Mixed Time Series Quasi-Likelihood Models for Uncovering Covid-19 Viral Load and Mortality Dynamics

TL;DR

This paper introduces a novel mixed-valued time series quasi-likelihood model (MixTSQL) for jointly analyzing viral load and mortality data in Covid-19, providing insights into their temporal relationship.

Contribution

The paper develops a new flexible mixed-type time series model that requires only mean-variance specifications and enables Granger causality testing without distributional assumptions.

Findings

Viral load Granger-causes mortality in São Paulo data.

The MixTSQL model effectively analyzes multivariate mixed-type time series.

Statistical guarantees ensure estimator consistency and asymptotic normality.

Abstract

Accurate real-time monitoring of disease transmission is crucial for epidemic control, which has conventionally relied on reported cases or hospital admissions. Such metrics are frequently susceptible to delays in reporting, various forms of bias, and under-ascertainment. Cycle threshold values obtained from reverse transcription quantitative polymerase chain reaction offer a promising alternative, serving as a proxy for viral load. In this paper, we aim to jointly model the viral load and the number of deaths (mortality), which involves a continuous bounded and a count time series, and therefore, a proper mixed-type model is needed. This is the motivation to introduce a new mixed-valued time series quasi-likelihood (MixTSQL) model capable of analyzing multivariate time series of different types, like continuous, discrete, bounded, and continuous positive. The MixTSQL model only requires a mean-variance specification with no distributional assumptions needed, and allows for testing Granger causality. Statistical guarantees are provided to ensure consistency and asymptotic normality of the proposed quasi-maximum likelihood estimators. We analyze weekly viral load and Covid-19 death counts in S\~ao Paulo, Brazil, using our MixTSQL model, which not only establishes the temporal order in which viral load Granger-causes mortality but also offers a comprehensive joint statistical analysis.