Examkin

Question

Difficulty: HardHypothesis Testing and Statistical Power

Investigators are conducting a randomized, two-period crossover trial evaluating a novel targeted biologic therapy for chronic spontaneous urticaria. The initial power analysis determined that a total of 40 patients (20 receiving the biologic followed by placebo, and 20 receiving placebo followed by the biologic) would provide 90% power to detect a clinically significant reduction in symptom severity scores at a two-tailed α\alpha of 0.05.

Following the initiation of the trial, an interim pharmacokinetic analysis reveals that the biologic has an unexpectedly long half-life. This results in a profound carryover effect that extends well beyond the planned 6-week washout period. To preserve the integrity of the data, the trial steering committee decides to discard all Period 2 data entirely. The study will now be analyzed as a standard two-arm parallel randomized controlled trial using exclusively the Period 1 data (20 patients in the biologic arm and 20 patients in the placebo arm).

Assuming the true effect size of the biologic remains unchanged, which of the following is the most likely statistical consequence of this protocol modification?

  1. The statistical power of the study will decrease primarily because the analysis must now incorporate inter-subject rather than intra-subject varianceAnswer
  2. B
    The probability of a Type II error will decrease because removing the carryover data eliminates a confounding effect modifier
  3. C
    The statistical power of the study will remain unchanged provided the investigators transition from a paired statistical test to an independent statistical test
  4. D
    The probability of a Type I error will increase because the positive predictive value of the study findings changes with a reduced sample size
  5. E
    The statistical power will increase because the premature closure of the second period prevents the dilution of the treatment effect by cognitive bias

Answer

The statistical power of the study will decrease primarily because the analysis must now incorporate inter-subject rather than intra-subject variance.
Statistical power is the probability of correctly rejecting the null hypothesis when a true difference exists (Power = 1−β1 - \beta). Power is heavily dependent on the variance of the data. In a crossover design, each patient acts as their own control. The statistical analysis (such as a paired t-test) evaluates the difference in outcomes within the same person, relying on intra-subject variance. Because an individual's baseline characteristics are perfectly matched with themselves, intra-subject variance is typically very low, yielding high statistical power.

When the trial is converted to a parallel-group design, the biologic group is now compared to a completely different group of people (the placebo group). The analysis (such as an independent samples t-test) must now incorporate inter-subject variance, which accounts for the natural physiological differences between different human beings. This variance is substantially larger. The combination of utilizing a larger variance term and halving the total number of outcome measurements drastically reduces the statistical power of the study and increases the risk of a Type II error.

Step-by-Step Solution

1
Identify the core statistical advantage of the original crossover design.
In a crossover trial, each subject receives both treatments, serving as their own control. This allows the statistical test to use intra-subject variance.
Intra-subject variance is almost always smaller than inter-subject variance, providing higher statistical power for a given number of participants.
2
Determine the impact of the protocol modification.
Discarding Period 2 converts the study into a parallel-group trial. The effective sample size of observations is halved, and the groups are now composed of different individuals.
The carryover effect contaminated Period 2, making the data unusable.
3
Analyze how the shift to a parallel design affects variance and statistical power.
Because different individuals are now being compared, the analysis must use inter-subject variance. The combination of a smaller sample size (fewer total measurements) and a larger variance term significantly decreases the ability to detect a true difference.
Statistical power is inversely proportional to variance and directly proportional to sample size.
4
Relate power to Type II error.
A decrease in statistical power corresponds directly to an increase in the probability of a Type II error (β\beta).
Power is mathematically defined as 1−β1 - \beta.

Key Concept

Crossover study designs yield higher statistical power than parallel designs primarily because they rely on intra-subject variance (comparing a patient to themselves) rather than inter-subject variance. Converting a crossover trial to a parallel trial increases variance and decreases power.
Rate this question

Topics

Hypothesis Testing and Statistical Power

More questions from this topic