The study, based on a database including three million families and a million cancer patients in Sweden, found an increased risk of an early death in second-generation patients with breast, lung, prostate and colon cancer.
The same may hold for other cancers as well, the researchers said, but only these four were present in sufficient numbers to be statistically significant.
It has long been known that family history is a risk factor for many forms of cancer, but this is the first evidence extending that filial bond to the child's chances of living with or overcoming the disease.
While environmental factors could not be ruled out entirely, the findings strongly suggest that genetic factors are at work.
Among the offspring of people who had died within 10 years of being diagnosed, the increased risk compared to cohorts whose parents has survived longer was 75 percent for breast cancer, 107 percent for prostate cancer, 44 percent for colorectal cancer, and 39 percent for lung cancer.
The findings, published in the British journal The Lancet, suggest that "cancer specific-survival of a patient can be predicted from previous parental survival from cancer at the same site," the authors conclude.
The team of researchers, led by Linda Lindstrom of the Karolinksa Institute in Stockholm, also say that the parent-child link could be a useful guide for treatment as well.
"Information on poor survival in a family might be vital in accurately predicting tumour progression in the newly diagnosed individual," they write.
In a comment, also published in The Lancet, Ora Paltiel of the Hadassah-Hebrew University Medical Centre in Jerusalem said the findings could inform life-and-death decisions, such as whether to opt for active treatment or observation in a new diagnosis of prostate cancer.
The study concluded that parent-child link in cancer survival rates held independently from income level, time of year, or geographic location.
Discrepancies in treatment were also unlikely to have been a factor because all people in Sweden have access to free or low case health care of comparable quality.
More studies will be needed, however, to determine the precise nature of the genetic factors resulting in the transmission of susceptibility to cancer from one generation to the next, the researchers said.