Is there a relationship between multiple infant deaths in a family and murder? It depends on who you ask.
On the one hand, there are those who still follow the three strike rule. "One SIDS death in a family is tragic; two suspicious; three murder." On the other hand, there have been innocent and grieving women convicted by either the carelessness, or mistakes, of physicians.
Waneta Hoyt: where science and the law collided
One ironic example that supports the followers of this camp was the case of Waneta Hoyt, although initially it was published to do just the opposite.
In October 1972, Dr. Alfred Steinchneider published a groundbreaking study in Pediatrics suggesting that there might be a hereditary flaw in some family genes that resulted in multiple infant deaths. His conclusions were largely based on his study of Waneta Hoyt's family, who lost five children to what was then believed to be Sudden Infant Death syndrome.
However, a prosecutor who came across the paper in 1986 while researching another case drew a different conclusion: He thought the deaths seemed like murder. In fact, he was so convinced of it that he tracked down the identity (many case studies published in medical journals use only the patient's initials to protect their privacy) and the medical records of the case. After a lengthy investigation, Hoyt signed a confession, and was convicted of murder. Dr. Steinchneider, as you might expect, received quite a bit of criticism, especially when it became known that his intervention (by contacting the authorities instead of journal editors) might have spared the lives of the youngest two siblings, who were alive when he became involved with the Hoyts.