210 Chapter 9 it is not impossible that patients who underwent surgery in baseline season did have a respiratory infection. Second, instrumental variables should only have an effect on the outcome (duration of mechanical ventilation) through the ‘treatment’ (respiratory infection)43. As discussed previously, there are many factors that are different between ILI season and baseline season, such as vitamin D status. The third assumption of a valid instrumental variable is that there is random assignment of the instrument43. This assumption holds in our study, as the season in which cardiac surgery is scheduled will be random for individual patients. As explained above, the positivity assumption holds if individuals can be either exposed or unexposed for every combination of covariates. For example, if all individuals aged >80 are prevented from receiving the treatment (exposure), the positivity assumption does not hold42. Positivity is likely to hold for all three of the chapters in part II of this thesis. In Chapter 4, there were no subgroups who had a structural positivity violation, as everyone in the population could have either a monoinfection or a co-infection. In Chapter 5, all patients could have received any of the treatments. In Chapter 6, there are no (combination of) covariates that prevents patients from undergoing cardiac surgery in any specific season. The consistency assumption could be violated if the effect of exposure is inconsistent between individuals41. The exposure should be “sufficiently well-defined”41. Coinfections in Chapter 4 were defined based on RT-PCR test results, which are welldefined exposures. However, patients were tested for SARS-CoV-2, influenza viruses, RSV and adenovirus, and not for other respiratory viruses. It is possible that a patients had a SARS-CoV-2 and RSV co-infection, but also an undetected rhinovirus infection. This limits the consistency, although both the exposed and unexposed groups are affected in the same way. The outcomes in this study are well defined and measured similarly between the exposed and unexposed groups. In Chapter 5, assignment into one of the different groups was based on pharmacy data of provided medication. This is likely to be a precise indicator of the treatment the patient received, creating welldefined treatment groups. As was the case in Chapter 4, the outcomes were well defined. Finally, in Chapter 6, the exposure was well-defined, using the number of ILI cases in the population to define the burden of disease in different seasons. However, as also described in Chapter 6, the severity of the ILI season can differ significantly between years. Summarising the considerations above, the study design for finding a causal relationship was most suitable for the viral co-infection study and the IL-6 inhibitor study. While residual confounding cannot be excluded, there are no large violations of the three identifiability criteria. For the study investigating the relationship between ILI season and duration of invasive mechanical ventilation and mortality, there are possible violations for the exchangeability and consistency criteria. However, the dose-response relation between ILI prevalence and mortality is interesting and supportive of a causal relation, although possibly not caused by respiratory complications of a respiratory viral infection.
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