Several social and medical attributes are associated with both avoidance or delay of vaccination and an increased risk of adverse events such as sudden infant death syndrome or childhood encephalopathy. Studies that fail to control adequately for such confounding factors are likely to underestimate the risks of adverse events attributable to vaccination. This paper reviews the literature on studies of severe adverse events after the administration of pertussis antigen-containing vaccines, with particular attention to the measures taken by different investigators to avoid this problem. Most published studies have reported a deficit of sudden infant death syndrome among vaccinees, which may reflect confounding in their study designs. An expression is derived to explore the extent of underestimation that may be introduced in such studies, under different sets of conditions. Confounding of this sort is a general problem for studies of adverse reactions to prophylactic interventions, as they may be withheld from some individuals precisely because they are already at high risk of the adverse event.