  The viral load of patients infected with SARS-CoV-2 varies on logarithmic
scales and possibly with age. Controversial claims have been made in the
literature regarding whether the viral load distribution actually depends on
the age of the patients. Such a dependence would have implications for the
COVID-19 spreading mechanism, the age-dependent immune system reaction, and
thus for policymaking. We hereby develop a method to analyze viral-load
distribution data as a function of the patients' age within a flexible,
non-parametric, hierarchical, Bayesian, and causal model. The causal nature of
the developed reconstruction additionally allows to test for bias in the data.
This could be due to, e.g., bias in patient-testing and data collection or
systematic errors in the measurement of the viral load. We perform these tests
by calculating the Bayesian evidence for each implied possible causal
direction. The possibility of testing for bias in data collection and
identifying causal directions can be very useful in other contexts as well. For
this reason we make our model freely available. When applied to publicly
available age and SARS-CoV-2 viral load data, we find a statistically
significant increase in the viral load with age, but only for one of the two
analyzed datasets. If we consider this dataset, and based on the current
understanding of viral load's impact on patients' infectivity, we expect a
non-negligible difference in the infectivity of different age groups. This
difference is nonetheless too small to justify considering any age group as
noninfectious.
