A team of researchers is investigating how the availability of recent medical cases affects doctors’ diagnostic decisions. They hypothesize that doctors may be more likely to consider diagnoses they’ve encountered recently, even if they’re statistically less probable.
The study involves 300 general practitioners (GPs) who are presented with a hypothetical patient case. The patient’s symptoms could indicate either Condition A (a rare but serious illness) or Condition B (a more common, less severe ailment). Before seeing the case, the GPs are randomly divided into three groups:
Group 1 (100 GPs): Recently treated a patient with Condition A.
Group 2 (100 GPs): Recently treated a patient with Condition B.
Group 3 (100 GPs): Control group, no recent exposure to either condition.
After reviewing the case, each GP estimates the probability of the patient having Condition A and decides whether to order an expensive, invasive test for Condition A.
Results:
Group 1: Mean estimated probability of Condition A = 35%, SD = 8%, 65% ordered the test
Group 2: Mean estimated probability of Condition A = 15%, SD = 5%, 20% ordered the test
Group 3: Mean estimated probability of Condition A = 25%, SD = 6%, 40% ordered the test
Actual prevalence of Condition A in patients with these symptoms: 20%
Cost of the test: $5,000
Cost of missing a Condition A diagnosis: $100,000
1. Conduct a one-way ANOVA to determine if there are statistically significant differences in estimated probabilities between the three groups. Use a significance level of 0.05.
2. Calculate the effect size (η² – eta squared) for the ANOVA result. Interpret the magnitude of the effect.
3. Perform post-hoc t-tests with Bonferroni correction to identify which specific groups differ significantly from each other in their probability estimates.
4. Calculate the relative risk of ordering the test for Group 1 compared to Group 3. Interpret this result.
5. Assuming the actual prevalence is correct, calculate the expected value of ordering the test versus not ordering it. Based on this, what should be the optimal decision rule?
6. For each group, calculate the percentage of GPs who made the optimal decision based on your decision rule in task 5. Which group performed best?
7. Discuss the potential implications of availability bias in medical decision-making, considering both patient outcomes and healthcare costs.
8. Propose a debiasing strategy that could help mitigate the impact of availability bias in clinical settings. How could you test the effectiveness of this strategy?
1. One-way ANOVA:
H₀: μ₁ = μ₂ = μ₃
H₁: At least one group mean is different
Calculate:
SSB = 100[(35-25)² + (15-25)² + (25-25)²] = 20,000
SSW = 99(8² + 5² + 6²) = 11,385
SST = SSB + SSW = 31,385
df(between) = 2, df(within) = 297, df(total) = 299
MSB = SSB/df(between) = 20,000/2 = 10,000
MSW = SSW/df(within) = 11,385/297 = 38.33
F = MSB/MSW = 10,000/38.33 = 260.89
Critical F(2,297) at α=0.05 ≈ 3.03
Since 260.89 > 3.03, we reject H₀. There are statistically significant differences between groups.
2. Effect size (η²):
η² = SSB/SST = 20,000/31,385 = 0.637
This indicates a large effect size, with about 63.7% of the variance in estimated probabilities explained by the group assignment.
3. Post-hoc t-tests with Bonferroni correction:
New α = 0.05/3 = 0.0167 for each test
1 vs 2: t = (35-15)/√(8²/100 + 5²/100) = 21.21, p < 0.0001
1 vs 3: t = (35-25)/√(8²/100 + 6²/100) = 10.00, p < 0.0001
2 vs 3: t = (15-25)/√(5²/100 + 6²/100) = -13.16, p < 0.0001
All pairs are significantly different.
4. Relative Risk for Group 1 vs Group 3:
RR = (65/100) / (40/100) = 1.625
GPs in Group 1 are 1.625 times more likely to order the test than those in Group 3.
5. Expected Value calculation:
P(Condition A) = 0.20
EV(Test) = 0.20(-$5,000) + 0.80(-$5,000) = -$5,000
EV(No Test) = 0.20(-$100,000) + 0.80($0) = -$20,000
Optimal decision rule: Always order the test, as it has a higher expected value.
6. Percentage making optimal decision:
Group 1: 65%
Group 2: 20%
Group 3: 40%
Group 1 performed best according to this decision rule.
7. Implications:
Availability bias can lead to both over-diagnosis and under-diagnosis, potentially resulting in unnecessary tests and treatments or missed serious conditions. This can harm patient outcomes and increase healthcare costs. It may also contribute to healthcare disparities if certain conditions are over-represented in medical education or media.
8. Debiasing strategy:
Implement a clinical decision support system that provides real-time statistical information about condition prevalence and test accuracy. To test its effectiveness, conduct a randomized controlled trial comparing diagnostic accuracy and cost-effectiveness between GPs using the system and those relying on clinical judgment alone.
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