Statistical Power and Positive Predictive Value in a Screening Audit
Your department is auditing a new lung cancer screening program. In the first year, 2,000 patients were screened with low-dose CT. Of these, 120 had a positive screen (Lung-RADS 4A or higher). Twenty of the 120 positive screens were ultimately diagnosed with lung cancer. Among the 1,880 negative screens, 4 were diagnosed with lung cancer within 12 months (interval cancers). The department chair wants to know whether the program is "working" and whether the positive predictive value is acceptable. A colleague argues that because the PPV is only about 17%, the program should be paused.
1. Calculate the PPV, the cancer detection rate, and the interval cancer rate. Interpret each in context.
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Positive predictive value (PPV) = TP / (TP + FP) = 20/120 = 16.7%. This means about 1 in 6 positive screens is a true cancer; the rest are false positives requiring follow-up imaging or biopsy. A PPV in this range is consistent with published lung screening programs (commonly ~10–25% depending on the threshold and prevalence).
Cancer detection rate = 20/2,000 = 1.0% (10 per 1,000), which is in the expected range for a prevalence screen in a high-risk cohort.
Interval cancer rate = 4/1,880 ≈ 0.21% (2.1 per 1,000 negative screens). A low interval cancer rate supports that the negative screens were reasonably reliable.
Interpretation: a 17% PPV is not a reason to pause the program - it reflects the trade-off inherent in screening a population with modest prevalence. The relevant question is whether the program's recall and biopsy rates are acceptable and whether the detected cancers are early-stage and treatable.
2. The chair asks how a larger sample would change the interpretation. Explain the relationship between sample size, confidence intervals, and the decision to pause the program.
Read the worked answer
With n = 120 positives, the 95% CI for PPV (Wilson) is roughly 11–24%. That is wide: the true PPV could plausibly be anywhere from ~1 in 9 to ~1 in 4. A single year's audit cannot distinguish a program performing at the low end from one at the high end.
Key points:
- Sample size drives precision, not the point estimate. Increasing the number of screens narrows the CI around the PPV and detection rate, allowing a defensible comparison to benchmarks.
- Pausing on a point estimate alone is a statistical error - it ignores sampling variability and the possibility that the observed PPV is consistent with acceptable performance.
- The decision should rest on process metrics (recall rate, biopsy complication rate, proportion of stage I diagnoses, adherence to Lung-RADS follow-up) and on whether the CI excludes an unacceptable threshold, not on a single year's PPV.
Recommendation: continue the program with prospective tracking, report CIs alongside point estimates, and revisit after accumulating more positives.