A research team is working on a new assay meant to increase the sensitivity of testing in cervical cancer. Current sensitivity is listed at 77%. If this research team's latest work culminates in the following results (listed in the table), has the sensitivity improved, and, if so, then by what percentage? Research team's latest results: | | Patients with cervical cancer | Patients without cervical cancer | |--------------------------|-------------------------------|----------------------------------| | Test is Positive (+) | 47 | 4 | | Test is Negative (-) | 9 | 44 |

Yes, the research team has seen an improvement in sensitivity of almost 7% according to the new results listed.

No, the research team has seen a decrease in sensitivity according to the new results listed.

No, the research team has not seen any improvement in sensitivity according to the new results listed.

Yes, the research team has seen an improvement in sensitivity of more than 10% according to the new results listed.

Yes, the research team has seen an improvement in sensitivity of less than 2% according to new results listed; this improvement is negligible and should be improved upon for significant contribution to the field.

Two research groups independently study the same genetic variant's association with diabetes. Study A (n=5,000) reports OR=1.25, 95% CI: 1.05-1.48, p=0.01. Study B (n=50,000) reports OR=1.08, 95% CI: 1.02-1.14, p=0.006. Both studies are methodologically sound. Synthesize these findings to determine the most likely true effect and evaluate implications for clinical and research interpretation.

The true effect is likely modest (closer to Study B's estimate); Study A likely overestimated due to smaller sample size, but both show statistical significance with clinically marginal effects

Study B is definitive because of its larger sample size and should replace Study A's findings

The study with the lower p-value (Study B) is automatically more reliable

The studies are contradictory and no conclusions can be drawn

Study A is correct because it was published first

A prestigious journal publishes a trial showing a new cancer drug extends survival by 2 months (p=0.001, 95% CI: 1.5-2.5 months). The drug costs $150,000 per patient and causes Grade 3-4 toxicity in 60% of patients. Three prior unpublished trials showed non-significant results (all p>0.20). Synthesize these findings to evaluate the evidence base.

This pattern suggests publication bias; the significant result may be a false positive among multiple trials, and the modest benefit must be weighed against substantial toxicity and cost

The confidence interval proves the drug should be standard of care

P-values below 0.01 override concerns about prior negative studies

The published study's highly significant p-value validates the drug's efficacy

The three unpublished trials are irrelevant to evaluating the published study

Correction methods (Bonferroni, FDR) | P-values and confidence intervals

The Multiple Comparisons Problem - More Tests, More Mess

Conducting multiple simultaneous hypothesis tests inflates the family-wise error rate (FWER) - the probability of making at least one Type I error (false positive).
Analogy: If the daily chance of rain is 10%, the chance of rain over a month is much higher.
FWER Formula: The probability of at least one Type I error across n tests is $1 - (1 - \alpha)^n$.
- With 20 tests at $\alpha = 0.05$, the FWER is $1 - (0.95)^{20} \approx \textbf{64%}$!

⭐ As the number of comparisons increases, the likelihood of finding a "significant" result purely by chance skyrockets. This is a major pitfall in studies analyzing numerous endpoints, like genome-wide association studies (GWAS).

Bonferroni Correction - The Strict Sheriff

Method: A simple, traditional method for controlling the family-wise error rate (FWER) when performing multiple comparisons.
Procedure: Adjusts the significance level ($\alpha$) to counteract the problem of multiple testing.
- Calculate a new, stricter significance threshold: $\alpha_{new} = \frac{\alpha_{original}}{n}$ (where n = number of tests).
- Alternatively, adjust each p-value: $p_{adjusted} = p_{original} \times n$. Compare this adjusted p-value to the original alpha (e.g., 0.05).
Takeaway: Very conservative. It strongly reduces the risk of Type I errors (false positives) but increases the risk of Type II errors (missing true findings).

⭐ With multiple hypotheses, the overall chance of a Type I error accumulates. Bonferroni corrects for this by making the significance criterion for each individual test much more stringent.

📌 Mnemonic: Bonferroni = 'Buys' fewer significant results because it's so strict.

False Discovery Rate (FDR) - The Savvy Detective

Concept: Instead of controlling the probability of making even one Type I error (like Bonferroni), FDR controls the expected proportion of false positives among all rejected null hypotheses (i.e., significant results).
Power: Less stringent than Bonferroni, yielding ↑ statistical power to detect true effects. It accepts a certain proportion of false positives to avoid missing true discoveries.

⭐ In fields with massive datasets like genomics (GWAS) and proteomics, FDR is the preferred method for multiple hypothesis testing, as Bonferroni would be too conservative, missing potentially vital discoveries.

Benjamini-Hochberg Procedure

High‑Yield Points - ⚡ Biggest Takeaways

Multiple comparisons inflate the family-wise error rate, increasing the chance of Type I errors (false positives).

The Bonferroni correction is a simple, highly conservative method that divides the alpha level (α) by the number of tests (n).

While it effectively controls Type I errors, Bonferroni significantly increases the risk of Type II errors (false negatives).

False Discovery Rate (FDR) is a less stringent method that controls the expected proportion of false positives among all rejected hypotheses.