Estimating Probability of Co-occurrence of Metastasis and Death at Certain Intervals after Surgery in Patients with Breast Cancer

Breast cancer is one of the most prevalent cancers and significant causes of mortality in women. An important problem is the cancer cell metastasis in other organs. Different mechanisms in the beginning, progression, and metastasis of breast cancer makes it difficult to determine patients’ ultimate fate (prognosis) and lifespan specifically although events ahead of the patients can be estimated using probabilities. This study was conducted to estimate the probability for the co-occurrence of metastasis and death at certain intervals of 5 years after surgery and 5 years after metastasis in patients with breast cancer. In this retrospective study, the data were collected from 608 women having breast cancer and going to the Breast Disease Center of ACECR in 2001-2009. The patients were studied from the time of surgery, and the two events were metastasis and death, respectively. The interval between the surgery and metastasis and that between the metastasis and death caused by cancer or end of follow-ups (for patients who did not die) were measured and analyzed in month. The probability for co-occurrence of the two intervals was estimated using the semiparametric method suggested by Una-Alvarez (2011) and R statistical software. Median time for the occurrence of metastasis after surgery and duration of follow-up were 34 months and 66 months, respectively. In total, 93 metastases and 46 deaths occurred. The co-occurrence probability interval for all samples was 0-0.087. It was found that the probability for co-occurrence of the two events in patients with more than 50 years old, a tumor larger than 5 cm, lymph node involvement, high stage of the disease, positive HER2, negative ER, and without radiotherapy was greater than that in other groups.Discussions and Considering the estimated co-occurrence probabilities, it seemed that factors such as the age over 50 years, tumors larger than 5 cm, lymph node involvement, higher stages, positive HER2, and negative ER increased the probability for the co-occurrence of metastasis and death in breast cancer patients.