Examkin

Question

Difficulty: HardHypothesis Testing and Statistical Power

A public health task force is funding a randomized, non-inferiority clinical trial comparing a novel 3-day oral antibiotic regimen to the standard 7-day oral regimen for uncomplicated urinary tract infections in pregnant patients. The non-inferiority margin (Δ\Delta) is set at a 5% difference in clinical cure rates. The researchers calculated that a sample size of 800 patients (400 per group) is required to achieve 80% statistical power at a one-sided α\alpha level of 0.025, anticipating a maximum 10% dropout rate. Midway through the trial, an independent data monitoring committee notes that the actual dropout rate has exceeded 30% due to patients relocating and missing follow-up appointments. If the researchers continue the trial without modifying the initial enrollment target, which of the following statistical consequences is most likely to occur?

  1. An increased probability of failing to declare the novel 3-day regimen non-inferior, even if it truly is non-inferior.Answer
  2. B
    An increased probability of erroneously concluding that the novel 3-day regimen is non-inferior when it is actually unacceptably inferior.
  3. C
    The high dropout rate will act as an effect modifier rather than a confounder, falsely elevating the apparent treatment effect size.
  4. D
    The positive predictive value of achieving a clinical cure will decrease because the effective disease prevalence in the cohort has dropped.
  5. E
    The disproportionate loss to follow-up introduces a cognitive anchoring bias that permanently invalidates the intention-to-treat analysis.

Answer

An increased probability of failing to declare the novel 3-day regimen non-inferior, even if it truly is non-inferior.
Statistical power is defined as the probability of correctly rejecting the null hypothesis when it is false, mathematically represented as 1−β1 - \beta. In a non-inferiority trial, the null hypothesis (H0H_0) states that the new treatment is inferior to the standard treatment by at least the pre-specified margin (Δ\Delta). A severe decrease in the effective sample size due to high dropout directly reduces the study's statistical power. Consequently, the Type II error rate (β\beta) increases. This means there is a higher mathematical risk of failing to reject the null hypothesis of inferiority, leading the researchers to incorrectly conclude that they cannot declare the new drug non-inferior, even if it truly is just as effective as the standard regimen.

Step-by-Step Solution

1
Determine the effect of a 30% dropout rate on the trial design.
The effective sample size is significantly smaller than the 800 patients originally calculated.
High attrition means fewer patients complete the trial, providing less data for the final analysis.
2
Correlate the reduced sample size with statistical power.
Statistical power decreases.
Power (1−β1 - \beta) is highly dependent on sample size; as the sample size drops, the variance increases, making it harder to detect a true effect, thus reducing power.
3
Relate the loss of power to error rates.
The Type II error rate (β\beta) increases.
Since Power = 1−β1 - \beta, a decrease in power directly correlates with a mathematical increase in the risk of committing a Type II error.
4
Define Type II error specifically in the context of a non-inferiority trial.
Failing to declare non-inferiority when the drug actually is non-inferior.
In a non-inferiority trial, the null hypothesis (H0H_0) assumes the new treatment is inferior. A Type II error is failing to reject this H0H_0 when it is false (i.e., failing to show non-inferiority when the drug is, in fact, not worse than the standard).

Key Concept

Type II Error (β\beta) and Statistical Power in Non-Inferiority Trials
Rate this question

Topics

Hypothesis Testing and Statistical Power

More questions from this topic