Statistics and Its Interface

Volume 10 (2017)

Number 2

New tree structured survival analysis for hip fracture of SOF data

Pages: 199 – 205



Hua Jin (School of Mathematical Sciences, South China Normal University, Guangzhou, China)

Ying Lu (Department of Health Research and Policy, Stanford University, Stanford, California, U.S.A.; and Cooperative Studies Program Center, Palo Alto Veterans Administration Health Care System, Palo Alto, Calif.)


Osteoporosis is a common disease among postmenopausal women and older men. It is critical to accurately predict osteoporotic fracture risk so that high-risk subjects can receive appropriate treatments before fractures occur. We want to establish classification algorithms for identifying subjects at high risk of hip fracture based on prospective cohort data from the Study of Osteoporotic Fracture (SOF). We propose a new algorithm that is similar to the traditional forward regression for survival analysis on the basis of restricted mean lifetime and apply it to the SOF data to form a classification tree. We also construct the second tree based on log-rank test statistic and the third tree using the martingale-type residuals from the Cox proportional hazards model without including any covariates of interest. We compare the three trees to each other. All the results suggest that the classification rule based upon our new method provide a good prognostic staging system for hip fracture both in classification efficiency and stability. Our proposed method may be a competitive alternative to conventional tree-structured survival analysis that uses multiple risk factors to provide powerful and understandable classification procedures.


log-rank test, osteoporotic fracture, restricted mean lifetime, forward tree-structured survival analysis

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