A Dengue Rapid Test in Two Seasons: What a Positive Result Is Worth
A district hospital in the Terai is deciding how to use a rapid immunochromatographic test for dengue in febrile patients. In a local validation study the test had a sensitivity of 90% and a specificity of 95%. During the monsoon about 20% of febrile patients attending the hospital have dengue; in the dry winter months prevalence falls to 2%. The rapid test costs NPR 400 per patient and a confirmatory ELISA costs NPR 1,200. The hospital sees about 500 febrile patients a month and cannot afford to send every sample for ELISA. The medical officer proposes two strategies: (A) rapid-test everyone and confirm only the positives with ELISA, or (B) send every sample straight to ELISA but restrict this to patients with warning signs. He asks what a positive rapid test actually means in each season, and which strategy detects cases at the lowest cost per confirmed case.
1. Compute the positive and negative predictive values of the rapid test in the monsoon and in winter, working per 1000 febrile patients.
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Monsoon (prevalence 20%). Of 1000 patients: 200 diseased → 180 true positives, 20 false negatives; 800 healthy → 40 false positives, 760 true negatives. PPV = 180 / (180 + 40) = 180/220 = 81.8%. NPV = 760/780 = 97.4%.
Winter (prevalence 2%). 20 diseased → 18 true positives, 2 false negatives; 980 healthy → 49 false positives, 931 true negatives. PPV = 18 / (18 + 49) = 18/67 = 26.9%. NPV = 931/933 = 99.8%.
Judgement. Sensitivity and specificity are unchanged, but the meaning of a positive result flips completely: in the monsoon a positive is right about four times out of five; in winter it is wrong about three times out of four. This is the base-rate effect, and it is why a test cannot be judged by its sensitivity and specificity alone. Equally important, the NPV is excellent in both seasons - a negative result is genuinely reassuring, so the test is best used to rule out in winter and to rule in in the monsoon.
2. Calculate the cost per confirmed case for strategy A and for 'ELISA for everyone', in each season, per 1000 patients. Which is cheaper, and what does the comparison hide?
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Monsoon, strategy A: 1000 × 400 = 400 000 NPR for rapid tests, plus 220 positives × 1200 = 264 000 NPR for ELISA → 664 000 NPR for 180 confirmed cases = NPR 3689 per confirmed case. Monsoon, ELISA for all: 1000 × 1200 = 1 200 000 NPR for 200 cases = NPR 6000 per case.
Winter, strategy A: 400 000 + 67 × 1200 = 400 000 + 80 400 = 480 400 NPR for 18 confirmed cases = NPR 26 689 per case. Winter, ELISA for all: 1 200 000 / 20 = NPR 60 000 per case.
So strategy A is cheaper per confirmed case in both seasons. What the comparison hides: (i) strategy A misses the 20 (monsoon) or 2 (winter) false negatives, so it is cheaper partly because it detects fewer cases - the ELISA-for-all arm finds 200, not 180; (ii) in winter, 49 of 67 ELISAs are spent chasing false positives, i.e. NPR 58 800 to confirm nothing; (iii) cost per case is the wrong metric for a disease where missing a case can be fatal - cost per death or severe case averted would favour sensitivity. A fair comparison must state both the cost and the number of cases found.
3. The medical officer wants a rule that works all year. Using the numbers, propose a testing policy and show how changing the tested population or the timing of sampling changes the predictive value.
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Restrict testing to raise pre-test probability. The test's PPV is driven almost entirely by prevalence. If the hospital only rapid-tests patients with warning signs or a compatible febrile illness within the first 5 days - a group whose true prevalence is closer to the monsoon figure of 20% - PPV returns to about 82% even in winter. Testing every febrile patient in January is what produces the 27% PPV.
Add a second, orthogonal test rather than more of the same. In winter, confirming only the 67 positives costs 80 400 NPR for 18 cases; a second different-format rapid test on those 67 would cut the false-positive burden further, and the sequential post-test probability rises sharply because the errors are not perfectly correlated.
Timing matters as much as season. The 90% sensitivity applies to early samples: NS1 antigen sensitivity falls after day 5 of illness, when IgM becomes the better target. If samples in this hospital are typically taken on day 6, sensitivity may be nearer 60%: monsoon PPV then falls to 0.12/(0.12 + 0.04) = 75%, and the missed-case count rises from 20 to 80 per 1000. The policy must therefore specify which day the sample is taken, not just which test is used.
Recommended policy. Rapid test all year, but (1) restrict it to patients within the first 5 days with a clinical picture compatible with dengue, (2) confirm all positives with ELISA before admitting or reporting, (3) treat a negative test in a patient with warning signs as insufficient and repeat or ELISA, and (4) audit the proportion of positives that ELISA confirms each month - if that proportion falls below about 50%, the testing threshold is too low.