Learning associations of COVID-19 hospitalizations with wastewater viral signals by Markov modulated models

Recent research highlights a strong correlation between COVID-19 hospitalizations and wastewater viral signals. Increases in wastewater viral signals may be early warnings of increases in hospital admissions. That indicates a promising opportunity to assess and predict the burden of infectious diseases and has driven the widespread adoption and development of wastewater monitoring tools by public health organizations. Previous studies utilize distributed lag models to explore associations of COVID-19 hospitalizations with lagged SARS-CoV-2 wastewater viral signals. However, the conventional distributed lag models assume the duration time of the lag to be fixed, which is not always plausible. This paper presents Markov-modulated models with distributed lasting time, treating the duration of the lag as a random variable defined by a hidden process. We evaluate exposure effects over the duration time and estimate the distribution of the lasting time using the wastewater data and COVID-19 hospitalization records from Ottawa, Canada during June 2020 to November 2022. The different COVID-19 pandemic waves are accommodated in the statistical learning. Moreover, two strategies for comparing the associations over different time intervals are exemplified using the Ottawa data. Of note, the proposed Markov modulated models, an extension of distributed lag models, are potentially applicable to many different problems where the lag time is not fixed.