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Difficulty: HardInferential Statistical Tests

Researchers are evaluating a new synthetic thyroid hormone replacement formulation compared to standard levothyroxine in patients with primary hypothyroidism. To minimize inter-individual physiological variability, the investigators employ a crossover study design. A total of 4545 adult patients are randomly assigned to receive either the new formulation or standard levothyroxine for 88 weeks. After an adequate 44-week washout period, each patient crosses over to receive the alternate therapy for another 88 weeks. The primary endpoint is the serum thyroid-stimulating hormone concentration, measured in mIU/L at the end of each 88-week treatment period. Preliminary data analysis confirms that the intra-individual differences in serum thyroid-stimulating hormone levels between the two treatment periods are normally distributed. Which of the following statistical tests is most appropriate to evaluate the difference in the primary endpoint between the two formulations?

  1. A
    Kruskal-Wallis analysis
  2. B
    McNemar test
  3. Paired Student t-testAnswer
  4. D
    Two-sample independent t-test
  5. E
    Wilcoxon signed-rank test

Answer

Paired Student t-test
The correct statistical test is the paired Student t-test. The crossover study design means that every patient receives both the new formulation and standard levothyroxine. Consequently, the TSH measurements at the end of each period are paired (dependent) because they come from the same individuals, allowing each patient to act as their own control. Furthermore, the dependent variable (serum TSH concentration) is continuous, and the stem explicitly states that the differences between the two treatment periods are normally distributed. The paired Student t-test is the appropriate parametric method to compare the means of two related continuous variables when they meet the assumption of normal distribution.

Step-by-Step Solution

1
Identify the independent variable and study design
The study compares two treatments (new formulation vs. standard levothyroxine) using a crossover design, meaning each patient receives both treatments.
Determines whether the data points are independent or paired. A crossover design yields paired (dependent) data since each subject acts as their own control.
2
Identify the dependent variable type
The primary endpoint is serum TSH concentration, which is measured on a continuous numerical scale.
The type of dependent variable dictates whether categorical or continuous statistical tests are required.
3
Assess the distribution of the data
The stem specifies that the intra-individual differences in TSH levels are normally distributed.
Normal distribution of paired differences satisfies the assumption for a parametric test, ruling out non-parametric alternatives.
4
Select the appropriate statistical test
Paired Student t-test
This is the definitive parametric test for comparing the means of two related or paired groups with normally distributed continuous data.

Key Concept

Selection of the paired Student t-test requires recognizing a crossover study design (yielding paired data) evaluating a continuous, normally distributed dependent variable.
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Topics

Inferential Statistical Tests

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