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Numerous studies have reported a protective association between asthma and acute lymphoblastic leukemia (ALL), but the causal structure of this association remains unclear. We present a hybrid simulation to examine the compatibility of this association with uncontrolled confounding by infection or another unmeasured factor. We generated a synthetic cohort using inputs on the interrelations of asthma, ALL, infections, and other suggested risk factors from the literature and the Danish National Birth Cohort. We computed odds ratios (ORs) between asthma and ALL in the synthetic cohort with and without adjustment for infections and other (including unmeasured) confounders. Only if infection was an extremely strong risk factor for asthma (OR of 10) and an extremely strong protective factor against ALL (OR of 0.1) was the asthma-ALL association compatible with the literature (OR of 0.78). Similarly, strong uncontrolled confounding by an unmeasured factor could downwardly bias the asthma-ALL association, but not enough to replicate findings in the literature. This investigation illustrates that the reported protective association between asthma and ALL is unlikely to be entirely due to uncontrolled confounding by infections or an unmeasured confounder alone. Simulation can be used to advance our understanding of risk factors for rare outcomes as demonstrated by this study.

Numerous studies have reported a protective association between asthma and acute lymphoblastic leukemia (ALL), but the causal structure of this association remains unclear. We present a hybrid simulation to examine the compatibility of this association with uncontrolled confounding by infection or another unmeasured factor. We generated a synthetic cohort using inputs on the interrelations of asthma, ALL, infections, and other suggested risk factors from the literature and the Danish National Birth Cohort. We computed odds ratios (ORs) between asthma and ALL in the synthetic cohort with and without adjustment for infections and other (including unmeasured) confounders. Only if infection was an extremely strong risk factor for asthma (OR of 10) and an extremely strong protective factor against ALL (OR of 0.1) was the asthma-ALL association compatible with the literature (OR of 0.78). Similarly, strong uncontrolled confounding by an unmeasured factor could downwardly bias the asthma-ALL association, but not enough to replicate findings in the literature. This investigation illustrates that the reported protective association between asthma and ALL is unlikely to be entirely due to uncontrolled confounding by infections or an unmeasured confounder alone. Simulation can be used to advance our understanding of risk factors for rare outcomes as demonstrated by this study.