Design-based inference in time-location sampling.

Time-location sampling (TLS), also called time-space sampling or venue-based sampling is a sampling technique widely used in populations at high risk of infectious diseases. The principle is to reach individuals in places and at times where they gather. For example, men who have sex with men meet in gay venues at certain times of the day, and homeless people or drug users come together to take advantage of services provided to them (accommodation, care, meals). The statistical analysis of data coming from TLS surveys has been comprehensively discussed in the literature. Two issues of particular importance are the inclusion or not of sampling weights and how to deal with the frequency of venue attendance (FVA) of individuals during the course of the survey. The objective of this article is to present TLS in the context of sampling theory, to calculate sampling weights and to propose design-based inference taking into account the FVA. The properties of an estimator ignoring the FVA and of the design-based estimator are assessed and contrasted both through a simulation study and using real data from a recent cross-sectional survey conducted in France among drug users. We show that the estimators of prevalence or a total can be strongly biased if the FVA is ignored, while the design-based estimator taking FVA into account is unbiased even when declarative errors occur in the FVA.