In New York City, 38 pregnancy-related deaths were caused by hemorrhaging from 2006 to 2010, the most recent data available. More than 630,000 live births took place during those years, according to the city’s Department of Health and Mental Hygiene.

Dr. Mary E. D’Alton, chairwoman of the department of obstetrics and gynecology at Columbia University Medical Center, said maternal deaths from hemorrhaging were “still quite rare,” though, she added, “I don’t think we can say it’s a problem of the past.”

Dr. D’Alton also works with the Safe Motherhood Initiative to help decrease preventable deaths related to childbirth. Still, she said, “There are rare exceptions when, despite the best management, death may not be preventable.”

Ms. Lam and Mr. Kwok, both natives of Hong Kong, had come to New York for Ms. Lam’s graduate studies at Columbia University’s business journalism program. She had graduated in May 2015 and was working as a reporter at Brightwire Inc., a financial news agency. But what she wanted most was a younger brother for Abel, Mr. Kwok said.

The couple had planned to move back to Hong Kong, but when Ms. Lam became pregnant, they decided to wait until October to avoid taking Ms. Lam on a long international flight. Moreover, they wanted the baby to be born an American citizen, with a United States passport. They trusted that the country’s medical care was the best.

The baby was due at the end of August. Doctors told Ms. Lam her pregnancy was healthy and normal, but that the baby might come a bit early, Mr. Kwok said.