Variable selection for recurrent event data with broken adaptive ridge regression. (English. French summary) Zbl 1492.62162
Summary: Recurrent event data occur in many areas such as medical studies and social sciences and a great deal of literature has been established for their analysis. On the other hand, only limited research exists on the variable selection for recurrent event data, and the existing methods can be seen as direct generalizations of the available penalized procedures for linear models and may not perform as well as expected. This article discusses simultaneous parameter estimation and variable selection and presents a new method with a new penalty function, which will be referred to as the broken adaptive ridge regression approach. In addition to the establishment of the oracle property, we also show that the proposed method has the clustering or grouping effect when covariates are highly correlated. Furthermore, a numerical study is performed and indicates that the method works well for practical situations and can outperform existing methods. An application is provided.
MSC:
| 62N99 | Survival analysis and censored data |
| 62J07 | Ridge regression; shrinkage estimators (Lasso) |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
References:
| [1] | Andersen, P. K., Borgan, O., Gill, R. D., & Keiding, N. (1993). Statistical Models Based on Counting Processes. Springer‐Verlag, New York. · Zbl 0769.62061 |
| [2] | Cai, J. & Schaubel, D. E. (2004). Marginal means/rates models for multiple type recurrent event data. Lifetime Data Analysis, 10, 121-138. · Zbl 1058.62098 |
| [3] | Chen, X. & Wang, Q. (2013). Variable selection in the additive rate model for recurrent event data. Computational Statistics and Data Analysis, 57, 491-503. · Zbl 1365.62365 |
| [4] | Cook, R. J. & Lawless, J. F. (2007). The Statistical Analysis of Recurrent Event Data. Springer‐Verlag, New York. · Zbl 1159.62061 |
| [5] | Fan, J. & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle property. Journal of the American Statistical Association, 96, 1348-1360. · Zbl 1073.62547 |
| [6] | Fleming, T. R. & Harrington, D. P. (1991). Counting Processes and Survival Analysis. Wiley, New York. · Zbl 0727.62096 |
| [7] | Frommlet, F. & Nuel, G. (2016). An adaptive ridge procedure for L_0 regularization. PLoS One, 11(2), e0148620. |
| [8] | Gorodnitsky, I. F. & Rao, B. D. (1997). Sparse signal reconstruction from limited data using focus: A re‐weighted minimum norm algorithm. IEEE Transactions on Signal Processing, 45, 600-616. |
| [9] | Kalbfleisch, J. D. & Prentice, R. L. (2002). The Statistical Analysis of Failure Time Data. Wiley, New York. · Zbl 1012.62104 |
| [10] | Lawless, J. F. & Nadeau, C. (1995). Some simple robust methods for the analysis of recurrent events. Technometrics, 37, 158-168. · Zbl 0822.62085 |
| [11] | Lawson, C. L. (1961). Contributions to the Theory of Linear Least Maximum Approximation, Ph.D. Thesis, University of California, Los Angeles, USA. |
| [12] | Lin, D. Y., Wei, L. J., Yang, I., & Ying, Z. (2000). Semiparametric regression for the mean and rate function of recurrent events. Journal of Royal Statistical Society, Series B, 69, 711-730. · Zbl 1074.62510 |
| [13] | Lin, D. Y., Wei, L. J., & Ying, Z. (2001). Semiparametric transformation models for point processes. Journal of the American Statistical Association, 96, 620-628. · Zbl 1017.62071 |
| [14] | Liu, Z. & Li, G. (2016). Efficient regularized regression with penalty for variable selection and network construction. Computational and Mathematical Methods in Medicine. 2016, 3456153. · Zbl 1367.92008 |
| [15] | Schaubel, D. E., Zeng, D. L., & Cai, J. W. (2006). A semiparametric additive rates model for recurrent event data. Lifetime Data Analysis, 12, 389-406. · Zbl 1109.62110 |
| [16] | Sun, J. & Zhao, X. (2013). The Statistical Analysis of Panel Count Data. Springer Science + Business Inc, New York. · Zbl 1282.62105 |
| [17] | Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B, 58, 267-288. · Zbl 0850.62538 |
| [18] | Tong, X., Zhu, L., & Sun, J. (2009). Variable selection for recurrent event data via nonconcave penalized estimating function. Lifetime Data Analysis, 15, 197-215. · Zbl 1282.62083 |
| [19] | Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American Statistical Association, 101, 1418-1429. · Zbl 1171.62326 |
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