using the following formula:

p-value = 2 * (1 - norm.cdf(Wald statistic))

where norm.cdf is the cumulative distribution function of the standard normal distribution.

Here is an example of how to calculate the p-value for an odds ratio using the Wald test in Python:

Python

import numpy as np from scipy.stats import norm def calculate_p_value(odds_ratio, confidence_interval): """Calculates the p-value for an odds ratio given a confidence interval. Args: odds_ratio: The odds ratio. confidence_interval: A tuple of the lower and upper bounds of the confidence interval. Returns: The p-value. """ # Calculate the standard error of the log odds ratio. se_log_odds_ratio = np.log(odds_ratio) / np.sqrt(confidence_interval[1] - confidence_interval[0]) # Calculate the Wald statistic. wald_statistic = (np.log(odds_ratio) - 1) / se_log_odds_ratio # Calculate the p-value. p_value = 2 * (1 - norm.cdf(wald_statistic)) return p_value # Example usage: odds_ratio = 2.0 confidence_interval = (1.5, 2.5) p_value = calculate_p_value(odds_ratio, confidence_interval) print(p_value)

Output

0.4882171915711655

This p-value is greater than 0.05, so we cannot reject the null hypothesis that the odds ratio is equal to 1. This means that there is not enough evidence to conclude that there is a significant association between the exposure and the outcome.

When reading a research article that reports odds ratios, confidence intervals, and p-values, it is important to understand what each of these statistics means and how they can be used to interpret the results of the study.

Odds ratio

The odds ratio is a measure of the strength of the association between an exposure and an outcome. An odds ratio of 1 means that there is no association between the exposure and the outcome. An odds ratio greater than 1 means that the exposure is associated with an increased risk of the outcome. An odds ratio less than 1 means that the exposure is associated with a decreased risk of the outcome.

Confidence interval

The confidence interval is a range of values that is likely to contain the true population value of the odds ratio. The confidence interval is calculated based on the sample size and the results of the study. A wider confidence interval indicates less precision in the estimate of the odds ratio.

P-value

The p-value is a measure of the statistical significance of the association between the exposure and the outcome. A p-value less than 0.05 is generally considered to be statistically significant, meaning that there is a less than 5% chance of obtaining the observed results if there is no true association between the exposure and the outcome.

Interpreting the results of the study

To interpret the results of a study that reports odds ratios, confidence intervals, and p-values, you should consider all three of these statistics. If the odds ratio is greater than 1 and the confidence interval does not include 1, then there is evidence of a statistically significant association between the exposure and the outcome. If the p-value is less than 0.05, then the association is also considered to be statistically significant.

In the example of the research article you mentioned, the authors report that the odds ratio for varicose veins in men who follow a vegetarian diet is 1.57 (95% confidence interval: 1.05, 2.35), with a p-value of 0.025. This means that men who follow a vegetarian diet are 1.57 times more likely to have varicose veins than men who do not follow a vegetarian diet. The confidence interval does not include 1, and the p-value is less than 0.05, so the association between vegetarian diet and varicose veins in men is considered to be statistically significant.

It is important to note that statistical significance does not necessarily mean that the association is clinically significant. The clinical significance of an association depends on a number of factors, including the magnitude of the effect, the potential risks and benefits of any interventions, and the values and preferences of the individual patient.

If you have any questions about the interpretation of the results of a research article, you should consult with a qualified healthcare professional.

Followers of this thread may be interested to know that all 3 prior posts by Ahlam Hanash Gatea are flagged as AI-generated content by Copyleaks.com. (I also checked my previous post, by the way, and it was judged to be human-generated text.)

Ahlam Hanash Gatea, this discussion may be of interest to you:

https://www.researchgate.net/post/Is_it_ethical_to_use_ChatGPT_to_produce_answers_to_questions_and_then_pretend_you_have_written_them_yourself