Integer-Valued Functional Data Analysis for Measles Forecasting

Abstract

Measles presents a unique and imminent challenge for epidemiologists and public health officials: the disease is highly contagious, yet vaccination rates are declining precipitously in many localities. Consequently, the risk of a measles outbreak continues to rise. To improve preparedness, we study historical measles data both prevaccine and postvaccine, and design new methodology to forecast measles counts with uncertainty quantification. We propose to model the disease counts as an integer-valued functional time series: measles counts are a function of time-ofyear and time-ordered by year. The counts are modeled using a negative-binomial distribution conditional on a real-valued latent process, which accounts for the overdispersion observed in the data. The latent process is decomposed using an unknown basis expansion, which is learned from the data, with dynamic basis coefficients. The resulting framework provides enhanced capability to model complex seasonality, which varies dynamically from year-to-year, and offers improved multimonth-ahead point forecasts and substantially tighter forecast intervals (with correct coverage) compared to existing forecasting models. Importantly, the fully Bayesian approach provides well-calibrated and precise uncertainty quantification for epi-relevant features, such as the future value and time of the peak measles count in a given year. An R package is available online. K E Y W O R D S Bayesian modeling, disease, MCMC, prediction, public health, time series 2 | KOWAL SUPPORTING INFORMATION Additional supporting information may be found online in the Supporting Information section.

Dynamic Regression Models for Time-Ordered Functional Data

“…The error termγ t (τ ) models both functional dependence in τ and dynamic dependence via a functional autoregressive model in (7), which has been shown to offer strong forecasting performance in the absence of predictors (Kowal et al, 2017b). Note that the auto-and cross-covariance functions of Y t (τ ) are available as a special case of Propositions 1 and 2 in Kowal (2019), and do not require separability in τ and t.…”

“…We address the setting of time-ordered functional data, where the primary goal is to forecast future functional observations with uncertainty quantification. Examples of time-ordered functional data include yearly sea surface temperature as a function of time-of-year (Besse et al, 2000), daily pollution curves as a function of time-of-day (Damon and Guillas, 2002;Aue et al, 2015), yearly mortality rates as a function of age (Hyndman and Ullah, 2007), and yearly disease counts as a function of time-of-year (Kowal, 2019).…”

Semiparametric Functional Factor Models with Bayesian Rank Selection

“…although non-Gaussian versions are available (Goldsmith et al, 2015;Kowal, 2019). We proceed using common observation points τ i,j = τ j and m i = m for notational simplicity, but this restriction may be relaxed.…”

Simultaneous transformation and rounding (STAR) models for integer-valued data

“…A challenging scenario for prediction and inference occurs when the outcome variables are integer-valued, such as counts, (test) scores, or rounded data. Integer-valued data are ubiquitous in many fields, including epidemiology (Osthus et al, 2018;Kowal, 2019), ecology (Dorazio et al, 2005), and insurance (Bening and Korolev, 2012), among many others (Cameron and Trivedi, 2013). Counts often serve as an indicator of demand, such as the demand for medical services (Deb and Trivedi, 1997), emergency medical services (Matteson et al, 2011), and call center access (Shen and Huang, 2008).…”