Nonparametric serial interval estimation with uniform mixtures

The serial interval of an infectious disease is a key instrument to understand transmission dynamics. Estimation of the serial interval distribution from illness onset data extracted from transmission pairs is challenging due to the presence of censoring and state-of-the-art methods mostly rely on parametric models. We present a fully data-driven methodology to estimate the serial interval distribution based on interval-censored serial interval data. The proposed nonparametric estimator of the cumulative distribution function of the serial interval is based on the class of uniform mixtures. Closed-form solutions are available for point estimates of different serial interval features and the bootstrap is used to construct confidence intervals. Algorithms underlying our approach are simple, stable, and computationally inexpensive, making them easily implementable in a programming language that is most familiar to a potential user. The nonparametric user-friendly routine is included in the EpiDelays package for ease of implementation. Our method complements existing parametric approaches for serial interval estimation and permits to analyze past, current, or future illness onset data streams following a set of best practices in epidemiological delay modeling.Author summary: Epidemiological delay distributions play a key role in outbreak analyses and in modeling infectious diseases. The serial interval is the time from illness onset in a primary case to illness onset in a secondary case and ranks among the most important delay quantities as it can be used to infer transmission patterns in mathematical and statistical models. From a statistical perspective, estimation of the serial interval distribution is complicated by the fact that the exact timing of illness onset is usually unknown and the latter event is only observed between two time points; a phenomenon called interval censoring. We propose a new inferential method to estimate the serial interval distribution from interval-censored illness onset data without relying on a parametric model. The nonparametric methodology comes with a low degree of mathematical complexity and the underlying algorithms are simple, fast and stable. A user-friendly routine written in the R programming language is available in the EpiDelays package. The proposed data-driven method accounts for a set of best practices in epidemiological delay modeling and can be used to obtain point estimates and confidence intervals for often reported serial interval features.