Regression analyses with clustered time-to-event data when numbers of event are small

• Main Authors: Feng-Shiang Cheng, 鄭鳳翔
• Other Authors: I-Feng Lin
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/70747709298584086585

碩士 === 國立陽明大學 === 公共衛生研究所 === 101 === Background: In public health and clinical studies, parameter estimates in Cox regression models are usually unreliable when event is rare or when follow-up time is not longer enough. Previous studies have suggested that the event per variable (EPV) should be more than 10 when data are not independent. When data are correlated, e.g. cluster sampling, Cox models with robust sandwich variance estimates (Lee, Wei, &; Amato, 1989) and Frailty model are commonly used. How EPVs affect the parameter estimates in Cox model with clustered data remains to be explored. Objectives：The aim of this study was to evaluate the accuracy of the parameter estimates of cox models with clustered data when EPV is small. Methods：Simulation studies have been conducted with different numbers of event per variable, different number of clusters and cluster sizes, and varying between-cluster variations. This simulation study compared the estimates by different estimatos in Cox models: Cox model estimated by partial likelihood、Cox model estimated by Firth’s Penalized likelihood、 Cox model estimated by robust variance estimator、and Cox model estimated with random effect in cluster data. Results and Conclusions： Bias: When data were clustered with small EPV (EPV=5), the “Frailty” estimator method were less biased in general , no matter what the ratio of numbers of cluster to cluster size were, for both categorical and continuous independent variables. In the extreme case when number of cluster (m) is far smaller than cluster size (n), m=5 and n=100, or when the between-cluster variation was small, the “Firth” method is least biased. Efficiency：When EPV is small and data are clustered, for categorical variables, the “Robust” method usually underestimate the standard error when numbers of cluster larger than cluster size. On the other hand, the “Frailty” and the “Standard” method usually overestimate the standard error. While numbers of cluster were much smaller than cluster size，the both “Robust” and “ Frailty” method has underestimated the standard error, but ”Standard” method has overestimated it. Coverage rate of 95% confidence intervals：The 95% coverage rate by “Robust” method was in generally less than 95%, i.e., there were greater chances that the results of hypothesis testing for the parameter would be statistically significant than it should have been. Converge rate：The ”Frailty” method has worse converge rate while the converge rates by the ”Robust” 、the ”Standard”, and the ”Firth” methods were almos reach 100%.