In a clinical trial of 2,150 subjects treated with a certain drug, 30 reported headaches. In a control group of 1,643 subjects given a placebo, 26 reported headaches. Denoting the proportion of headaches in the treatment group by \( p_t \) and denoting the proportion of headaches in the control (placebo) group by \( p_c \), the relative risk is \( p_t/p_c \). The relative risk is a measure of the strength of the effect of the drug treatment. Another such measure is the odds ratio, which is the ratio of the odds in favor of a headache for the treatment group to the odds in favor of a headache for the control (placebo) group, found by evaluating \( \frac{p_t / (1 - p_t)}{p_c / (1 - p_c)} \). The relative risk is calculated to find the relative risk for the headache data.The relative risk = \(\Box\) (Round to three decimal places as needed.) Sure, here is a transcription suitable for an educational website:---In evaluating the effectiveness of a drug treatment, one measure used is the odds ratio. This is calculated by taking the ratio of the odds in favor of a headache for the treatment group to the odds in favor of a headache for the control (placebo) group. This can be expressed as:\[\frac{p_t / (1 - p_t)}{p_c / (1 - p_c)}\]Where \( p_t \) is the probability of a headache in the treatment group, and \( p_c \) is the probability of a headache in the control group.The relative risk and odds ratios are important metrics commonly used in medicine and epidemiological studies. These measures help to determine the likelihood of an outcome occurring in a treatment group relative to a control group.**Task:** Find the relative risk and odds ratio for the headache data given. What do the results suggest about the risk of experiencing a headache from the drug treatment?--- This explanation provides the necessary context and details for understanding the importance and application of the odds ratio in medical studies.

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In a clinical trial of 2150 subjects treated with a certain drug, 30 reported headaches. In a control group of 1643 subjects given a placebo, 26 reported headaches. Denoting the proportion of headaches in the treatment group by p, and denoting the proportion of headaches in the control (placebo) group by pe the relative risk is p/p. The relative risk is a measure of the strength of the effect of the drug treatment. Another such measure is the odds ratio, which is the ratio of the odds in favor of a headache for the Pt/ (1-Pt) treatment aroun to the odds in favor of a headache for the control (placebo) aroun found bv evaluatina The relative Find the relative risk for the headache data. The relative risk = (Round to three decimal places as needed.)

In a clinical trial of 2150 subjects treated with a certain drug, 30 reported headaches. In a control group of 1643 subjects given a placebo, 26 reported headaches. Denoting the proportion of headaches in the treatment group by p, and denoting the proportion of headaches in the control (placebo) group by pe the relative risk is p/p. The relative risk is a measure of the strength of the effect of the drug treatment. Another such measure is the odds ratio, which is the ratio of the odds in favor of a headache for the Pt/ (1-Pt) treatment aroun to the odds in favor of a headache for the control (placebo) aroun found bv evaluatina The relative Find the relative risk for the headache data. The relative risk = (Round to three decimal places as needed.)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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