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First 5000 Characters:The force of infection, or the rate at which susceptible individuals become infected, is an important public health measure for assessing the extent of outbreaks and the impact of control programs. Here we present methods for estimating force of infection from serological surveys of infections which produce lasting immunity, taking into account imperfections in the test used, and uncertainty in such imperfections. The methods cover both single serological surveys, in which age is a proxy for time at risk, and repeat surveys in the same people, in which the force of infection is estimated more directly. Fixed values can be used for the sensitivity and specificity of the tests, or existing methods for belief elicitation can be used to include uncertainty in these values. The latter may be applicable, for example, when the specificity of a test depends on co-circulating pathogens, which may not have been well characterized in the setting of interest. We illustrate the methods using data from two published serological studies of dengue.
The force of infection, or the rate at which susceptible individuals become infected, is an important public health measure used to assess the speed and extent of an epidemic, and the impact of disease control programs, as well as to prioritize and identify regions requiring further control, and vaccine implementation (1) (2) (3) (4) (5) . For infections inducing lasting immunity, the force of infection is usually estimated via serological surveys ('serosurveys') of immunological status. Ideally, assays used in serosurveys should be highly sensitive and specific while also suitable for high throughput, in terms of the cost and personnel required (6) (7) (8) (9) (10) (11) . In practice, however, available assays may not completely meet all these criteria, as is currently evident with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus responsible for coronavirus disease (COVID19) (12) .
The force of infection may be estimated from single or repeated serosurveys. In the former case, the simplest analysis is to assume that the force of infection was constant over calendar time and age, and consider age as the time at risk (13) . More sophisticated models allow for changing force of infection over time, or over age, or even allow for maternal antibodies if the analysis includes new-borns or infants under a year of age (4, 14) .
Repeated surveys in the same individuals provide more robust estimates of the force of infection during a given study period (4, 7) . Using repeated surveys, rate ratios can be obtained from binomial regression with complementary log-log link and the logarithm of the time between surveys as an offset (13) . While age is used as the time at risk in the analysis of a single survey, in repeated surveys it can be considered a risk factor like any other.
However, errors in test status are usually ignored, whether analysing one or more surveys.
In particular, for repeat surveys, individuals testing positive at baseline are usually considered no longer at risk (1, 4, 7) .
The choice of assay may substantially affect the study's interpretation (15) . Various methods have taken into account certain kinds of test imperfection, for either single or repeated surveys. In particular, Trotter & Gay (16) developed a compartmental model of multiple surveys, in which the force of infection and imperfect sensitivity were estimated for . CC-BY 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted June 11, 2020. Here we provide methods to estimate force of infection, from a single serosurvey or two serosurveys in the same individuals, accounting for imperfect sensitivity and/or specificity, and uncertainty in these parameters.
We started from methods for estimating prevalence based on an imperfect diagnostic test, as reviewed by Lewis & Torgerson (21) , and use similar notation. Estimation is done using a Bayesian framework and Markov chain Monte Carlo (MCMC) (22) . We assume that the immune response being measured is long-lasting so that, for example, apparent seroreversions, i.e. changes over time from positive to negative, are due to test errors rather than loss of immunity. We use "seroprevalence" to mean the proportion of individuals with the underlying immune response, which the diagnostic tests measure with error.
The probability of testing positive (T + ) is specified as a function of the unobserved true status (π), and the assumed values for sensitivity (S e ) and specificity (S p ):
Then, representing a constant seroconversion rate, a binomial regression is specified with a complementary log-log link, and the logarithm of age as an offset. The only other term in the . CC-BY 4.0 International license It is made available under a is the author/funder, who has