Semi-Parametric Estimation of Incubation and Generation Times by Means of Laguerre Polynomials

TL;DR

This paper introduces a semi-parametric method using Laguerre Polynomials to estimate incubation and generation time distributions in epidemics, addressing challenges of incomplete data with theoretical guarantees and simulation validation.

Contribution

It proposes a novel semi-parametric sieve-estimation approach based on Laguerre Polynomials for estimating key epidemic time distributions from limited data.

Findings

Method achieves consistency under specified conditions.

Simulation studies demonstrate good finite sample performance.

Applicable to early pandemic data with incomplete observations.

Abstract

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 challenging problem since it is normally not possible to obtain precise observations of these two variables. Instead, in the beginning of a pandemic, it is possible to observe for infection pairs the time of symptom onset for both people as well as a window for infection of the first person (e.g. because of travel to a risk area). In this paper we suggest a simple semi-parametric sieve-estimation method based on Laguerre-Polynomials for estimation of these distributions. We provide detailed theory for consistency and illustrate the finite sample performance for small datasets via a simulation study.