Pooled testing efficiency increases with test frequency

Pooled testing increases efficiency by grouping individual samples and testing the combined sample, such that many individuals can be cleared with one negative test. This short paper demonstrates that pooled testing is particularly advantageous in the setting of pandemics, given repeated testing, rapid spread, and uncertain risk. Repeated testing mechanically lowers the infection probability at the time of the next test by removing positives from the population. This effect alone means that increasing frequency by x times only increases expected tests by around x. However, this calculation omits a further benefit of frequent testing: Removing infections from the population lowers intragroup transmission, which lowers infection probability and generates further efficiency. For this reason, increasing testing frequency can paradoxically reduce total testing cost. Our calculations are based on the assumption that infection rates are known, but predicting these rates is challenging in a fast-moving pandemic. However, given that frequent testing naturally suppresses the mean and variance of infection rates, we show that our results are very robust to uncertainty and misprediction. Finally, we note that efficiency further increases given natural sampling pools (e.g., workplaces, classrooms) that induce correlated risk via local transmission. We conclude that frequent pooled testing using natural groupings is a cost-effective way to provide consistent testing of a population to suppress infection risk in a pandemic.

The COVID-19 pandemic has generated a health and economic crisis not seen in more than a century. Opening businesses and schools is necessary to regain economic activity, but the potential public health costs are dramatic. One policy to circumvent this stark trade-off is to open the economy, while implementing surveillance testing that can quickly identify infected individuals—particularly those without symptoms—and prevent them from spreading the disease. Unfortunately, testing at this scale appears infeasible given the cost and capacity constraints. This paper makes a simple but essential point about these costs: When using pooling testing, frequent testing of correlated samples makes testing dramatically more efficient (and therefore less costly) than understood both by existing research and policy makers.In pooled testing (1), multiple samples are combined and tested together using one test, and the entire pool is cleared given a negative test result. Pooling is an old concept, and a large literature has emerged on optimal strategies (1–10); more recently, others have discussed how it might be used to increase COVID-19 test efficiency (11, 12). However, all of these papers focus on one-time testing of a set of samples with known and independent infection risk, which matches common use cases such as screening donated blood for infectious diseases (13–18). These environmental assumptions are violated when dealing with a novel pandemic with rapid spread. In this case, people need to be tested multiple times, testing pools are likely formed from populations with correlated infection risk, and risk levels at any time are very uncertain. How do these changes impact testing strategy?We start with the well-known observation that pooled testing is more efficient when the infection probability is lower, because the likelihood of a negative pooled test is increased. This observation has been used to conclude that pooled testing is not cost-effective for “high-risk” populations, such as health care workers or for people in areas experiencing an outbreak. While this statement is true for one-off testing, it does not hold when the population is tested repeatedly. As an extreme example, if a person in a high-risk area was just tested and determined to be negative, their probability of infection when tested an hour later is extremely low, simply because there is not much time to be infected between the tests. In other words, the infection probability at the time of testing depends both on the flow rate of infection and the timing of testing.We quantify the impact of testing frequency on infection probability and its consequent impact on pooled-testing efficiency. For example, we show that, given reasonable levels of independent risk, testing twice as often cuts the infection probability at the time of testing by (about) half, which lowers the expected number of tests at each testing round to about 70% of the original number. The savings are akin to a “quantity discount” of 30% in the cost of testing. Therefore, rather than requiring 2 times the number of tests, doubling the frequency only increases costs by a factor of 1.4. More generally, we demonstrate that testing more frequently requires fewer tests than might be naively expected: Increasing frequency by x times only uses about x as many tests, implying a quantity discount of (1−1/x).The benefits to frequency are even greater when the disease spreads within the testing population. In this case, testing more frequently has an additional benefit: By quickly removing infected individuals, infection spread is contained, future infection probabilities are lowered, and testing efficiency rises further. We analytically quantify this additional benefit as a function of the exponential-like growth path of the disease. We show that, in this case—somewhat paradoxically—the quantity discount can be so great that more frequent testing can actually reduce the total number of tests. For example, if the disease dynamics are such that doubling the testing frequency reduces the infection probability at the time of testing by more than fourfold, then doubling the frequency will require fewer tests in expectation.In our simple model, we assume that infection probabilities are known when constructing optimal pool sizes and efficiency statistics. However, the prediction of infections in a fast-changing pandemic is an extremely difficult inference problem (see, e.g., ref. 19). Given this issue, it is appropriate to worry that uncertainty and potential misprediction will make pool size choices challenging, reduce pooled testing efficiency, and render our conclusions void. For example, testing data from Massachusetts in the fall of 2020 shows high average testing positivity rates (7%) that vary widely across time and space (SD of 6%) in potentially unpredictable ways. (These data are publicly available at https://www.mass.gov/info-details/covid-19-response-reporting.) Using one-off pooled testing given this population—which has an extremely high positivity rate partially due to self-selection of people who desire a test—will be very inefficient given the high rates and the potential for misoptimization. However, as discussed above, frequent testing of a consistent population reduces the mean and variance of infection probabilities at the time of testing because there is little time between testing for mean- and variance-inducing spread to occur, and the selection issue is removed. For example, as noted in ref. 20, the town of Wellesley, MA, employed weekly testing of consistent subpopulations in the fall of 2020, and the average positivity rates stayed low (0.3%) and didn’t vary considerably (SD of 0.3%). When positivity rates have low mean and variance, we show that the efficiency of pooled testing is strongly robust to reasonably miscalibrated estimations and constant pool sizes, such that pooled testing remains very attractive. Finally, we note that better estimation of the positivity distribution is also helped by frequent testing, which naturally produces a constant stream of recent test result data from the relevant population.We note one final efficiency benefit associated with the most natural implementation of frequent testing. When frequently testing a consistent subpopulation (such as those living or working together), it is likely that the infection spreads within the subpopulation. This correlation increases the benefits of pooled testing even in a static testing environment (a finding concurrently noted in ref. 21). Intuitively, an increased correlation in a pool with fixed individual risk lowers the likelihood of a positive pooled test result, which increases efficiency.Throughout the paper, we consider a very stylized environment with a number of simplifications to present transparent results. While removing these constraints further complicates the problem and raises a number of important logistical questions, we do not believe that their inclusion changes our main insights. For example, our simple model assumes that a person who becomes infected will test positive indefinitely, whereas, in reality, they will potentially recover at some point. This does not impact our results when the time between tests is less than the recovery period, but it lowers the relative cost of pooled testing when frequency is low, because the prevalence is lower due to recoveries. However, our main qualitative conclusion—testing more frequently leads to fewer tests for each testing period—still holds in this case.Another important simplification is that we model a test with perfect sensitivity. [As noted in ref. 22, test specificity of standard protocols such as PCR appears to be very close to one. However, if specificity is a concern, the past literature (9, 23) has clear methods to optimize in the case of imperfect tests.] There are multiple ways in which pooled testing interacts with test sensitivity. First, there is a natural negative impact: Combining samples can potentially dilute the viral load below the limit of detection of the test. However, this implies that the false negatives will occur when the viral load is very low and the person is less likely to be infectious.^* Second, this dilution concern is counteracted, when testing frequently, by the large increase in overall sensitivity coming from running a larger number of tests.^† Third, as noted in ref. 22, false negatives may result from poor-quality samples. However, frequency again has benefits: By testing the same population repeatedly, subjects become better experienced with proper sampling protocols, and those who provide poor samples can be identified and corrected.Finally, we largely abstract away various practical implementation costs and constraints. First, we assume that every test, whether individual or pooled, has the same cost. However, pooled testing necessitates a more complicated setup in the laboratory, requiring more space and trained personnel (or a robotic setup) to correctly mix the samples together. While these costs are relatively moderate if spread over a long period of time, a laboratory might be reluctant to change their operations when the duration of the pandemic is very unclear. Second, we assume that there is no time delay between testing and receiving the test result. In reality, it takes time to transport samples to the laboratory and test them, and pooled testing takes more time than individual testing because it potentially requires an additional retesting step. Fortunately, the difference in these delays can be minimized when using the common “hold-out” method: Only a portion of each individual sample is used to construct the pooled sample, such that the remaining portions of the individual samples can be immediately individually tested if the pooled sample tests positive. However, even if the difference is minimized, any delay still impacts our analysis. In particular, by assuming no delay, increasing the testing frequency minimizes the likelihood of undiscovered new infections in the time between tests, such that the infection probability at the time of testing can be kept arbitrarily low. But, when there is a delay in receiving test results, it is not possible to stop infection and spread during the delay period even if testing is continuous. Therefore, it might be simply impossible to lower the infection probability below the ∼5% threshold at which the cost benefit of pooled testing is considered clear. In this extreme case, we do not recommend pooled testing. However, if the risk and spread are so extreme that 5% of a group is expected to be newly infected every few days even with very frequent testing, an alternative policy relying on isolation seems far more likely.Although we see this paper as noting a general insight of the relationship between pooled testing and testing frequency, it is useful to discuss the particular historical context in which the paper was written. The first paper draft of the paper was completed in June 2020, during the first wave of the COVID-19 pandemic. At that point, testing supply was low and prices were high because laboratories were building up testing capacity in a relatively strict regulatory environment. By early 2021, multiple organizations—such as Mirimus, Ginkgo, and the Broad—were offering frequent pooled testing at much cheaper prices than individual testing, and multiple organizations with correlated risk—such as employers, cities, and school districts—were employing these tests. For example, in February 2021, Massachusetts implemented a policy of providing universal weekly pooled testing for all K-12 students and faculty and staff.^‡ And, nationally, the Rockefeller Foundation called for use of frequent pooled testing as an essential aspect of school reopening (30).^§ The authors, based on the main insights of this paper, supported many of these policy initiatives and recommendations. Interestingly, the cost of pooled testing in Massachusetts (between $3 and $10 per student per test) is almost precisely the predicted amount using pooling in the first draft of the paper, providing a useful empirical validation of the model.The paper proceeds as follows: Pooled Testing reviews one important finding in the pooled testing literature that efficiency rises as infection probability falls; Increasing Test Frequency Interaction discusses the relationship between testing frequency and efficiency; Robustness to Uncertainty demonstrates how correlated infection leads to larger pool sizes and greater efficiency; and Conclusions concludes.     

Provision of phenotype-matched blood units: no need for pre-transfusion antibody screening.

BACKGROUND AND OBJECTIVES: The Hong Kong government is planning to introduce an electronic smart identity card for all seven million citizens in 2003. If the smart card contains the full red cell phenotype/genotype of the individual, it may be possible to transfuse phenotype-matched blood units without pre-transfusion antibody screening. We conducted a feasibility study. DESIGN AND METHODS: Red cell phenotype was determined for 407 donor blood units and 493 patients for whom an antibody screen had been ordered. The computer program selected phenotype-matched blood from the donor stock for the patients according to actual transfusion request. For patients with a positive antibody screen, full crossmatching was carried out with the computer-selected phenotype units. The frequencies of the various red cell phenotypes in the population were calculated from Red Cross data of antigen frequencies. The probabilities of finding at least one unit of phenotype-matched blood from a 300-unit hospital stock and a 4,000-unit Red Cross stock were determined for each phenotype. Cost analysis was performed. RESULTS: Ninety-two out of 493 patients received a total of 395 blood units. The required number of phenotype-matched blood units could be found for 92 patients using a 300-unit pool and for all patients using a 4,000-unit pool. We calculated that phenotype-matched blood could be provided for more than 98% of patients without antibody screening. The total cost of the project is US$ 98 million with potential savings of US$ 14 million per year. INTERPRETATION AND CONCLUSIONS: It is feasible and cost-effective to transfuse patients with phenotype-matched blood without antibody screening using a smart card system.     

Cost comparison of predictive genetic testing versus conventional clinical screening for familial adenomatous polyposis

BACKGROUND: Mutations of the APC gene cause familial adenomatous polyposis (FAP), a hereditary colorectal cancer predisposition syndrome. AIMS: To conduct a cost comparison analysis of predictive genetic testing versus conventional clinical screening for individuals at risk of inheriting FAP, using the perspective of a third party payer. METHODS: All direct health care costs for both screening strategies were measured according to time and motion, and the expected costs evaluated using a decision analysis model. RESULTS: The baseline analysis predicted that screening a prototype FAP family would cost $4975/ pound3109 by molecular testing and $8031/ pound5019 by clinical screening strategy, when family members were monitored with the same frequency of clinical surveillance (every two to three years). Sensitivity analyses revealed that the genetic testing approach is cost saving for key variables including the kindred size, the age of screening onset, and the cost of mutation identification in a proband. However, if the APC mutation carriers were monitored at an increased (annual) frequency, the cost of the genetic screening strategy increased to $7483/ pound4677 and was especially sensitive to variability in age of onset of screening, family size, and cost of genetic testing of at risk relatives. CONCLUSIONS: In FAP kindreds, a predictive genetic testing strategy costs less than conventional clinical screening, provided that the frequency of surveillance is identical using either strategy. An additional significant benefit is the elimination of unnecessary colonic examinations for those family members found to be non-carriers.     

Serologic versus molecular testing for screening for hepatitis C virus infection in patients with hematologic malignancies

Testing for antibody against hepatitis C virus (anti-HCV) is a low-cost diagnostic method worldwide; however, an optimal screening test for HCV in patients with cancer has not been established. We sought to identify an appropriate screening test for HCV infection in patients with hematologic malignancies and/or hematopoietic cell transplants (HCT). Patients in our center were simultaneously screened using serological (anti-HCV) and molecular (HCV RNA) assays (February 2019–November 2019).In total, 214 patients were enrolled in this study. Three patients (1.4%) were positive for anti-HCV, and 2 (0.9%) were positive for HCV RNA. The overall percentage agreement was 99.5% (95% CI: 97.4–99.9). There were no cases of seronegative HCV virus infection. The positive percentage agreement was 66.7% (95% CI: 20.8–93.9), and the negative percentage agreement was 100.0% (95% CI: 98.2–100.0). Cohen kappa coefficient was 0.80 (95% CI: 0.41–1.00, P < .0001).The diagnostic yield of screening for chronic HCV infection in patients with cancer is similar for serologic and molecular testing.     

Controversies in vascular screening art versus science

Whether or not to screen asymptomatic members of the general public for various forms of vascular disease is a controversial issue with huge medical, social, and financial ramifications. This article reviews several criteria for determining the appropriateness of vascular screening, including: (1) is it possible to detect occult vascular disease ;early'?; (2) what should we screen for, and how should we do it?; (3) who should be screened?; and (4) what standards for vascular screening should be set? While some of these controversies may ultimately be resolvable using an evidence-based approach, it is apparent that there are issues which will not be amenable to strict scientific analysis. Individualized approaches to screening will therefore remain the rule for the foreseeable future.     

Agreement in measuring socio-economic status: area-based versus individual measures

Area-based socio-economic status (SES) measures are frequently used in epidemiology. Such an approach assumes socio-economic homogeneity within an area. To quantify the agreement between area-based SES measures and SES assessed at the individual level, we conducted a cross-sectional study of 943 children who resided in 155 small enumeration areas and 117 census tracts from 18 schools in Montreal, Quebec. We used street address information together with 1986 census data and parental occupation to establish area-based and individual level SES indicators, respectively. As compared with the SES score determined at the level of the individual, 13 different area-based SES indices classified the children within the same quintile 28.7% (+/- 2.8%) of the time. The discrepancy was within one quintile in 35.3% (+/- 2.3%) of cases, two quintiles in 20.6% (+/- 3.6%), three quintiles in 11.3% (+/- 4.2%) and four quintiles in 4.1% (+/- 0.2%). In conclusion, we observed a substantial discrepancy between area- based SES measures and SES assessed at the individual level. Caution should therefore be used in designing or interpreting the results of studies in which area-based SES measures are used to test hypotheses or control for confounding.     

Serological testing in screening for adult celiac disease.

Assays for celiac-related antibodies are becoming widely available, and the present review aims to clarify the use of these investigations in the diagnosis of, management of and screening for adult celiac disease. The sensitivities and specificities of various antibody tests are discussed, along with their clinical use as an adjunct to small bowel biopsy, and as a first-line investigation for patients with atypical symptoms of celiac disease or patients at high risk of developing sprue.