Antonello Maruotti, Saleh Ibrahim, Emilio Porcu, and Horst Simon’s contribution to the Discussion of ‘Some statistical aspects of the Covid-19 response’ by Wood et al.’

We congratulate the authors for their thoughtful analysis of the statistical challenges in shaping policy decisions during the COVID-19 pandemic, especially regarding monitoring and risk assessment.Their work highlights how data analysis must address not just how models are used, but why-focusing on inference, intervention evaluation, and communication with both stakeholders and the public.A critical issue remains the quality and suitability of data and models.Under the "garbage in, garbage out" paradigm, poor data inputs, unrealistic assumptions, or oversimplified epidemiological features can heavily lead to unreliable results [3].While compartmental models are foundational in epidemiology, their reliability depends on high-quality, up-to-date data.Data-driven approaches [6] may offer more robust alternatives, especially under uncertainty or limited data.This concern is well illustrated by reproduction number, R t , estimation in Italy.The serial interval, a fundamental input in the estimation process of the reproduction number, was derived from just 90 case pairs in Lombardy during February 2020 [2], using a fixed Gamma distribution that remained unchanged across time and regions.This one-size-fits-all assumption introduced substantial regional variability and questionable reliability in R t estimates [4].Cross-country comparisons pose further challenges.While excess mortality is a common metric, it requires model-based analysis [9,5, 8,1], rather than simple historical averages comparisons.Even then, international comparisons can be biased by differing socio-demographic structures.Standardized mortality rates and their evolution over time may offer a more accurate indicator for such comparisons.The evaluation of non-pharmaceutical interventions (NPIs), especially lockdowns, must consider timing, context, and which outcomes are being measured.