Estimating the strength of symptom propagation from primary-secondary case pair data

Symptom propagation occurs when the symptoms of secondary cases are related to those of the primary case as a result of epidemiological mechanisms. Determining whether - and to what extent - symptom propagation occurs requires data-driven methods. Here we quantify the strength of symptom propagation as the increase in risk of a secondary case developing severe symptoms if the primary case has severe symptoms. We first used synthetic results to determine the data requirements to robustly estimate the strength of symptom propagation and to investigate the effect of severity-dependent reporting bias. Categorising symptom severity into two group (mild or severe; asymptomatic or symptomatic), our estimation requires only four summary statistics - the number of primary-secondary case pairs of each combination of symptom presentations. Our analysis showed that a relatively small number (100) of synthetic primary-secondary case pairs was sufficient to obtain a reasonable estimate of the strength of symptom propagation and 1,000 pairs meant errors were consistently small across replicates. Our estimates were robust to severity-dependent reporting bias. We also explored how symptom propagation can be separated from other individual-level factors affecting severity, using age dependence as an example. Although synthetic data generated from an age-structured model led to overestimations of the strength of symptom propagation, allowing disease severity to be age-dependent restored the accuracy of parameter estimation. Finally, we applied our methodology to estimate the strength of symptom propagation from three publicly available data collected during the COVID-19 pandemic with data on presence or absence of symptoms: England households, Israel households, and Norway contact tracing. Our age-free methodology indicated a 12-17% increase in the risk of being symptomatic if infected by someone symptomatic. Our positive estimates for the strength of symptom propagation persisted when applying our age-dependent methodology to the two household data sets with age-structured information (England and Israel). These findings demonstrate evidence for symptom propagation of SARS-CoV-2 and provide consistent estimates for its strength. Our synthetic data analysis supports the conclusion that these correlations are not a result of reporting bias or age-dependent effects. This work provides a practical tool for estimating the strength of symptom propagation that has minimal data requirements, enabling application across a wide range of pathogens and epidemiological settings.