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Zorluk: OrtaStatistical Inference and Hypothesis Testing

A multicenter randomized controlled trial is initiated to evaluate the efficacy of a novel monoclonal antibody compared to standard care in patients with severe, refractory rheumatoid arthritis. The primary endpoint is the rate of achieving clinical remission at 12 months. The trial is originally designed to enroll 1,000 patients to achieve 80%80\% statistical power. However, due to slow recruitment, the trial is terminated early after enrolling only 350 patients. The final analysis reveals a relative risk (RR) for clinical remission of 1.35 in the novel therapy group compared to standard care, with a 95%95\% confidence interval (CI) of 0.92 to 1.98 (p=0.11p = 0.11). The investigators conclude that there is no significant difference between the two treatments. Which of the following is the most accurate statistical critique of these findings?

  1. The failure to reach the target enrollment likely resulted in insufficient power, increasing the risk of a Type II error.Cevap
  2. B
    The results are invalid because the retrospective nature of this study design cannot establish causal relationships.
  3. C
    The relative risk and p-value suggest that unrecognized confounding by indication skewed the outcome toward the null.
  4. D
    The reduced sample size inherently decreases the positive predictive value of the primary clinical endpoint.
  5. E
    The novel therapy is statistically superior because the 95% confidence interval does not cross zero.

Cevap

The trial's failure to reach its target enrollment means it was underpowered, strongly increasing the risk of a Type II error.
Statistical power is defined as 1−β1 - \beta (where β\beta is the probability of a Type II error). Power is the probability that a study will correctly reject a false null hypothesis—in other words, the ability of a study to detect a true difference if one actually exists. Power is heavily dependent on the sample size; as the sample size decreases, statistical power decreases, and the risk of a Type II error increases. Because this trial was terminated early and only enrolled a fraction of its required sample size, it was severely underpowered. The results (p=0.11p = 0.11 and a CI crossing 1.0) led the investigators to fail to reject the null hypothesis. However, due to the lack of power, this is likely a Type II error (a 'false negative' study).

Adım Adım Çözüm

1
Analyze the study design and enrollment
The study was designed for 1,000 patients (to achieve 80% power) but only enrolled 350 (35% of the target).
Sample size is the primary determinant of statistical power in a clinical trial.
2
Interpret the statistical results
Relative Risk (RR) is 1.35, 95%95\% CI is 0.92 to 1.98, and p=0.11p = 0.11.
The confidence interval crosses 1.0 and the p-value is >0.05> 0.05, indicating the results are not statistically significant.
3
Synthesize the findings to identify the statistical flaw
A non-significant result in a severely underpowered study indicates a high likelihood of a Type II error (beta error).
The study failed to reject the null hypothesis, but because the sample size was too small, it lacked the ability to detect a true difference even if one existed.

Anahtar Kavram

Type II Error and Statistical Power
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Statistical Inference and Hypothesis Testing

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