RtEstim: Effective reproduction number estimation with trend filtering

To understand the transmissibility and spread of infectious diseases, epidemiologists turn to estimates of the effective 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 RtEstim that solves a convex optimization problem—Poisson trend filtering—using the proximal Newton method. It produces a locally adaptive estimator for effective reproduction number estimation with heterogeneous smoothness. RtEstim 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][1]. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement Daniel J. McDonald is partially supported by Centers for Disease Control and Prevention under U011P001121 and 75D30123C15907, and National Sciences and Engineering Research Council under ALLRP 581756-23 and RGPIN 2021-02618. Paul Gustafson is partially supported by National Sciences and Engineering Research Council Discovery Grant under RGPIN-2019-03957. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All data produced are available online at the "jiapivialiu/rt-est-manuscript" Github repository with the following url: [1]: https://dajmcdon.github.io/rtestim/index.html