# Comment on "Under-reported data analysis with INAR-hidden Markov chains"

## TL;DR

This paper critiques a previous model for disease reporting, showing it can be reformulated as a different INAR model with a geometric lag, affecting how reporting probabilities are estimated.

## Contribution

It demonstrates that a Poisson INAR(1) model with underreporting is equivalent to a fully observed INAR(inf) model with geometric lag, highlighting the impact of lag structure assumptions.

## Key findings

- Poisson INAR(1) with underreporting is equivalent to an INAR(inf) with geometric lag.
- Estimated reporting probabilities depend on the lag structure.
- Reformulation affects interpretation of disease reporting models.

## Abstract

In Fernandez-Fontelo et al (Statis. Med. 2016, DOI 10.1002/sim.7026) hidden integer-valued autoregressive (INAR) processes are used to estimate reporting probabilities for various diseases. In this comment it is demonstrated that the Poisson INAR(1) model with time-homogeneous underreporting can be expressed equivalently as a completely observed INAR(inf) model with a geometric lag structure. This implies that estimated reporting probabilities depend on the assumed lag structure of the latent process.