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.