Application of Frailty Quantile Regression Model to Investigate of Factors Survival Time in Breast Cancer: A Multi-Center Study.

Background: The prognostic factors of survival can be accurately identified using data from different health centers, but the structure of multi-center data is heterogeneous due to the treatment of patients in different centers or similar reasons. In survival analysis, the shared frailty model is a common way to analyze multi-center data that assumes all covariates have homogenous effects. We used a censored quantile regression model for clustered survival data to study the impact of prognostic factors on survival time.

Methods: This multi-center historical cohort study included 1785 participants with breast cancer from four different medical centers. A censored quantile regression model with a gamma distribution for the frailty term was used, and p-value less than 0.05 considered significant.

Results: The 10^th and 50^th percentiles (95% confidence interval) of survival time were 26.22 (23-28.77) and 235.07 (130-236.55) months, respectively. The effect of metastasis on the 10^th and 50^th percentiles of survival time was 20.67 and 69.73 months, respectively (all p-value < 0.05). In the examination of the tumor grade, the effect of grades 2 and 3 tumors compare with the grade 1 tumor on the 50^th percentile of survival time were 22.84 and 35.89 months, respectively (all p-value < 0.05). The frailty variance was significant, which confirmed that, there was significant variability between the centers.

Conclusions: This study confirmed the usefulness of a censored quantile regression model for cluster data in studying the impact of prognostic factors on survival time and the control effect of heterogeneity due to the treatment of patients in different centers.