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Histograms of estimated basic reproduction numbers of fictional pandemic. The dotted line indicates the true R 0 and the solid line is the density of a normal distribution with the sample mean and standard deviation.
Source publication
In epidemics many interesting quantities, like the reproduction number, depend on the incubation period (time from infection to symptom onset) and/or the generation time (time until a new person is infected from another infected person). Therefore, estimation of the distribution of these two quantities is of distinct interest. However, this is a ch...
Context in source publication
Context 1
... order to estimate the basic reproduction number, we plug the true and the estimated generation time densities into equation (1.1) and take the inverse of it (in this fictional pandemic we choose r = log(2)/5 which means that the case numbers double every five days). The histogram of the estimates is shown in Figure 5. We emphasize that these are simulated results and we cannot draw any conclusions about COVID-19. ...
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Citations
... Backer et al. (2020) and Miura et al. (2022) use a Bayesian parametric approach to estimate the incubation period of COVID-19 and of Mpox, respectively. Groeneboom (2021) derives a smooth non-parametric estimator of the incubation time distribution by adding a bandwidth parameter that controls the trade-off between noise and bias and Kreiss and Van Keilegom (2022) propose a semi-parametric method to estimate the incubation period based on Laguerre polynomials. ...
... A common strategy to transit from discrete to continuous observations is to assume that exact times are uniformly distributed throughout the day and hence to perturb symptom onset times and exposure window bounds by a uniform random variable between 0 and 1 (see e.g. Kreiss and Van Keilegom, 2022). ...
Motivation
The incubation period is of paramount importance in infectious disease epidemiology as it informs about the transmission potential of a pathogenic organism and helps to plan public health strategies to keep an epidemic outbreak under control. Estimation of the incubation period distribution from reported exposure times and symptom onset times is challenging as the underlying data is coarse.
Methodology
We develop a new Bayesian methodology using Laplacian-P-splines that provides a semi-parametric estimation of the incubation density based on a Langevinized Gibbs sampler. A finite mixture density smoother informs a set of parametric distributions via moment matching and an information criterion arbitrates between competing candidates.
Results
Our method has a natural nest within EpiLPS, a tool originally developed to estimate the time-varying reproduction number. Various simulation scenarios accounting for different levels of data coarseness are considered with encouraging results. Applications to real data on COVID-19, MERS-CoV and Mpox reveal results that are in alignment with what has been obtained in recent studies.
Conclusion
The proposed flexible approach is an interesting alternative to classic Bayesian parametric methods for estimation of the incubation distribution.
... But more flexible methods have been presented as well. They consist of semiparametric regression analysis of doubly censored (Wong, Zhou, and Hu 2022) and a simple semiparametric sieve-estimation method based on Laguerre Polynomials (Kreiss and Van Keilegom 2022). Also Deng, You, Liu, Qin, and Zhou (2021) use theory from renewal process by considering the incubation period as the interarrival time, and the duration between departure from Wuhan and onset of symptoms as the mixture of forward time and interarrival time with censored intervals. ...
... Another unobserved random variable of interest is the incubation time, i.e. the difference between the observed time at which one person has symptoms and the infection time. Kreiss and Van Keilegom (2022) exploit the relationship between the observed symptoms time and some related truncation and location variables to propose a semiparametric approach that allows estimating the densities of the incubation and generation times via a sieve of Laguerre polynomials. The new model is then applied to analyse a real dataset of transmission pairs from the early period of the COVID-19 pandemic. ...
An introduction to this Special Issue on Data Science for COVID-19 is included in this paper. It contains a general overview about methods and applications of nonparametric inference and other flexible data science methods for the COVID-19 pandemic. Specifically, some methods existing before the COVID-19 outbreak are surveyed, followed by an account of survival analysis methods for COVID-related times. Then, several nonparametric tools for the estimation of certain COVID rates are revised, along with the forecasting of most relevant series counts, and some other related problems. Within this setup, the papers published in this special issue are briefly commented in this introductory article.
The incubation period is of paramount importance in infectious disease epidemiology as it informs about the transmission potential of a pathogenic organism and helps to plan public health strategies to keep an epidemic outbreak under control. Estimation of the incubation period distribution from reported exposure times and symptom onset times is challenging as the underlying data is coarse. We develop a new Bayesian methodology using Laplacian-P-splines that provides a semi-parametric estimation of the incubation density based on a Langevinized Gibbs sampler. A finite mixture density smoother informs a set of parametric distributions via moment matching and an information criterion arbitrates between competing candidates. Algorithms underlying our method find a natural nest within the EpiLPS package, which has been extended to cover estimation of incubation times. Various simulation scenarios accounting for different levels of data coarseness are considered with encouraging results. Applications to real data on COVID-19, MERS and Mpox reveal results that are in alignment with what has been obtained in recent studies. The proposed flexible approach is an interesting alternative to classic Bayesian parametric methods for estimation of the incubation distribution.
Consider a situation where one is interested in estimating the density of a survival time that is subject to random right censoring and measurement errors. This happens often in practice, like in public health (pregnancy length), medicine (duration of infection), ecology (duration of forest fire), among others. We assume a classical additive measurement error model with Gaussian noise and unknown error variance and a random right censoring scheme. Under this setup, we develop minimal conditions under which the assumed model is identifiable when no auxiliary variables or validation data are available, and we offer a flexible estimation strategy using Laguerre polynomials for the estimation of the error variance and the density of the survival time. The asymptotic normality of the proposed estimators is established, and the numerical performance of the methodology is investigated on both simulated and real data on gestational age.
