Performance of Three Tests for SARS-CoV-2 on a University Campus Estimated Jointly with Bayesian Latent Class Modeling

Abstract

Accurate tests for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have been critical in efforts to control its spread. The accuracy of tests for SARS-CoV-2 has been assessed numerous times, usually in reference to a gold standard diagnosis. One major disadvantage of that approach is the possibility of error due to inaccuracy of the gold standard, which is especially problematic for evaluating testing in a real-world surveillance context. We used an alternative approach known as Bayesian latent class modeling (BLCM), which circumvents the need to designate a gold standard by simultaneously estimating the accuracy of multiple tests. We applied this technique to a collection of 1,716 tests of three types applied to 853 individuals on a university campus during a 1-week period in October 2020. We found that reverse transcriptase PCR (RT-PCR) testing of saliva samples performed at a campus facility had higher sensitivity (median, 92.3%; 95% credible interval [CrI], 73.2 to 99.6%) than RT-PCR testing of nasal samples performed at a commercial facility (median, 85.9%; 95% CrI, 54.7 to 99.4%). The reverse was true for specificity, although the specificity of saliva testing was still very high (median, 99.3%; 95% CrI, 98.3 to 99.9%). An antigen test was less sensitive and specific than both of the RT-PCR tests, although the sample sizes with this test were small and the statistical uncertainty was high. These results suggest that RT-PCR testing of saliva samples at a campus facility can be an effective basis for surveillance screening to prevent SARS-CoV-2 transmission in a university setting. IMPORTANCE Testing for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been vitally important during the COVID-19 pandemic. There are a variety of methods for testing for this virus, and it is important to understand their accuracy in choosing which one might be best suited for a given application. To estimate the accuracy of three different testing methods, we used a data set collected at a university that involved testing the same samples with multiple tests. Unlike most other estimates of test accuracy, we did not assume that one test was perfect but instead allowed for some degree of inaccuracy in all testing methods. We found that molecular tests performed on saliva samples at a university facility were similarly accurate as molecular tests performed on nasal samples at a commercial facility. An antigen test appeared somewhat less accurate than the molecular tests, but there was high uncertainty about that.

Keywords: Bayesian statistics; COVID-19; RT-PCR; SARS-CoV-2; epidemiology; molecular diagnostic; public health surveillance.

FIG 1

Posterior parameter estimates. (A) Prevalence among individuals participating in surveillance testing; (B) prevalence among individuals participating in testing for reasons other than surveillance; (C) test sensitivity; and (D) test specificity. The colors in A and B distinguish the prior from posterior distributions, and the colors in C and D distinguish the different types of tests. Values outside the range 0 to 1 occur only as a result of smoothing. Decimal values are shown along the x axes, consistent with the definitions of these quantities as probabilities, rather than percentages, in Materials and Methods.

FIG 2

Estimates of the frequency of different testing outcomes. Out of 1,000 tests, the panels show the number of (A) true positives, (B) false positives, (C) false negatives, and (D) true negatives. The colors distinguish the different types of tests. Values outside the range 0 to 1,000 occur only as a result of smoothing.

FIG 3

Estimates of the predictive values of each test during the study period. The panels show estimates of (A) the positive predictive value and (B) the negative predictive value. The colors distinguish the different types of tests. Values outside the range 0 to 1 occur only as a result of smoothing. Decimal values are shown along the x axes, consistent with the definitions of these quantities as probabilities, rather than percentages, in Materials and Methods.

FIG 4

Positive predictive value (A to C) and negative predictive value (D to F) over the course of the entire semester. These values represent the probability that a positive or negative test result under random surveillance screening would have accurately relayed the true positive or negative status of the individual being tested. The change over time was a result of the time-varying prevalence of detectable infection (black lines, right axis). The uncertainty reflects uncertainty about the sensitivity and specificity of each type of test: commercial (red), saliva (green), and antigen (blue). Decimal values are shown along the y axes, consistent with the definitions of these quantities as probabilities, rather than percentages, in Materials and Methods.