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Difficulty: Very hardStatistical Inference and Hypothesis Testing

An academic neurology department conducts a prospective cohort study to evaluate a novel disease-modifying therapy for patients with secondary progressive multiple sclerosis. The primary outcome is the time to first documented persistent disability progression. Initial unadjusted survival analysis comparing the novel therapy to the institutional standard of care yields a hazard ratio (HR) of 0.72 (95% CI: 0.48 - 1.08, p = 0.11).

Subsequently, the investigators perform a pre-specified multivariate Cox proportional hazards regression, adjusting for patient age at diagnosis, baseline Expanded Disability Status Scale (EDSS) score, and T2 lesion volume on initial MRI. This adjusted analysis demonstrates an HR of 0.61 (95% CI: 0.41 - 0.90, p = 0.01).

Based on these statistical findings, which of the following is the most accurate conclusion regarding the study results?

  1. The unadjusted analysis fails to demonstrate a statistically significant delay in disability progression, but covariate adjustment reveals a significant protective effect.Answer
  2. B
    The unadjusted p-value indicates an 11% probability that the novel therapy has no effect on disability progression, which decreases to 1% after adjustment.
  3. C
    The significant shift in the hazard ratio upon adjustment confirms that baseline EDSS score and MRI lesion volume are effect modifiers.
  4. D
    Because the unadjusted 95% confidence interval includes 1.0, the novel therapy and standard care are proven to be statistically equivalent.
  5. E
    The adjusted analysis is invalid because multivariate regression is only appropriate when the unadjusted bivariate analysis achieves a p-value of less than 0.05.

Answer

The unadjusted analysis fails to demonstrate a statistically significant delay in disability progression, but covariate adjustment reveals a significant protective effect.
The correct answer accurately synthesizes the provided statistical parameters. In time-to-event analysis, a Hazard Ratio (HR) of 1.0 indicates no difference in risk between groups. For the unadjusted data, the 95% Confidence Interval ranges from 0.48 to 1.08. Because this interval includes 1.0, the finding is not statistically significant at the standard alpha level of 0.05 (corroborated by the p-value of 0.11). However, in the adjusted model, the HR is 0.61 with a 95% CI of 0.41 to 0.90. Because this entire interval is less than 1.0, the adjusted analysis demonstrates a statistically significant protective effect (a 39% reduction in the hazard of disability progression).

Step-by-Step Solution

1
Interpret the unadjusted statistical data.
The unadjusted HR is 0.72, and the 95% CI (0.48 - 1.08) crosses 1.0. The p-value is 0.11 (> 0.05).
In survival analysis, an HR of 1.0 means no difference in risk. Because the CI includes 1.0, the result is not statistically significant.
2
Interpret the adjusted statistical data.
The adjusted HR is 0.61, and the 95% CI (0.41 - 0.90) lies entirely below 1.0. The p-value is 0.01 (< 0.05).
Because the upper bound of the CI (0.90) is less than 1.0, the novel therapy is associated with a statistically significant reduction in the hazard of disability progression compared to standard care.
3
Differentiate between confounding and effect modification.
The change in the HR from 0.72 to 0.61 upon adding variables to the model indicates that those variables were acting as negative confounders, masking the true effect.
Adjusting for covariates controls for confounding. Effect modification is assessed by looking at the treatment effect within specific subgroups (stratification), not by simply adjusting the overall model.
4
Identify the correct definition of a p-value and statistical equivalence.
A p-value is not the probability that the null hypothesis is true. Furthermore, a non-significant result (CI crossing 1.0) does not prove equivalence.
These are classic logical fallacies in statistical inference. Equivalence testing requires predefined margins, and frequentist p-values do not assign probability to the hypothesis itself.

Key Concept

Interpretation of Confidence Intervals and p-values in adjusted versus unadjusted statistical models.
Estimated Time:2m 0s
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Topics

Statistical Inference and Hypothesis Testing

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