I just submitted the following application to the BMBR call in the UK and thought I would share it for interest, feedback (though as this is now submitted please be kind) and to see if anyone is thinking along similar lines and wants to collab in the future.
Thanks a lot to those of you who already gave feedback or agreed to be uncosted collabs where I will bother you if this gets funded. Note that this draws on ideas from Generation interval estimation as a censoring problem - #3 by samabbott and Handling multimodal delay distributions - #2 by adrianlison amongst other places.
Abstract
Generation times underpin infectious disease transmission modelling and so inform public health decision-making, help determine outbreak spread, and allow evaluation of control measures. During the COVID-19 pandemic, UK reproduction number estimates relied on potentially inappropriate generation time estimates from different populations, introducing systematic bias into transmission assessments. Generation times are part of a broader family of transmission-pair-dependent (TPD) delay distributions—including serial intervals (time between symptom onset in connected cases), test-to-test intervals, and other measures that require knowing relationships between individuals. Despite their critical importance, public health agencies lack robust methods for estimating these delays during outbreaks. Current approaches suffer from limitations: inadequate handling of observation biases, inflexibility to diverse transmission contexts (households versus community settings), implausible assumptions about infectiousness-symptom relationships, and inability to produce robust high-resolution estimates. The observation process adds further complexity, transmission pairs may be partially or completely unobserved, with events recorded at different stages. One reason these challenges persist is because delay estimation methods used in infectious disease modelling have developed in methodological isolation from survival analysis, despite both fields addressing fundamentally similar time-to-event problems. Recent work demonstrates the value of bridging these disciplines, but methods remain underutilised for TPD delays.
This project will develop a coherent framework for TPD delay estimation, extending our established methods for delays that depend on events from a single individual. Building on proven mixture model approaches for serial intervals with unknown transmission pairs, we will extend these methods to support the complex observation patterns typical of outbreak data. We will create flexible non-parametric methods that adjust for interval censoring and right truncation to enable estimation of delays in challenging scenarios where parametric delay distributions are not representative. For simpler surveillance scenarios, we will develop robust, granular, and fast estimation methods where the infection process can be incorporated through informative priors rather than requiring joint modelling. We will extend this approach to handle flexible infection processes across diverse reporting settings, addressing uncertainty around transmission pairs, unobserved transmission chains, and partial observation of events. Building on growing recognition of the need to bridge survival analysis and infectious disease modelling, we will establish cross-domain collaborations to identify transferable innovations for transmission-pair-dependent delay estimation. Finally, we will evaluate whether unified time-to-event frameworks for infection and delay processes provide advantages over current compartmental or renewal approaches with separate delay estimation.
Starting with enhancements to existing tools, the project will deliver a unified framework for transmission-pair-dependent delay estimation during outbreaks, implemented as open-source software. By addressing methodological gaps and providing robust implementations of our solutions, this project will enable more accurate real-time outbreak analysis and support evidence-based decisions.
Full research plan: research-plan.pdf (126.4 KB)