Estimating the false-negative test probability of SARS-CoV-2 by RT-PCR

Introduction

Currently, most SARS-CoV-2 infected individuals are identified by successful amplification of the virus from nasopharyngeal or oropharyngeal swabs using a reverse-transcription PCR (RT-PCR) assay. These tests are highly specific but there are many reasons why sensitivity is imperfect [1]. Indeed, multiple studies have observed negative RT-PCR results on at least one occasion for SARS-CoV-2 infected individuals [1-8]. Such false-negative results have implications for correct diagnosis [9] and subsequent community transmission [10], and for control initiatives, not only during emergence but also in any subsequent waves of transmission. Successful attempts to test and trace resurgent outbreaks require a better understanding of how test results can confirm or rule out whether an individual is infected with the virus, but also need to be taken in context with other available information (such as the timing and type of test performed).

A series of previous studies have described cohorts of tested individuals. Ai and colleagues [2] retrospectively considered 1,014 infected patients, of whom 413 (41%) tested negative by RT-PCR at initial presentation. Xie et al. [1] similarly considered 167 infected patients of whom, five (3%) tested negative by RT-PCR at initial presentation. Fang et al. [3] found that RT-PCR was only able to identify 36/51 (71%) of SARS-CoV-2 infected patients when using swabs taken 0–6 days after symptom onset. Liu et al. [8] and Zhao et al. [7] demonstrated that the proportion of positive tests among infected patients reduced with each week after symptom onset, and Luo et al. [11] reported that the initial sensitivity of oropharyngeal swabs in secondary contacts was 71%. Meanwhile, in a study of 213 patients, Yang et al. [4] found lower positive test rates from oropharyngeal swabs (24%) compared with nasopharyngeal swabs (57%). Although these particular studies relate to longitudinal testing of infected patients, the data are not disaggregated per patient. Some authors have, however, presented sequential test data from individual patients [5,6,12].

We aim to estimate the likelihood of correctly identifying the SARS-CoV-2 infection status of an individual by RT-PCR tests using sequential test data from individual cases. These data are used to characterise how the probability of a false-negative test result depends on the number of days between symptom onset and the test date, and how this is affected by the type of swab used (oropharyngeal or nasopharyngeal). We also estimate the number of false negatives in different cohorts of tested individuals under the assumption that they are only tested once, and assess the effect of test specificity on these results.

Methods

Results

Our most complex model included two fixed effects (a smooth effect of day and a different intercept for each swab type) as well as a random intercept for each study and each patient (model AIC = 805.79). Removing the random intercept for study was supported (AIC = 805.31, ΔAIC = -0.47), suggesting that the baseline probability of detection was consistent across different cohorts, test targets and sample processing procedures. Excluding swab type was not supported (AIC = 813.15, ΔAIC = 7.83), nor was excluding the effect of days since symptom onset (AIC = 974.30, ΔAIC = 168.99). The final model structure with the highest support contained the fixed effect of swab type, the effect of time since symptom onset and a random intercept for each patient. The full model output is given in Supplementary File 1.

Oropharyngeal swabs taken immediately upon symptom onset were predicted to be 5.64% less likely to yield a positive result than a nasopharyngeal swab (logit-scale effect size −1.00 (95% CI: −1.54 to 0.46)). The probability of a positive test decreased with number of days past symptom onset. For a nasopharyngeal swab, the percentage chance of a positive test declined from 96.40% (95% CI: 90.98 to 98.6) on day of symptom onset to 75.47% (95% CI: 66.88 to 82.51) on day 10 since symptom onset (SSO), and only a 3.30% (95% CI: 0.53 to 17.90) chance of a positive result on day 31 SSO. For an oropharyngeal swab, the probabilities were 90.76% (95% CI: 77.84 to 96.52), 53.00% (95% CI: 38.27 to 67.46) and 1.23% (95% CI: 0.18 to 7.86) for day of symptom onset and days 10 and 31 SSO, respectively. The model fit is shown in Figure 1 and the underlying quantitative results (data) are available in Supplementary File 2.

As shown above, the probability of a false-negative test result depends on the number of days since symptom onset. This means that simple reports of positive and negative test counts among individuals who are only tested once will underestimate the true number of positive tests in a cohort. We can illustrate the potential impact this has on average false-negative test probabilities by assuming that time from symptom onset to testing follows a gamma distribution.

Figure 2 explores how varying the shape and rate of this gamma distribution affects the average false-negative test probability in a cohort, and highlights that in scenarios where infected individuals are typically tested late, false-negative test probability can be four times larger than when patients are typically tested early. We also show that the probability of incorrectly identifying an individual as uninfected due to a false-negative test considerably reduces if all negative tests are repeated 24 hours later. We note that the realised error rate (the actual proportion of false-negative tests) will be proportional to the underlying prevalence of infection, and that the probability of a false-negative will only equal the proportion of negative tests (as there will be no true negatives from uninfected individuals) if everyone in the cohort is infected.

Discussion

Testing from a single nasopharyngeal or oropharyngeal swab by RT-PCR is not guaranteed to yield a (true) positive result for SARS-CoV-2 infection, and the probability of obtaining a true positive result decreases with time from symptom onset. In other words, the longer the time from symptom onset to a suspected case being tested, the higher the likelihood of a false-negative result. Repeat testing of suspected but RT-PCR negative infections may not always be feasible, for example when testing capacity is limited, but our results suggest that repeat testing drastically decreases the chances of failing to identify infected individuals.

Meanwhile, early estimates for case and infection fatality rates of SARS-CoV-2 relied on perfect test sensitivity among international travellers [24,25], risking an upward bias by not accounting for the possibility of false-negative tests.

Contrastingly, we showed how even small false-positive test probabilities can have an opposite effect on any assessment of the true number of infections in a tested cohort and bias case and infection fatality risk estimates in the opposite direction. Better understanding of the false-positive test probability, and accounting for precisely when and how individuals have been tested would therefore improve the quality of any estimates that rely on the number of positive tests in a cohort of tested individuals.

Our results based on available data from early in the pandemic, have implications for SARS-CoV-2 testing strategies put in place at the time. RT-PCR testing regimes varied considerably between countries, determined by policy decisions, testing capacity and perceived incidence. Some countries have opted (or, rather, were able) to test large portions of the population, including those who are asymptomatic or self-isolating with mild symptoms. In countries such as South Korea, where testing has been thorough [26,27], the distribution of test timing is crucial. If many of those tested were infected days or weeks prior to testing but only had mild or asymptomatic infections (and therefore did not present for treatment), they would be more likely to return a false-negative result. While RT-PCR testing of key workers is of great importance (particularly those working with vulnerable groups), our results suggest that there may be little benefit to testing indiscriminately; in fact, conducting a single test on someone who had symptoms 10 days ago will have a nearly 25% chance of being a false-negative (using a nasopharyngeal swab, or 47% for an oropharyngeal swab). As a means of determining population level exposure to SARS-CoV-2, serological tests of known specificity and sensitivity are far more likely to provide an accurate profile. If specificity and sensitivity are known, then recovery of the likely level of population exposure is possible, even if it is not possible to determine which individuals have been exposed. This, however, would assume that all those infected would go on to develop and maintain detectable serological responses, which may not always be the case in mild infections, those asymptomatic, or across all age groups [28-33].

In almost all countries, tests will be conducted on patients presenting with symptoms at a hospital in order to streamline treatment and prevent further infection. We do not suggest that the problem of false negatives is under appreciated by medical professionals; it is presently recognised in guidelines from both the World Health Organization (WHO) [34] and the European Centre for Disease Prevention and Control (ECDC) [35] that a single negative test is insufficient to rule out infection, with discharge criteria stating that a patient should only be released if two repeat tests return negative results. Early in the outbreak, clinicians used a chest computed tomography scan to look for evidence of SARS-CoV-2 in symptomatic patients who returned a negative result, minimising the risk of false negatives [2,36].

We also note that RT-PCR tests will return positive results even if the virus is inert – only by culturing the sample is it possible to verify that a patient is actually infectious. To date, the available information suggests that it is possible for individuals with mild disease to shed for at least 18 days [37], and those with severe disease for at least 20 [18]. However, evidence is mounting that successful culture of the virus is associated with high viral loads and perhaps not yet having a detectable serological response [6,18,38], which suggests that quantitative estimates of (still detectable) viral load and/or seroconversion could be used as tools to safely discharge infected individuals from quarantine or hospital [18]. In light of this evidence, our study cannot readily assist with such decisions, not least because the higher false-negative test probabilities we report with time SSO are themselves almost certainly related to lower viral loads over time. Thus, further research involving quantitative estimates of how viral load changes with time since symptom onset would be useful. Repeat measurements and calculation of viral load in infected individuals allow a more precise interpretation of the RT-PCR results, specifically whether a negative or high cycle threshold (CT) result is consistent with the previous trend in that particular patient or is anomalous, and so determine how likely the individual is to still be infectious. Based on limited data available early in the pandemic, our results nonetheless suggest that multiple negative tests would be consistent with the viral load having reduced to a sub-infectious level, but a single negative test could represent only a spurious test result.

Major implications of our results relate directly to contact tracing of infected individuals. Since it is possible for infected individuals to test negative for infection soon after the development of symptoms, it is theoretically incorrect to assume that a single negative test in a suspected symptomatic index case rules out infection in their close contacts who may be better advised, in a best-case scenario, to self-isolate regardless. It may therefore be prudent to assume that contacts of suspected infected individuals may be infected themselves and isolate, regularly testing them until either there is firm evidence that the putative index case was not actually infected (or at least infectious) at the time of the contact, or assess if the incubation period for the contact has passed without evidence that the contacts have themselves been infected.