key: cord-0285694-d1fsipjr authors: Juul, J. L.; Graesboell, K. title: Are fast test results preferable to high test sensitivity in contact-tracing strategies? date: 2021-02-19 journal: nan DOI: 10.1101/2021.02.17.21251921 sha: 9ed6353eddcf35780cbce1400a25e38e1c0a973c doc_id: 285694 cord_uid: d1fsipjr Across the world, countries are fighting to reduce the spread of COVID-19. The backbone of the response is a test-trace-isolate strategy, where suspected infected get tested and isolated and possible secondary cases get traced, tested and isolated. Because more accurate tests often take longer to analyze, and the benefits of contact tracing are strengthened by rapid diagnosis, there exists a trade-off in test sensitivity and test waiting time in test-trace-isolate strategies. Here we ask: How many false negatives can be tolerated in a rapid test so that it reduces transmission better than a slower, more accurate test? How does this change with contact tracing efficiency and test waiting time? We find that a rapid, less sensitive test performs best for many test-parameter choices and that this is true even for modest contact tracing efficiency. For COVID-19-like viral parameters, a test with 40% false negatives and immediate result might reduce transmission as well as a test with no false negatives and a 3-day waiting time. Our analysis suggests employing rapid tests to reduce test waiting times as a viable strategy to reduce transmission when testing infrastructure is under stress. To quantify the impact of test-trace-isolate strategies on growing epidemics, we simulate the branching structure of the chains of infections, also referred to as the "epidemic tree". 18, 19 Our model lets us keep track of who infected whom, which is essential when simulating contact tracing and quarantining infectious people. In the model ( Figure 1A) , infected individuals give rise to new cases, unless quarantined following testing and tracing efforts. We initiate a simulation with some number of newly infected people, N seed ∈ N. The simulation progresses in discrete timesteps, corresponding to days, and we make the simplifying assumption that every infected person, goes through the same phases before recovering: 3 days of being presymptomatic and noninfectious followed by 8 infectious days. As for COVID-19, 20 some fraction of cases, p asymp , remain asymptomatic for the entire infectious period; all other infected cases experience symptoms starting on day 7 after infection. In the absence of testing, tracing and isolation, an infectious person would give rise to k secondary cases. For each infected, we assume that k is drawn from the probability distribution P (k). When each of these k secondary cases is infected, we determine the time of infection by drawing an integer from the probability distribution P time (t). P time (t) takes positive values on the days where the infected is infectious and, mimicking COVID-19, 1,15 peaks around symptom onset ( Figure 1B ). These infections take place unless the infected is in quarantine at the time the infection would occur. Infectious people quarantine only when waiting for a test to be taken, receiving a test result, or after testing positive. In our model, an infectious person orders a test if either of two things happens: 1) The person is traced; 2) The person develops symptoms. In either case, the person orders a test immediately and then waits δ = δ test +δ result days for the result. The test waiting time is divided into δ test days waiting for the test to be taken followed by δ result days to receive the result. The test correctly identifies the case with probability equal to its sensitivity, 1 − p false , where p false is the false negative rate. If the test comes back positive, each of the person's secondary cases is traced with independent probability p trace . We obtain indistinguishable results when simulating the same δ with varying values of δ test and δ result . Thus, the key parameters of the model are the test waiting time δ, test sensitivity 1 − p false , and tracing efficiency p trace . Following t max timesteps, we count the number of nodes that completed their whole 3 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 19, 2021. ; https://doi.org/10.1101/2021.02.17.21251921 doi: medRxiv preprint infectious period, n parents . We also count the number of people these nodes infected, n children . The output of the simulation is the effective reproduction number of simulated disease: R eff = n children /n parents . We use the model to examine the trade-off between test waiting time and test accuracy depending on the tracing efficiency. In our simulations, we therefore vary the parameters δ, 1 − p false , and p trace and fix all other parameters (for δ ≥ 1, we set δ result = 1). For P (k) we choose a Poisson distribution with mean R 0 = 2 (slightly lower than estimated in early stages of the pandemic 21, 22 ) and for P time (t) we choose the right-skewed distribution depicted in Fig. 1B . Finally, we choose t max = 50. To develop some intuition, let us first introduce the results we obtain when fixing the tracing efficiency, p trace = 0.80. This constraint leaves 2 free parameters: The test sensitivity, 1 − p false , and the test delay, δ. We now compare the effective reproduction number R slow eff obtained by using a slow, but accurate test (parameters: p slow false = 0 and some δ slow ≥ 1 day) to the reproduction number, R rapid eff , obtained with a less accurate, but rapid test (parameters: some p rapid false and δ rapid = 0 days). To evaluate whether speed or accuracy is to be preferred, we compute the difference in obtained effective reproduction numbers of the virus under the different choices of tests, Let us choose some test delay, e.g. δ slow = 2 days (perhaps corresponding to a PCR test with a 1-day waiting time to get tested and a subsequent 1-day waiting time to get the result). In this case, how will ∆R eff depend on the risk of getting a false negative test result? For very high sensitivity (low p false ), this faster test will be almost as accurate as the slower test it is being compared to. For this reason, the fast test will be preferable to the slower one ( Fig. 2A top colorbar) . If we now imagine slowly decreasing the test sensitivity, ∆R eff will gradually increase until it reaches a breaking point where the slow and rapid tests reduce the effective reproduction number equally well: ∆R eff = 0. Decreasing the sensitivity even further makes ∆R eff positive, meaning that for this high probabilities of false negatives, the accurate test is to be preferred. If we now make the same plot but with a higher waiting time to receive the slow test, the breaking point will move to a lower test sensitivity. The second colorbar in Fig. 2A shows 4 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted February 19, 2021. ; https://doi.org/10.1101/2021.02.17.21251921 doi: medRxiv preprint the result for δ slow = 3 days. The breaking point moved from sensitivity ≈ 0.91 to ≈ 0.63 with this single day increase in waiting time -corresponding to a fourfold increase in p false ! Increasing the waiting time once more, setting δ slow = 4, moves the breaking point further to the left. In this latter case, a 54% chance of a false negative is better than a 4 day wait for accuracy. Having established some intuition for the simulations, we proceed to varying the third parameter: the tracing efficiency. By varying the tracing efficiency, for each choice of δ slow we get 2-dimensional heatmaps instead of the one-dimensional colorbars presented in the previous paragraphs (Fig. 2B-D) . In these heatmaps, the breaking points become white curves. Every point to the right of the breaking-point curve is a parameter combination where a faster test is preferable. Every point to the left of the breaking-point curve is a parameter combination that favors an accurate test. Notice how all the breaking-point curves start in the lower-right corner (where tests are completely accurate but no contact tracing is done) and how quickly they move to the left with increasing tracing efficiency. Figure 2E plots the obtained R rapid eff . For each simulated choice of parameters, each computed R eff is averaged over 10 simulations. For clarity, the heatmaps in Fig. 2 have been smoothed with a Gaussian filter. Testing, tracing and isolating positive cases is central in many countries' strategy to fight the current COVID-19 pandemic. [23] [24] [25] We have demonstrated that there is a sizeable trade-off between test sensitivity and test waiting times in such strategies, and that it is often beneficial to prioritize test speed over test sensitivity. Moreover, we find that this benefit of rapid tests increases quickly with increases in test waiting times, and that even modest tracing efficiency unlocks the advantages of rapid tests. This indicates that additional waiting time for test results must be avoided and that it often makes sense to reduce test sensitivity in order to do so. It is to be expected that testing systems will occasionally get under stress during a pandemic, and having a way to avoid build-up of waiting times in this scenario is crucial. Designing such stress-relieve strategies presents an interesting direction for future research. Some of the assumptions we have made can be questioned. Three such assumptions are: 5 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted February 19, 2021. ; https://doi.org/10.1101/2021.02.17.21251921 doi: medRxiv preprint That quarantine hinters any transmission; that symptomatic individuals do not quarantine after testing (false) negative; and that the probability of getting a false negative result does not depend on the infected's infectiousness at the time the test was taken. We note that all of these assumptions will favor reducing transmission by slower, more accurate tests: That people do not break isolation benefits the tests with long waiting times; false negative results leading to completely normal behavior damages only the tests that allow for false negative results; lastly, making false negatives less likely at high viral load would make the rapid tests more reliable early in the course of disease, when many new secondary cases could be avoided following diagnosis. That we have chosen our assumptions as to disfavor rapid low-sensitivity tests means that our results can be interpreted as conservative estimates of the benefits of reducing test waiting time with less sensitive tests. Our choices of the probability distributions P (k) and P time (t) can also be questioned. A better choice for P (k) might be a heavy-tailed distribution that could account for superspreading behavior. 26 Overall, our analysis suggests employing rapid tests to reduce test waiting times as a viable strategy to reduce transmission even at modest waiting times and contact tracing efficiency. 6 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted February 19, 2021. ; https://doi.org/10.1101/2021.02.17.21251921 doi: medRxiv preprint cations 12, 1 (2021). . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) Figure 1A ) The value on the vertical axis for day x after infection is the probability that a given secondary case gets infected on day x. For asymptomatic cases, P time (t) is as depicted -the only difference being that the final, symptomatic, phase is replaced with an asymptomatic phase. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 2. A Comparison of effective reproduction number, ∆R eff = R slow eff −R rapid eff , when using a slow but accurate test with sensitivity 1 (no false negatives), and a test waiting time of δ slow days and using a rapid but less accurate test with a given sensitivity and test waiting time of δ rapid = 0 days. In this inset, we assume that 80% of secondary cases are successfully traced following a positive test. The colorbars show results obtained for different choices of δ slow (top colorbar: δ slow = 2 days, middle: δ slow = 3 days, bottom: δ slow = 4 days), and the rapid-test sensitivity (horizontal axis in each colorbar). In each colorbar a breaking point separates sensitivity values favoring the slower, accurate test and values favoring the rapid test. B Comparison of effective reproduction numbers when the result of the slower test arrives after δ slow = 2 days, as a function of the sensitivity and tracing efficiency. C Same as in B but with δ slow = 3 days. D Same as in B, C but with the slower result arriving after δ slow = 4 days. E Heatmap of the effective reproduction number obtained using the rapid, less accurate test, R rapid eff . The breaking-point lines of B, C, D are plotted in black. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted February 19, 2021. ; https://doi.org/10.1101/2021.02.17.21251921 doi: medRxiv preprint Covid-19: Mass testing in slovakia may have helped cut infections Proceedings of the Royal Society of London. Series B: Biological Sciences Covid-19 strategy update Proceedings of the Royal Society of London. Series B: Biological Sciences