A simulation-based procedure to estimate base rates from Covid-19 antibody test results I: Deterministic test reliabilities

We design a procedure (the complete Python code may be obtained at https://github.com/abhishta91/antibody_montecarlo) using Monte Carlo (MC) simulation to establish the point estimators described below and confidence intervals for the base rate of occurence of an attribute (e.g., antibodies against Covid-19) in an aggregate population (e.g., medical care workers) based on a test. The requirements for the procedure are the tests sample size (N) and total number of positives (X), and the data on tests reliability. The modus is the prior which generates the largest frequency of observations in the MC simulation with precisely the number of test positives (maximum-likelihood estimator). The median is the upper bound of the set of priors accounting for half of the total relevant observations in the MC simulation with numbers of positives identical to the tests number of positives. O_LSTOur rather preliminary findings areC_LSTO_LIThe median and the confidence intervals suffice universally. C_LIO_LIThe estimator [Formula] may be outside of the two-sided 95% confidence interval. C_LIO_LIConditions such that the modus, the median and another promising estimator which takes the reliability of the test into account, are quite close. C_LIO_LIConditions such that the modus and the latter estimator must be regarded as logically inconsistent. C_LIO_LIConditions inducing rankings among various estimators relevant for issues concerning over-or underestimation. C_LI JEL-codes: C11, C13, C63