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Difficulty: MediumStatistical Inference and Hypothesis Testing

A prospective cohort study is conducted to evaluate a new low-molecular-weight heparin (LMWH) protocol versus standard unfractionated heparin (UFH) for deep vein thrombosis (DVT) prophylaxis in high-risk pregnant women. The study follows 2,000 women from the first trimester through the postpartum period. The primary endpoint, incidence of symptomatic DVT, occurs in 20 women in the LMWH group and 40 women in the UFH group. The unadjusted relative risk is 0.50 (95% CI: 0.29 - 0.85; p=0.01p = 0.01). A secondary analysis stratifies the participants by maternal age. In women under 35 years old, the relative risk is 0.48 (95% CI: 0.22 - 1.05; p=0.06p = 0.06). In women 35 years and older, the relative risk is 0.52 (95% CI: 0.25 - 1.08; p=0.07p = 0.07). Routine third-trimester laboratory results for the cohort show a mean hemoglobin of 10.8 g/dL and hematocrit of 32%. Which of the following statements represents the most accurate interpretation of this study's findings?

  1. The loss of statistical significance in the age-stratified subgroups is most likely due to a Type II error resulting from reduced sample size.Answer
  2. B
    The stratified analysis demonstrates that maternal age acts as a significant effect modifier on the efficacy of the LMWH protocol.
  3. C
    The case-control design of this study prevents the direct calculation of DVT incidence, limiting the validity of the relative risk.
  4. D
    If a diagnostic test for DVT used in this study is applied to a lower-risk general obstetric population, its positive predictive value will increase.
  5. E
    The third-trimester laboratory findings indicate pathological anemia in this cohort, representing an adverse effect that requires medical intervention.

Answer

The statement accurately identifying that the loss of statistical significance in the age-stratified subgroups is most likely due to a Type II error resulting from reduced sample size.
The correct interpretation relies on understanding statistical power and Type II errors. In the overall cohort, the sample size was large enough to demonstrate a statistically significant reduction in DVT risk (the 95% CI did not include 1.0). When the cohort was stratified by age, the point estimates (0.48 and 0.52) remained remarkably consistent with the overall effect (0.50). However, the subgroups inherently contain fewer patients than the full cohort. This reduction in sample size decreases the statistical power of the analysis, causing the confidence intervals to widen. When a confidence interval widens enough to cross the null value (1.0), the result loses statistical significance. Failing to reject a false null hypothesis due to insufficient power is the definition of a Type II error.

Step-by-Step Solution

1
Analyze the overall primary outcome.
The overall relative risk is 0.50 with a 95% CI of 0.29 - 0.85 and p=0.01p = 0.01.
This establishes that LMWH is significantly more effective than UFH in the entire cohort, as the confidence interval does not cross the null value of 1.0.
2
Evaluate the results of the stratified analysis.
The relative risks in both subgroups (0.48 and 0.52) are similar to the overall risk (0.50), but the 95% CIs widened to cross 1.0.
Stratification inherently reduces the sample size in each analyzed group compared to the whole cohort.
3
Apply statistical principles to determine the cause of the widened intervals.
A smaller sample size decreases statistical power, widening the confidence interval and increasing the probability of a Type II error.
When point estimates remain stable but intervals widen to encompass the null, it indicates the study lacked sufficient power to detect the true difference in the smaller subgroups, leading to a false negative conclusion (Type II error).

Key Concept

Statistical Inference: Power and Type II Error in Subgroup Analysis
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Topics

Statistical Inference and Hypothesis Testing

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