Determining the correlated factors of breast cancer recurrence by Poisson Beta-Weibull non- mixture cure model

Therapies for many of diseases, especially cancer, have been improved significantly in the recent years, resulting in an increase in the number of patients who do not experience mortality. Therefore, the application of cure models is more suitable for survival analysis in this population than the usual survival models are. The aim of this study was to estimate the recurrence-free cure rate of breast cancer using the Poisson Beta Weibull (PBW) cure model and to determine the correlating factors.

The data for this study came from a cohort of 271 breast cancer patients who had visited Motamed Cancer Institute, Tehran, between 1997 and 2006 and were followed up from 2013 to 2017. In this study, the time interval between diagnosis and recurrence of the disease was calculated, and the effect of factors was estimated using a Cox survival model as the most common method of survival analysis. Then, by calculating the cure rate from recurrence, the effect of factors on patients’ survival and cure was analyzed using Weibull and PBWcure models. Data were analyzed using R, v 3.4.1, at a significance level of 5%.

The results showed that 17 (6.3%) of patients experienced relapse after treatment. One-, 3-, and 5-year survival rates for the patients were 0.97, 0.96, and 0.93, respectively. The results of this study showed that PBW Model has a better fit to data with the smallest AIC. Based on this model, estrogen receptor positivity was a significant factor affecting patients' cure (HR = 0.27) and the cure fraction was estimated to be 92%.

Estrogen receptor positivity is the most important factor affecting patients’ cure. The Poisson Beta Weibull cure model has a better fit to data. Since the model analyzes factors affecting both survival and cure, using this model is recommended in the analysis of the events with low incidence.