Learning outcomes

The skills and methods taught in this course apply broadly across infectious disease epidemiology, from outbreak response to routine surveillance of endemic diseases. While examples often use outbreak scenarios for clarity, participants should consider how these approaches apply to their epidemiological contexts.

Delay distributions

understanding of common probability distributions used for epidemiological delays
familiarity with using Stan to estimate parameters of a probability distribution
understanding of the ubiquity of delays in epidemiological data
familiarity with interpreting posterior distributions and quantifying parameter uncertainty

Biases in delay distributions

understanding of how interval censoring affects the estimation and interpretation of epidemiological delay distributions
understanding of right truncation in epidemiological data and its impact on real-time analysis
familiarity with statistical methods for adjusting delay estimates for censoring and truncation
understanding of how biases compound during exponential growth phases of epidemics

Using delay distributions to model the data generating process

understanding of using delay distributions to model population-level data generating processes
familiarity with convolutions to combine count data with individual probability distributions
understanding of double interval censoring and discretisation for population-level data
understanding of the need to introduce additional uncertainty to account for the observation process at a population level

\(R_t\) estimation and the renewal equation

understanding of the reproduction number and challenges in its estimation
understanding of the renewal equation as an epidemiological model for infection generation
familiarity with the generation time as a particular type of delay distribution
understanding of the role of the generative model in the estimation of \(R_t\)
familiarity with geometric random walk models for smoothing \(R_t\) estimates

Nowcasting

understanding of nowcasting as a particular right truncation problem
understanding of the difference between report date and event dates
familiarity with simple nowcasting using known delay distributions
familiarity with improving the model of the data generating process with geometric random walk models to improve nowcast performance in some circumstances

Joint nowcasting with unknown delays

understanding of the reporting triangle structure for epidemiological surveillance data
understanding of the benefits of joint estimation of delay distributions and nowcasts
understanding of population-level modelling with observation error
understanding of the link between Rt estimation and nowcasting

Combining nowcasting and forecasting (bridge to the forecasting course)

understanding of the challenges of forecasting with incomplete data due to reporting delays
understanding of the link between nowcasting and forecasting
understanding of pipeline approaches for combining nowcasting and forecasting
understanding of joint approaches for simultaneous nowcasting and forecasting
understanding of the trade-offs between timeliness and completeness in real-time analysis
familiarity with evaluating nowcasts and short-horizon forecasts using proper scoring rules (e.g. the Continuous Ranked Probability Score, CRPS)

Jointly fitting multiple data sources

understanding of why combining multiple data sources can improve inference
understanding of the step from the informal, iterative model building used through the rest of the course to a more formal modelling workflow
familiarity with the steps of that workflow, from the research question, through the process model and an observation model for each data source, to the choices about data integration and inference
understanding of how model checking, identifiability and conflict between data sources feed back into revising the model
familiarity with extending the renewal-with-delays model to several data sources with their own delays, scalings and likelihoods
understanding of the joint estimation of \(R_t\) and infections from cases, deaths and a wastewater signal
awareness of the data-conflict problem and how a shared latent process may be used to reconcile disagreeing data sources

Modelling complex reporting processes

awareness of the complex, multi-dimensional reporting processes found in real surveillance data
understanding of the different kinds of day-of-week effect, on the expected counts by reference date, on the delay distribution by reference date, and on the reporting process by report date
understanding of batch reporting, where data are reported less often than events occur, and of the trade-off between modelling the process at the reporting timestep and keeping a daily process
understanding of delays that vary over time, and of how a random walk on the delay lets a nowcast follow that drift
familiarity with epinowcast as a way of modelling these features by extending individual modules of the model