rtestim: Time-varying reproduction number estimation with trend filtering.

To understand the transmissibility and spread of infectious diseases, epidemiologists turn to estimates of the instantaneous reproduction number. While many estimation approaches exist, their utility may be limited. Challenges of surveillance data collection, model assumptions that are unverifiable with data alone, and computationally inefficient frameworks are critical limitations for many existing approaches. We propose a discrete spline-based approach that solves a convex optimization problem—Poisson trend filtering—using the proximal Newton method. It produces a locally adaptive estimator for instantaneous reproduction number estimation with heterogeneous smoothness. Our methodology remains accurate even under some process misspecifications and is computationally efficient, even for large-scale data. The implementation is easily accessible in a lightweight R package rtestim. Author summary: Instantaneous reproduction number estimation presents many challenges due to data collection, modelling assumptions, and computational burden. Our motivation is to develop a model that produces accurate estimates, is robust to model misspecification, is straightforward to use, and is computationally efficient, even for large counts and long time periods. We propose a convex optimization model with an ℓ₁ trend filtering penalty. It couples accurate estimation of the instantaneous reproduction number with desired smoothness. We solve the optimization using the proximal Newton method, which converges rapidly and is numerically stable. Our software, conveniently available in the R package rtestim, can produce estimates in seconds for incidence sequences with hundreds of observations. These estimates are produced for a sequence of tuning parameters and can be selected using a built-in cross validation procedure. [ABSTRACT FROM AUTHOR]