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Difficulty: HardHypothesis Testing and Statistical Power

An oncology research network is preparing to launch a randomized, placebo-controlled trial evaluating a new monoclonal antibody for the prevention of disease recurrence in high-risk melanoma patients. The trial is originally powered at 80%80\% to detect a hazard ratio of 0.700.70 with a two-sided α\alpha level of 0.050.05. Prior to patient enrollment, the data and safety monitoring board (DSMB) reviews recent post-marketing surveillance data from a similar drug class that revealed rare but fatal autoimmune toxicities. Consequently, the DSMB mandates that the study must use a more stringent two-sided α\alpha level of 0.010.01 to minimize the risk of a false-positive efficacy finding. Due to an absolute cap on available grant funding, the investigators are unable to increase the total number of enrolled patients or extend the follow-up duration. Which of the following is the most likely statistical consequence of implementing the DSMB's mandate under these constraints?

  1. The trial's statistical power will fall below 80%, increasing the probability of a Type II error.Answer
  2. B
    The positive predictive value of a statistically significant trial result will decrease.
  3. C
    The trial data must now be analyzed using non-parametric inferential statistical tests.
  4. D
    The more stringent threshold will act as a confounding variable, artificially reducing the observed treatment effect size.
  5. E
    The probability of erroneously concluding that the novel antibody is effective will increase.

Answer

The trial's statistical power will fall below 80%, increasing the probability of a Type II error.
In statistical hypothesis testing, the power of a study (the probability of correctly rejecting a false null hypothesis) is determined by the α\alpha level, the sample size, and the true effect size. The α\alpha level (Type I error rate) and β\beta level (Type II error rate) are inversely related for any given sample size and effect size. By lowering the α\alpha level from 0.050.05 to 0.010.01, the researchers require a higher burden of statistical proof to declare significance. Because the sample size is fixed due to absolute funding constraints and the true effect size is assumed constant, this stricter significance threshold directly increases β\beta, the probability of failing to detect a true difference (a Type II error). Consequently, the statistical power, calculated as 1−β1 - \beta, will fall below the originally planned 80%80\%.

Step-by-Step Solution

1
Identify the relationship between alpha, beta, and sample size.
Alpha (Type I error rate) and beta (Type II error rate) are inversely related when sample size and effect size are held constant.
A stricter alpha shifts the critical value, requiring a larger observed effect to reject the null hypothesis.
2
Determine the effect of the DSMB mandate on the alpha level.
The alpha level is reduced from 0.05 to 0.01, making the criteria for statistical significance more stringent.
The DSMB wants to reduce the chance of a false positive due to the severe side effect profile.
3
Evaluate the impact of the fixed constraints.
Because funding is capped, sample size and follow-up time cannot be increased to compensate for the stricter alpha.
Without a larger sample size to improve precision, the inverse relationship between alpha and beta is unavoidable.
4
Conclude the final statistical consequence.
Beta increases, meaning power (1 - beta) must decrease below the originally planned 80%.
The increased stringency increases the likelihood of failing to detect a true clinical benefit.

Key Concept

The inverse relationship between Type I error (alpha) and Type II error (beta) given a fixed sample size and effect size.
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Topics

Hypothesis Testing and Statistical Power

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