Let a supine infant be susceptible to SIDS only in that central segment. Let the probability of a prone sleeping child = Pp and that of a supine merely sleeping child = Ps. For simplicity we include the side sleeping position with the prone, and we require Pp + Ps = 1. Then the probability of dying of SIDS at age m while prone (Ppsids) is written as, Ppsids=Pp??Pg??Pa??([Pn+Pi]?PnPi). (4) One can then write the probability of supine SIDS (Pssids) as, Pssids=Ps??Pg??Pa??Pn??Pi. (5) Combining (4) and (5) we get the total probability of SIDS (Psids) as Psids=Pp??Pg??Pa??(Pn+Pi)+(Ps?Pp)??Pg??Pa??Pn??Pi. (6) We then note that the sum of Pn + Pi has a similar mathematical form as Pn Pi as follows: Pn+Pi=1(m??+??0.31)+1(41.2?m)=[(41.2?m)+(m+0.31)][(m+0.31)??(41.2?m)], (7a) Pn+Pi=41.5[(m+0.31)(41.
2?m)], (7b) Pn??Pi=1[(m+0.31)(41.2?m)]. (7c) Thus the mathematical form for the age distribution of both supine SIDS and prone SIDS can be represented by the same relationship of C Pa/[(m + 0.31) (41.2 ? m)], where C is a constant, which implies that, in terms of relative probability at different values of m, (7b) and (7c) are the same. This is consistent with the report that there were similar frequencies of pathological findings in both supine and prone SIDS confirming that the mode and cause of SIDS death is apparently the same for both sleep positions . This derivation shows how the Venn Diagram and JohnsonSBage distribution predict that supine and prone SIDS have the same age distribution, with lower rates for the supine SIDS.
This corresponds to the supine requirement to have all 4 risk factors (Pg Pa Pn Pi) as opposed to only 3 risk factors (Pa Pg Pi or Pa Pg Pn) that can allow a prone SIDS to happen more readily. Factors that make the prone sleep position a risk factor for SIDS are rebreathing of exhaled breath with reduced oxygen and increased carbon dioxide  and the finding that presence of a fan in the infants sleep environment, that disperses exhaled breath, decreases the SIDS rate . 4. Discussion Other hypotheses than the X-linkage hypothesis of Naeye et al.  for the male excess in SIDS and other causes of infant respiratory mortality have appeared in the literature [45�C47]. Finnstr?m  reviewed this topic and concluded that ��The mechanism behind the excess perimortality rate in male infants is not known.
A genetic factor leading to reduced tolerance to hypoxia is possible.�� Torday et al.  analyzed amniotic fluid and showed the male fetus developed pulmonary surfactants slower than the female fetus and suggested that this deficit at birth may cause the male excess in infant respiratory distress syndrome (RDS) that matches that of SIDS. This is not likely because the measured deficit Carfilzomib should decrease with maturity as the infant ages, but CDC reports that the male fraction of RDS between 28 and 364 days [0.617] is greater than the male fraction [0.