The Sudden Infant Death Syndrome is a Probability Process

The Sudden Infant Death Syndrome (SIDS) is sudden-unexpected death of an infant that remains unexplained after thorough forensic autopsy, death scene investigation and review of the infant's medical history. As the results of a few spins of a roulette wheel cannot establish whether the wheel is honest (uniform value distribution), medical investigations of a few SIDS cases have not been able to uncover the mechanistic cause of death. We propose that this is because statistical analyses of large numbers of independent observations may be required to unmask the apparent probability processes that govern these quite different phenomena. The SIDS male fraction ~0.60 appears as a binomial probability sample characteristic of a condition caused by an X-linked gene. The unique SIDS age distribution (minimum at birth, mode ~63 days, median ~94 days, falling exponentially to zero at ~41.2 months) appears as a probability sample from an underlying Johnson SB (4-parameter lognormal) distribution of ages. The presence of this lognormal distribution is prima facie evidence that a probability process is involved. Matching binomial and SB distribution equations to these physiological phenomena, we propose: The SIDS binomial gender distributions arises from an X-linked recessive allele (q ≈ 2/3) non-protective against acute anoxic encephalopathy; and SIDS Johnson SB age distributions arise from such genetically susceptible infants having three independent risk factors: neurological prematurity (m + 0.31)-1 decreasing with age in months m; risk of respiratory infection increasing with age (41.2 - m)-1; and risk of physiological anemia rising and falling with age (2á´¨σ2)-1/2[exp(-0.5[(y-µ)/σ]2)] , where y = Log[(m + 0.31)/(41.2 - m)] = µ + σ z, µ is median of y, σ is standard deviation of y, with z a standard normal deviate. We show infant Respiratory Distress Syndrome and Suffocation by Inhalation of Food or Foreign Object have approximately the same male fractions as SIDS, supporting the hypothesis that the same allele of an X-linked gene is responsible for death in all these cases.