The false positive rate for PVR for SARS cov2 is not known. A recent article in the BMJ
addresses this issue and allows an interactive calculation on assumed results according to the prevalence of the infection. The problem is that in low prevalence areas, a specificity of the PCR of 99%, although it sounds small could lead to a large error in estimation of positive cases and a poor predictive value for negative cases. Although no official figures for the specificity of the PCR in field setting are available, some indirect deductions can be made. In China, after a small outbreak of the virus in Qingdao, the authorities tested the whole population of the town, 10.2 million people, and found no positive results.
Another way of inferring the specificity of the testing in the field can be deduced from daily published figures, for example from this website, World meters
I extracted the figures from this website of countries with less than 5000 reported cases, and with a population of over 3 million and with data available of total number of tests performed.
There were 17 countries that fell into this group:
World Country Cases Tests Pos/test FP1% FP 0.1% FP0.01%
207 Laos 24 65,305 3.2 -6 653 65 6
188 Cambodia 291 180,378 0.00160 1,804 180 18
187 Mongolia 340 88,230 0.00380 823 82 8
177 Taiwan 553 101,218 0.00540 1,012 100 10
176 Burundi 560 49,642 0.01120 496 49 5
174 PNG 589 29,254 0.02010 293 29 3
165 Vietnam 1,177 1,246,480 0.00094 1,246 125 13
164 Niger 1,219 37,027 0.03290 370 37 4
163 Liberia 1,426 30,332 0.04700 303 30 3
160 NZ 1,950 1,090,702 0.00179 10,907 1,091 109
158 Togo 2,296 117,117 0.01960 1,171 117 12
154 Benin 2,643 238,105 0.01110 2,381 238 24
153 S.Sudan 2,903 12,044 0.24103 102 10 1
152 Uruguay 3,044 314,820 0.00966 3,148 315 32
150 Mali 3,537 73,365 0.04820 734 73 7
147 Thai 3,775 977,854 0.00386 9,778 977 97
138 CAR 4,863 32,711 0.14866 327 33 3
Number on left is world rating total cases, next column name of country, total number of cases, total number of tests performed, percentage positive tests/test performed, Exp 1%= expected number of false positive tests at 99% specificity, Exp. 0.1%=expected number of false tests if 99.9% specificity and exp 0.01%= expected false positives if specificity 99.99%.
The sample was further reduced to countries with less than 1% positive cases/ test performed. The purpose was to look at the problem of false positives in the context of low incidence:
Country Cases Pos/tested 1%FP 0.1%FP 0.01%FP
Cambodia 291 0.16% 1804 180 18
Taiwan 553 0.38% 1012 101 10
Vietnam 1177 0.09% 1246 125 13
New Zealand 1950 0.18% 10907 1090 109
Uruguay 3044 0.97% 3148 315 32
Thailand 3775 0.39% 9778 978 98
In all 6 countries the number of false positives would exceed the number of observed cases, sometimes as in the case of New Zealand of x5 and in Thailand by x3 If the FP rate was 1%. The numbers of possible false positives still remain a high proportion of cases at 99.9% specificity also in the case of these two countries. It is obviously not possible to determine the exact figure for specificity, and in turn, the likelihood of false positives from these figures, but it would be a fair assumption that the figure lies more in the region between 0.1% and 0.01% rather than 1%.