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4.150 Approval from the FDA for Antidepressants The FDA (US Food and Drug Administration) is responsible for approving all new drugs sold in the US. In order to approve a new drug for use as an antidepressant, the FDA requires two results from randomized double-blind experiments showing the drug is more effective than a placebo at a \(5 \%\) level. The FDA does not put a limit on the number of times a drug company can try such experiments. Explain, using the problem of multiple tests, why the FDA might want to rethink its guidelines. 4.151 Does Massage Really Help Reduce Inflammation in Muscles? In Exercise 4.112 on page \(301,\) we learn that massage helps reduce levels of the inflammatory cytokine interleukin-6 in muscles when muscle tissue is tested 2.5 hours after massage. The results were significant at the \(5 \%\) level. However, the authors of the study actually performed 42 different tests: They tested for significance with 21 different compounds in muscles and at two different times (right after the massage and 2.5 hours after). (a) Given this new information, should we have less confidence in the one result described in the earlier exercise? Why? (b) Sixteen of the tests done by the authors involved measuring the effects of massage on muscle metabolites. None of these tests were significant. Do you think massage affects muscle metabolites? (c) Eight of the tests done by the authors (including the one described in the earlier exercise) involved measuring the effects of massage on inflammation in the muscle. Four of these tests were significant. Do you think it is safe to conclude that massage really does reduce inflammation?

Step by step solution

01

Understanding the Problem of Multiple Testing

Multiple testing implies that several statistical tests are being performed. The problem with multiple testing is that the likelihood of observing a statistically significant result purely by chance, increases. This is because each test carried out has a certain probability (usually expressed at the 5% level, i.e., p ≤ 0.05) of resulting in a Type I error - rejecting a true null hypothesis. If multiple tests are performed, the probability of making a Type I error increases. Hence, even if a test comes out to be significant, it might be due just to random chance.

02

Applying the Concept to the FDA Guidelines

In the context of the FDA guidelines, if multiple tests are performed on a drug, the chance of at least two tests showing the drug is effective (when in reality it might not be) increases. This is why the FDA might want to rethink its guidelines. It might be beneficial to implement a multiple testing correction method, such as the Bonferroni Correction or the False Discovery Rate (FDR), to control the probability of making Type I errors.

03

Analyzing the Massage Experiment

Given this new information, it might be reasonable to have less confidence in the result that massage reduces inflammation. The researchers performed 42 tests, thus increasing the chances of getting a significant result purely by chance. The result could be the product of random variation rather than an actual effect. However, without knowing the exact p-values of the tests, we can't make firm determinations. It's recommended to apply multiple testing correction to determine whether the results remain significant.

04

Interpreting the Effects on Muscle Metabolites and Inflammation

Without any significant results across the 16 tests on muscle metabolites, it suggests that massage might not have a noticeable effect on muscle metabolites. However, we can't be certain without more research and possibly controlling for other factors. Regarding the inflammation tests, it's worth noting that even half of the tests being significant is quite a high proportion, which might indicate that massage does have a real effect on reducing inflammation. However, due to the potential issue of multiple testing, it is essential to apply corrections to ensure these results are not due to chance.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

FDA Guidelines

The FDA (Food and Drug Administration) plays a vital role in the approval of new drugs, ensuring that they are both effective and safe for public use. For antidepressants, the FDA requires that at least two experiments demonstrate effectiveness over a placebo, at a significance level of 5%. This ensures that the drug is not only promising but also statistically proven to work under test conditions. However, the current guidelines allow unlimited attempts by drug companies to achieve this result. This lack of restriction could potentially lead to an issue known as multiple testing, where the chance of achieving at least two significant results merely by chance increases. Therefore, some argue that the FDA might need to rethink and tighten its guidelines to prevent approval of any drugs that may pass these tests due to statistical fluke or error.

Type I Error

In statistical testing, a Type I error occurs when a test wrongly indicates a positive result, rejecting a true null hypothesis. Essentially, it means finding an effect or difference when none actually exists. For pharmaceutical testing, this error can be particularly problematic. When conducting multiple tests, the probability of encountering a Type I error increases. With each test typically set at a 5% significance level, multiple tests will cumulatively heighten the likelihood of incorrectly identifying a drug as effective. This makes controlling Type I errors crucial, especially in medical and health-related fields, as approving drugs with no true effectiveness could lead to unfavorable and unsafe consequences.

Statistical Significance

Statistical significance is a measure that indicates whether the results of a study or experiment are unlikely to have occurred due to chance. Often set at a threshold of 5%, it provides a confidence level to the outcomes. For a drug to be considered successful in clinical trials, its effect must reach this level of significance compared to a placebo. However, the notion of significance becomes muddled when multiple tests are involved. Performing many tests increases the chances of one or more tests achieving significance purely by luck. This means statistically significant results in such cases do not necessarily equate to true effectiveness, highlighting the need for careful interpretation and potential adjustment in how results are evaluated.

Bonferroni Correction

The Bonferroni Correction is a statistical adjustment method used to counteract the problem of multiple comparisons. When many statistical tests are performed simultaneously, the risk of Type I errors (false positives) increases. The Bonferroni method reduces this risk by adjusting the significance level. It divides the original significance threshold (commonly 0.05) by the number of tests conducted. For instance, if 10 tests are run, the new significance threshold would be 0.005 for each test. This correction ensures that the overall likelihood of a Type I error is maintained at the pre-set significance level. While effective, the Bonferroni Correction can be quite conservative, especially when dealing with a large number of tests, potentially increasing the chance of Type II errors (false negatives). Therefore, it's important to balance between controlling Type I errors and losing true positive results in the process.