Estimation of Covid-19 Prevalence from Serology Tests: A Partial Identification Approach
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We propose a partial identification method for estimating disease prevalence from serology studies. Our data are results from antibody tests in some population sample, where the test parameters, such as the true/false positive rates, are unknown. Our method scans the entire parameter space, and rejects parameter values using the joint data density as the test statistic. The proposed method is conservative for marginal inference, in general, but its key advantage over more standard approaches is that it is valid in finite samples even when the underlying model is not point identified. Moreover, our method requires only independence of serology test results, and does not rely on asymptotic arguments, normality assumptions, or other approximations. We use recent Covid-19 serology studies in the US, and show that the parameter confidence set is generally wide, and cannot support definite conclusions. Specifically, recent serology studies from California suggest a prevalence anywhere in the range 0 inconclusive. However, this range could be narrowed down to 0.7 actual false positive rate of the antibody test was indeed near its empirical estimate ( 0.5 confidently estimated in the range 13 suggests significant geographic variation in Covid-19 exposure across the US. Combining all datasets yields a 5 suggest that serology testing on a massive scale can give crucial information for future policy design, even when such tests are imperfect and their parameters unknown.
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