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Difficulty: MediumStatistical Inference and Hypothesis Testing

A regional health authority implements a pilot program to evaluate a strategy for reducing hospital readmission rates among patients with heart failure. Fifty community hospitals are randomized to either utilize a novel telehealth monitoring system or continue with standard discharge protocols. After 1212 months, the data shows a 15%15\% reduction in readmissions in the telehealth group compared to the standard care group. However, the 95%95\% confidence interval (CI) for the relative risk is 0.720.72 to 1.051.05. Based on these results, the investigators conclude that the telehealth system does not significantly affect readmission rates. Three years later, a comprehensive national registry study involving over 500500 hospitals definitively confirms that the telehealth system genuinely reduces readmission rates by 14%14\%. Which of the following best explains why the initial pilot program failed to demonstrate a statistically significant benefit?

  1. High probability of committing a Type II errorAnswer
  2. B
    Presence of unrecognized confounding variables
  3. C
    Inappropriate selection of a retrospective study design
  4. D
    Low positive predictive value of the readmission metric
  5. E
    Careless misinterpretation of the confidence interval limits

Answer

High probability of committing a Type II error
The correct answer identifies a Type II (β\beta) error. A Type II error occurs when investigators fail to reject the null hypothesis when it is actually false (i.e., concluding there is no difference when one truly exists). In this scenario, the pilot program's 95%95\% confidence interval crossed 1.01.0, correctly leading the researchers to state the results were not statistically significant for that specific dataset. However, the later national registry proved the intervention truly worked. The initial study missed the true effect likely because its small sample size (5050 hospitals) provided insufficient statistical power.

Step-by-Step Solution

1
Analyze the results of the initial pilot program.
The relative risk had a 95% CI of 0.72 to 1.05, crossing the null value (1.0), meaning the result was not statistically significant.
To determine the study's stated conclusion regarding the null hypothesis.
2
Compare the pilot program's conclusion with the true population parameter revealed later.
The initial study concluded no significant difference, but the later definitive study proved a true difference actually exists.
To identify if a statistical error occurred during hypothesis testing.
3
Identify the type of statistical error made in the initial study.
Failing to reject a false null hypothesis is a Type II (beta) error, commonly caused by low statistical power due to small sample sizes.
To select the option that perfectly explains the discrepancy.

Key Concept

Type II error occurs when a study fails to reject the null hypothesis even though a true difference exists in the population, typically due to inadequate statistical power (often from a small sample size).
Estimated Time:1m 15s
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Topics

Statistical Inference and Hypothesis Testing

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