Seroprevalence estimation using cross-sectional serosurveys can be challenging due to inadequate or unknown biological cut-off limits of detection. In recent years, diagnostic assay cut-offs, fixed assay cut-offs and more flexible approaches as mixture modelling have been proposed to classify biological quantitative measurements into a positive or negative status. Our objective was to estimate the prevalence of anti-HCV antibodies among drug users (DU) in France in 2011 using a biological test performed on dried blood spots (DBS) collected during a cross-sectional serosurvey. However, in 2011, we did not have a cut-off value for DBS. We could not use the values for serum or plasma, knowing that the DBS value was not necessarily the same. Accordingly, we used a method which consisted of applying a two-component mixture model with age-dependent mixing proportions using penalised splines. The component densities were assumed to be log-normally distributed and were estimated in a Bayesian framework. Anti-HCV prevalence among DU was estimated at 43.3% in France and increased with age. Our method allowed us to provide estimates of age-dependent prevalence using DBS without having a specified biological cut-off value.

Population seroprevalence can be estimated from serosurveys by classifying quantitative measurements into positives (past infection/vaccinated) or negatives (susceptible) according to a fixed assay cut-off. The choice of assay cut-offs has a direct impact on seroprevalence estimates. A time-resolved fluorescence immunoassay (TRFIA) was used to test exposure to human parvovirus 4 (HP4). Seroprevalence estimates were obtained after applying the diagnostic assay cut-off under different scenarios using simulations. Alternative methods for estimating assay cut-offs were proposed based on mixture modelling with component distributions for the past infection/vaccinated and susceptible populations. Seroprevalence estimates were compared to those obtained directly from the data using mixture models. Simulation results showed that when there was good distinction between the underlying populations all methods gave seroprevalence estimates close to the true one. For high overlap between the underlying components, the diagnostic assay cut-off generally gave the most biased estimates. However, the mixture model methods also gave biased estimates which were a result of poor model fit. In conclusion, fixed cut-offs often produce biased estimates but they also have advantages compared to other methods such as mixture models. The bias can be reduced by using assay cut-offs estimated specifically for seroprevalence studies.

A cut-off phenomenon is shown to occur in a sample of n independent, identically distributed Ornstein-Uhlenbeck processes and its average. Their distributions stay far from equilibrium before a certain O(log(n)) time, and converge exponentially fast after. Precise estimates show that the total variation distance drops from almost 1 to almost 0 over an interval of time of length O(1) around log(n)/(2α), where α is the viscosity coefficient of the sampled process. The distribution of the hitting time of 0 by the average of the sample is computed. As n tends to infinity, the hitting time becomes concentrated around the cut-off instant, and its tails match the estimates given for the total variation distance.

For most repairable systems, the number N(t) of failed components at time t appears to be a good quality parameter, so it is critical to study this random function. Here the components are assumed to be independent and both their lifetime and their repair time are exponentially distributed. Moreover, the system is considered new at time 0. Our aim is to compare the random variable N(t) with N(∞), especially in terms of total variation distance. This analysis is used to prove a cut-off phenomenon in the same way as Ycart (1999) but without the assumption of identical components.