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Combination Diagnostic Strategies: Parallel, Serial and Two-Step Testing
A combination strategy turns the results of two or more tests into one decision. The TB study used here defines two rules: in parallel testing a participant counts as positive when one or both of the two tests are positive and as negative when both are negative; in sequential testing a participant counts as positive only when both tests are positive.1 A statistics paper on sequential testing names the first rule believe the positive and describes it as diagnosing disease if either of two tests is positive.2
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| Rule | The result is positive when | If the two tests err independently (Editverse arithmetic) |
|---|---|---|
| Single test | The one test is positive. | Sensitivity s and specificity p of that test. |
| Parallel (OR rule) | One or both tests are positive. | Sensitivity 1 − (1 − s1)(1 − s2), which is at least as high as either test alone; specificity p1 × p2, which is at most as high as either test alone. |
| Serial (AND rule) | Both tests are positive. | Sensitivity s1 × s2, at most as high as either test alone; specificity 1 − (1 − p1)(1 − p2), at least as high as either test alone. |
The formulas in the last column are Editverse arithmetic, not statements from a source; they hold only when the two tests are independent given the true disease status. A two-step algorithm is the clinical version of the same idea: a second test is run after the first. In the C. difficile paper discussed below, a PCR assay is performed first and followed by a second assay such as a toxin enzyme immunoassay.3 In the TB paper the first step is a cheap triage test that narrows who goes on to molecular confirmation.1
Two definitions are used throughout. Sensitivity is the proportion of people with the condition who test positive, and specificity is the proportion of people without it who test negative; the positive likelihood ratio is sensitivity divided by one minus specificity and the negative likelihood ratio is one minus sensitivity divided by specificity. Predictive values depend on prevalence, while likelihood ratios, like sensitivity and specificity, do not.4 Whether a sequential strategy is worth using also depends on cost: one methods paper reports that sequential strategies most often raise accuracy over a single test but are not always preferred, and that prevalence plays a large role once cost is considered.5
A Real Case: Four Blood Tests for TB Triage in Uganda
Komakech and colleagues enrolled 767 people aged 15 or older with TB-suggestive symptoms at three facilities in Kampala between 9 May 2023 and 2 August 2024; 623 were eligible for analysis and 111 (18%) were positive on the reference standard, a positive culture and/or Xpert MTB/RIF Ultra result.1 They compared four host-blood tests: C-reactive protein (CRP), the monocyte-to-lymphocyte ratio (MLR), interferon gamma-induced protein 10 (IP-10) and haemoglobin. The paper is CC BY 4.0, so we reused its printed counts and drew our own figures. CRP and IP-10 were measured on stored plasma, and the IP-10 cut-off was chosen with the Youden index.1
The four single tests
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| Test (positive when) | True positives | True negatives | Sensitivity | Specificity |
|---|---|---|---|---|
| CRP (at least 10 mg/L) | 101 of 111 | 398 of 512 | 91.0% | 77.7% |
| MLR (at least 0.378) | 80 of 111 | 411 of 512 (printed as 410) | 72.1% | 80.3% |
| IP-10 (at least 28.75) | 95 of 111 | 375 of 512 | 85.6% | 73.2% |
| Haemoglobin (below 12 g/dL female, 13 g/dL male) | 77 of 111 | 389 of 512 | 69.4% | 76.0% |
The counts are Table 1 of the paper.1 Table 1 prints 410 true negatives for MLR next to a specificity of 80.3%, and 410 of 512 is 80.1%; 411 of 512 gives the printed 80.3%, and 411 is also the value that makes the combination tables add up (see the reproduction section below), so we use 411.
Six pairs, two rules
The authors combined each pair of tests in parallel and in sequence at the same cut-offs.1 Because the same positivity rule gives the same classification whichever test is run first, they report that the order of testing did not change the accuracy estimates.1 The table shows the observed combined results with counts.
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| Pair | Parallel (either positive): sensitivity | Parallel: specificity | Serial (both positive): sensitivity | Serial: specificity |
|---|---|---|---|---|
| CRP + MLR | 95.5% (106/111) | 68.9% (353/512) | 67.6% (75/111) | 89.1% (456/512) |
| CRP + IP-10 | 95.5% (106/111) | 65.0% (333/512) | 81.1% (90/111) | 85.9% (440/512) |
| CRP + Hb | 96.4% (107/111) | 63.1% (323/512) | 64.0% (71/111) | 90.6% (464/512) |
| MLR + IP-10 | 94.6% (105/111) | 62.9% (322/512) | 63.1% (70/111) | 90.6% (464/512) |
| MLR + Hb | 88.3% (98/111) | 63.7% (326/512) | 53.2% (59/111) | 92.4% (473/512) |
| IP-10 + Hb | 93.7% (104/111) | 58.8% (301/512) | 61.3% (68/111) | 90.4% (463/512) |
Seven counts in this analysis are reconciled to the printed percentages rather than taken from the printed cells (six in this table and one in the single-test table above); each is listed in Reproducing the printed tables.
What this case shows: how parallel and serial rules move sensitivity and specificity in real data for six pairs, and how far that departs from independence arithmetic. What it does not show: how the strategies perform in other settings, in children or with fresh capillary blood for CRP and IP-10, because the study enrolled people aged 15 or older in Kampala and measured CRP and IP-10 on stored plasma.1
For CRP plus MLR in parallel, 106 of 111 cases were found against 101 for CRP alone, a gain of 5 cases, and 159 of 512 people without TB were falsely flagged against 114, a cost of 45 more false alarms. In series, 75 of 111 cases were found, 26 fewer than CRP alone, and 56 of 512 people without TB were falsely flagged, 58 fewer. The authors describe a WHO target of at least 90% sensitivity and 60% specificity for a triage test; CRP alone and the parallel pair meet it, and the serial pair does not.1 If CRP were run first in a sequential workflow, 215 of 623 people (34.5%) would be CRP positive and need the second test. That is Editverse arithmetic from the single-test counts, because in the study every test was run in every participant.
Recomputing the Combined Results in R
The paper prints counts for each test and for each pair, but not the full cross tabulation of one test against the other. We therefore recovered the number positive on both tests by inclusion and exclusion: the people positive on both plus the people positive on either equal the sum of the two single-test counts, and the same identity holds for true negatives. We then predicted each pair from the single-test rates assuming independence, and compared that with what was observed.1 The code below reproduces the prediction for CRP plus MLR.
# Komakech 2026: CRP and MLR in 111 reference-positive and 512 reference-negative people
s1 <- 101/111; s2 <- 80/111 # sensitivities
p1 <- 398/512; p2 <- 411/512 # specificities
round(c(par_sens = 1 - (1 - s1) * (1 - s2),
par_spec = p1 * p2,
ser_sens = s1 * s2,
ser_spec = 1 - (1 - p1) * (1 - p2)), 3)
# 0.975 0.624 0.656 0.956 (observed: 0.955 0.689 0.676 0.891)The table gives the observed result minus the independence prediction, in percentage points, for all six pairs.
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| Pair | Parallel sensitivity | Parallel specificity | Serial sensitivity | Serial specificity |
|---|---|---|---|---|
| CRP + MLR | −2.0 | +6.5 | +2.0 | −6.5 |
| CRP + IP-10 | −3.2 | +8.1 | +3.2 | −8.1 |
| CRP + Hb | −0.8 | +4.0 | +0.8 | −4.0 |
| MLR + IP-10 | −1.4 | +4.1 | +1.4 | −4.1 |
| MLR + Hb | −3.2 | +2.7 | +3.2 | −2.9 |
| IP-10 + Hb | −1.9 | +3.1 | +1.9 | −3.1 |
The direction is the same in all six pairs. Parallel specificity is higher than predicted by 2.7 to 8.1 points and serial specificity is lower by 2.9 to 8.1 points; parallel sensitivity is lower than predicted by 0.8 to 3.2 points and serial sensitivity higher by 0.8 to 3.2 points. This pattern is what you would expect if the tests tended to err in the same people, so the second test adds less new information than independence assumes. As a rough descriptive check, the independence value lies outside the 95% Clopper-Pearson interval of the observed combined specificity in 2 of 6 parallel pairs and 6 of 6 serial pairs, and outside the interval of the observed combined sensitivity in 1 of 6 parallel pairs and 0 of 6 serial pairs; this check ignores the sampling error in the single-test rates, so we treat it as descriptive only. With no perfect reference standard, wrongly assuming conditional independence can also bias estimates of error rates, as Vacek showed in 1985.6
Reproducing the printed tables
Reproduces exactly when the counts are taken from the printed percentages. With the printed counts, the inclusion and exclusion identity fails in several cells; with the counts implied by the printed percentages, it holds exactly for true positives in all six pairs and for true negatives in five of the six, with MLR plus haemoglobin out by one true negative. The cells that disagree are listed below. We cannot tell from the paper whether the counts or the percentages are the printed error, but the identity supports the percentages. The paper also labels one serial row MLR at least 0.338 where every other row uses 0.378.1 For CRP plus MLR, our recomputed PPV, NPV and diagnostic odds ratio match the printed 0.400, 0.986 and 47.0 in parallel and 0.573, 0.927 and 17.0 in series.1
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| Where in the paper | Printed | Implied by the printed percentage |
|---|---|---|
| Table 1, MLR true negatives | 410 of 512 (specificity 80.3%) | 411 of 512 |
| Table 3, CRP + IP-10, parallel true positives | 90 of 111 (sensitivity 95.5%) | 106 of 111 |
| Table 4, CRP + MLR, serial true negatives | 444 of 512 (specificity 89.1%) | 456 of 512 |
| Table 4, MLR + haemoglobin, serial true positives | 52 of 111 (sensitivity 53.2%) | 59 of 111 |
| Table 4, MLR + haemoglobin, serial true negatives | 478 of 512 (specificity 92.4%) | 473 of 512 |
| Table 4, IP-10 + haemoglobin, serial true positives | 57 of 111 (sensitivity 61.3%) | 68 of 111 |
| Table 4, IP-10 + haemoglobin, serial true negatives | 473 of 512 (specificity 90.4%) | 463 of 512 |
Predictive values at other prevalences
Sensitivity and specificity do not change with prevalence, but predictive values do.4 The table applies the published CRP plus MLR sensitivities and specificities to the study prevalence of 17.8% (111 of 623) and to 5%, and shows what 1,000 people tested at the study prevalence would look like. These are Editverse illustrations; they assume the published accuracy would hold in the new population, which it may not.
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| Strategy (CRP + MLR) | PPV at 17.8% prevalence | NPV at 17.8% prevalence | PPV at 5% prevalence | Per 1,000 tested: found, missed, false alarms |
|---|---|---|---|---|
| CRP alone | 47.0% | 97.5% | 17.7% | 162, 16, 183 |
| Parallel (either positive) | 40.0% | 98.6% | 13.9% | 170, 8, 255 |
| Serial (both positive) | 57.3% | 92.7% | 24.5% | 120, 58, 90 |
A Second Case: Two-Step Testing for C. difficile
Bettger and colleagues introduced a two-step algorithm at a US tertiary care centre on 16 August 2018, following the 2018 IDSA recommendations as the paper describes them: a PCR assay first, then a toxin enzyme immunoassay (EIA).3 Between 17 August 2018 and 30 September 2019 there were 216 PCR-positive tests with EIA data from 215 patients; 61 were PCR positive and EIA positive (concordant) and 155 (71.8%) were PCR positive and EIA negative (discordant).3 The paper is CC BY 4.0.
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| Group in the C. difficile study | Tests | Treated | Readmitted for C. difficile within 30 days |
|---|---|---|---|
| Concordant: PCR positive and toxin EIA positive | 61 | 58 of 61 (95.1%) | 5 of 60 (8.3%) |
| Discordant: PCR positive and toxin EIA negative | 155 | 103 of 155 (66.5%) | 2 of 154 (1.3%) |
Counts are from Table 1 of the paper; percentages were recomputed by Editverse.3 Among discordant patients, 52 of 155 (33.5%) were not treated. The authors report that mortality did not differ between the groups and that 30-day readmission with C. difficile was higher in the concordant group (p = 0.02), and, in their conclusion, that the algorithm did not change clinical management because the majority of discordant cases were treated as true infection. Following the analysis, the hospital returned to a one-step algorithm with the toxin EIA performed by request.3 What this case shows: a second step produces a large discordant group (155 of 216), and the authors conclude that the algorithm did not change clinical management because most discordant cases were treated as true infection; about a third (52 of 155) went untreated. What it does not show: which discordant results were true infections; the authors write that the actual significance of these cases is unclear. In Editverse reading, the analysis has no reference standard such as toxigenic culture to settle this.
Choosing a Strategy: What the Numbers Say
These are Editverse readings of the case above, not rules.
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| Situation | Strategy the TB numbers favour | Evidence in the TB study |
|---|---|---|
| A missed case is costly and a more specific confirmatory test follows | Parallel | CRP + MLR in parallel found 106 of 111 cases against 101 for CRP alone, with 45 more false alarms (159 against 114 of 512). |
| A positive result triggers a costly or harmful step | Serial | CRP + MLR in series cut false alarms from 114 to 56 of 512 but found 75 of 111 cases, 26 fewer than CRP alone. |
| One test already meets the target | Consider whether a second test is needed | The authors describe a WHO target of at least 90% sensitivity and 60% specificity; CRP alone gave 91.0% and 77.7%. |
| Your population has a different prevalence | Recompute PPV and NPV for your prevalence | At 5% prevalence the PPVs fall to 17.7% (CRP alone), 13.9% (parallel) and 24.5% (serial). |
Reporting a Combination Strategy with STARD 2015
STARD 2015 is a list of 30 essential items for reporting diagnostic accuracy studies, grouped under the title, abstract, introduction, methods, results and discussion; it also defines the role of a test as its position relative to other tests, for example triage, replacement or add-on.7 The items most relevant to a combination are below, matched to the TB study.7,1
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| STARD 2015 item | What it asks | Where it shows in the TB study |
|---|---|---|
| 3 | Intended use and clinical role of the index test. | The tests are framed as triage ahead of confirmatory molecular testing. |
| 12a | Definition of and rationale for the index test cut-offs, pre-specified or exploratory. | CRP and MLR cut-offs came from WHO advice and earlier studies; the IP-10 cut-off came from the Youden index. |
| 14 | Methods for estimating or comparing accuracy. | Two tests combined in parallel (one or both positive) and in sequence (both positive). |
| 19 | Flow of participants, using a diagram. | 767 enrolled, 144 excluded, 623 analysed. |
| 23 | Cross tabulation of the index test results by the reference standard. | Counts by reference standard are given for each test and each pair (true positives of 111, true negatives of 512); the test-by-test joint table is not given. |
| 24 | Estimates of accuracy and their precision. | 95% Clopper-Pearson intervals. |
Giving the counts for each test and for the combined rule, as the TB paper does, lets readers recompute your results; giving the joint cross tabulation would let them test independence directly.
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Frequently Asked Questions
What is the difference between serial and parallel testing?
In the Ugandan TB triage study (623 people aged 15 or older), parallel testing called a person positive when one or both of two tests were positive, and serial testing called a person positive only when both were. For CRP plus MLR, parallel testing gave 95.5 percent sensitivity and 68.9 percent specificity, and serial testing gave 67.6 percent and 89.1 percent, against 91.0 percent and 77.7 percent for CRP alone. Editverse recomputed these from the printed counts.
When is parallel testing a sensible choice?
Parallel testing raises sensitivity and lowers specificity, so it suits a setting in which a missed case is costly and a more specific confirmatory test follows. In the TB study the authors describe triage tests that narrow confirmatory molecular testing to people most likely to have TB. In the data, CRP plus MLR in parallel found 5 more cases of 111 than CRP alone and added 45 false alarms among 512 people without TB.
When is serial testing a sensible choice?
Serial testing raises specificity and lowers sensitivity, so it suits a setting in which a false positive leads to a costly or harmful step. In the TB data, CRP plus MLR in series reduced false alarms from 114 to 56 among 512 people without TB, but found 75 of 111 cases, which is 26 fewer than CRP alone.
Can I work out combined sensitivity and specificity from the two single-test values?
Only if the two tests err independently in people with and without the disease. Under that assumption parallel sensitivity is one minus the product of the two miss rates, and serial specificity is one minus the product of the two false positive rates. In the TB study the real combined results differed from this arithmetic: parallel specificity was 6.5 points higher and serial specificity 6.5 points lower than predicted for CRP plus MLR. Vacek showed in 1985 that wrongly assuming independence can bias error estimates, so use the observed counts from the same people.
Does the order of tests matter in a serial strategy?
The TB authors state that when the same positivity rule was used, the order of testing did not change the accuracy estimates. Order does change how many people need the second test. Editverse arithmetic from the single-test counts: if CRP were run first, 215 of 623 people (34.5 percent) would be CRP positive and need an MLR. In the study every test was run in everyone, so this workflow was not itself tested.
How do combinations change predictive values?
Predictive values depend on prevalence, whereas likelihood ratios do not, according to StatPearls. At the TB study prevalence of 17.8 percent, the PPV for CRP plus MLR was 40.0 percent in parallel, 47.0 percent for CRP alone and 57.3 percent in series, and the NPV was 98.6, 97.5 and 92.7 percent. At 5 percent prevalence the same sensitivities and specificities give PPVs of 13.9, 17.7 and 24.5 percent. These prevalence figures are an Editverse illustration.
What happens when the two steps of an algorithm disagree?
In a C. difficile study of 216 PCR positive tests, 155 (71.8 percent) were toxin EIA negative. Of these discordant results, 66.5 percent were treated, against 95.1 percent of concordant ones. The authors conclude that the algorithm did not change clinical management, because most discordant cases were treated as true infection, and they write that the actual significance of discordant results is unclear. In Editverse reading, with no reference standard such as toxigenic culture the study cannot say which were true infections. The hospital then returned to a one-step algorithm with the toxin EIA performed by request.
What should a paper report when it combines tests?
STARD 2015 asks for the intended use and role of the index test (item 3), the cut-offs and whether they were pre-specified (item 12a), the methods for estimating accuracy (item 14), a participant flow diagram (item 19), a cross tabulation of index test results by the reference standard (item 23) and estimates with precision (item 24). For two tests, giving the counts for each test and for the combined rule lets readers recompute your results.
References
- Komakech K, Sserwadda I, Sserubiri J, Joloba M, Theron G, Cobelens F, Ssengooba W. Head-to-head evaluation of host blood biomarkers for point-of-care TB triage: diagnostic accuracy study. J Clin Microbiol. 2026;64(8):e00046-26. doi:10.1128/jcm.00046-26. Open access, CC BY 4.0 (licence read in the PMC XML, PMC13464034); counts reused, figures drawn and derived numbers computed by Editverse in R. pubmed.ncbi.nlm.nih.gov/42506936/
- Ahmed AE, McClish DK, Schubert CM. Accuracy and cost comparison in medical testing using sequential testing strategies. Stat Med. 2011;30(29):3416-3430. doi:10.1002/sim.4358. Abstract read on PubMed. pubmed.ncbi.nlm.nih.gov/21976377/
- Bettger CC, Giancola SE, Cybulski RJ Jr, Okulicz JF, Barsoumian AE. Evaluation of a two step testing algorithm to improve diagnostic accuracy and stewardship of Clostridioides difficile infections. BMC Res Notes. 2023;16(1):172. doi:10.1186/s13104-023-06398-9. Open access, CC BY 4.0 (licence read in the PMC XML, PMC10426052). pubmed.ncbi.nlm.nih.gov/37580824/
- Shreffler J, Huecker MR. Diagnostic testing accuracy: sensitivity, specificity, predictive values and likelihood ratios. StatPearls. Treasure Island (FL): StatPearls Publishing; 2023 (last updated 6 March 2023, per the PubMed record, PMID 32491423). NCBI Bookshelf NBK557491, read on 3 November 2026. www.ncbi.nlm.nih.gov/books/NBK557491/
- McClish DK, Wilk AR, Schubert CM. Choosing between the BP and BN sequential strategies. Pharm Stat. 2019;18(5):533-545. doi:10.1002/pst.1945. Abstract read on PubMed. pubmed.ncbi.nlm.nih.gov/31069929/
- Vacek PM. The effect of conditional dependence on the evaluation of diagnostic tests. Biometrics. 1985;41(4):959-968. Abstract read on PubMed. pubmed.ncbi.nlm.nih.gov/3830260/
- Bossuyt PM, Reitsma JB, Bruns DE, et al. STARD 2015: an updated list of essential items for reporting diagnostic accuracy studies. BMJ. 2015;351:h5527. doi:10.1136/bmj.h5527. The 30-item list and key terms were read in the PMC full text (PMC4623764). pubmed.ncbi.nlm.nih.gov/26511519/
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Editverse Research Team | Updated November 2026