Estimating epidemiological delay distributions for infectious diseases

Abstract

Abstract Understanding and accurately estimating epidemiological delay distributions is important for public health policy. These estimates directly influence epidemic situational awareness, control strategies, and resource allocation. In this study, we explore challenges in estimating these distributions, including truncation, interval censoring, and dynamical biases. Despite their importance, these issues are frequently overlooked in the current literature, often resulting in biased conclusions. This study aims to shed light on these challenges, providing valuable insights for epidemiologists and infectious disease modellers. Our work motivates comprehensive approaches for accounting for these issues based on the underlying theoretical concepts. We also discuss simpler methods that are widely used, which do not fully account for known biases. We evaluate the statistical performance of these methods using simulated exponential growth and epidemic scenarios informed by data from the 2014-2016 Sierra Leone Ebola virus disease epidemic. Our findings highlight that using simpler methods can lead to biased estimates of vital epidemiological parameters. An approximate-latent-variable method emerges as the best overall performer, while an efficient, widely implemented interval-reduced-censoring-and-truncation method was only slightly worse. Other methods, such as a joint-primary-incidence-and-delay method and a dynamic-correction method, demonstrated good performance under certain conditions, although they have inherent limitations and may not be the best choice for more complex problems. Despite presenting a range of methods that performed well in the contexts we evaluated, residual biases persisted, predominantly due to the simplifying assumption that the distribution of event time within the censoring interval follows a uniform distribution; instead, this distribution should depend on epidemic dynamics. However, in realistic scenarios with daily censoring, these biases appeared minimal. This study underscores the need for caution when estimating epidemiological delay distributions in real-time, provides an overview of the theory that practitioners need to keep in mind when doing so with useful tools to avoid common methodological errors, and points towards areas for future research. Summary What was known prior to this paper Importance of accurate estimates: Estimating epidemiological delay distributions accurately is critical for model development, epidemic forecasts, and analytic decision support. Right truncation: Right truncation describes the incomplete observation of delays, for which the primary event already occurred but the secondary event has not been observed (e.g. infections that have not yet become symptomatic and therefore not been observed). Failing to account for the right truncation can lead to underestimation of the mean delay during real-time data analysis. Interval censoring: Interval censoring arises when epidemiological events occurring in continuous time are binned into time intervals (e.g., days or weeks). Double censoring of both primary and secondary events needs to be considered when estimating delay distributions from epidemiological data. Accounting for censoring in only one event can lead to additional biases. Dynamical bias: Dynamical biases describe the effects of an epidemic’s current growth or decay rate on the observed delay distributions. Consider an analogy from demography: a growing population will contain an excess of young people, while a shrinking population will contain an excess of older people, compared to what would be expected from mortality profiles alone. Dynamical biases have been identified as significant issues in real-time epidemiological studies. Existing methods: Methods and software to adjust for censoring, truncation, and dynamic biases exist. However, many of these methods have not been systematically compared, validated, or tested outside the context in which they were originally developed. Furthermore, some of these methods do not adjust for the full range of biases. What this paper adds Theory overview: An overview of the theory required to estimate distributions is provided, helping practitioners understand the underlying principles of the methods and the connections between right truncation, dynamical bias, and interval censoring. Review of methods: This paper presents a review of methods accounting for truncation, interval censoring, and dynamical biases in estimating epidemiological delay distributions in the context of the underlying theory. Evaluation of methods: Methods were evaluated using simulations as well as data from the 2014-2016 Sierra Leone Ebola virus disease epidemic. Cautionary guidance: This work underscores the need for caution when estimating epidemiological delay distributions, provides clear signposting for which methods to use when, and points out areas for future research. Practical guidance: Guidance is also provided for those making use of delay distributions in routine practice. Key findings Impact of neglecting biases: Neglecting truncation and censoring biases can lead to flawed estimates of important epidemiological parameters, especially in real-time epidemic settings. Equivalence of dynamical bias and right truncation: In the context of a growing epidemic, right truncation has an essentially equivalent effect as dynamical bias. Typically, we recommend correcting for one or the other, but not both. Bias in common censoring adjustment: Taking the common approach to censoring adjustment of naively discretising observed delay into daily intervals and fitting continuous-time distributions can result in biased estimates. Performance of methods: We identified an approximate-latent-variable method as the best overall performer, while an interval-reduced-censoring-andtruncation method was resource-efficient, widely implemented, and performed only slightly worse. Inherent limitations of some methods: Other methods, such as jointly estimat