对参数带约束条件的生存模型的回归分析
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摘要
为了降低成本、提高研究效率,对与时间相依的数据,有偏抽样方法是广泛应用的基础抽样方法.在建模过程中,它可以从参数的先验信息中提取更有价值的信息.随着数字信息的发展,在许多领域都可以收集到协变量维数大于样本容量的高维数据.变量选择法和独立筛选法是非常有效的降维方法.在比例风险模型中,对参数带有约束条件的回归分析,采用了修正的MM算法,但对不同的模型,此优化算法不再适用.为了克服优化问题的计算复杂难实现的困难,将蚁群算法和粒子群算法等优化算法应用到参数带约束条件的回归分析中.
To reduce the cost and improve the efficiency of cohort studies,biased-sampling design is a widely used scheme for time-to-event data.In modeling process,biased-sampling studies can benefit further from taking parameters′prior information.With the explosion of digital information,high-dimensional data is frequently collected in prevalent domains,in which the dimension of covariates can be much larger than the sample size.Variable selection methods and independence have been developed to reduce the dimension of the survival data with censoring,recently.About regression analysis of the proportional hazards model with parameter constraints,the Modified MM algorithm was proposed,but the algorithm can not be applied to other models.To overcome this difficulty,ant colony algorithm and particle swarm optimization are applied for the calculation of the constrained estimator.
To reduce the cost and improve the efficiency of cohort studies,biased-sampling design is a widely used scheme for time-to-event data.In modeling process,biased-sampling studies can benefit further from taking parameters′prior information.With the explosion of digital information,high-dimensional data is frequently collected in prevalent domains,in which the dimension of covariates can be much larger than the sample size.Variable selection methods and independence have been developed to reduce the dimension of the survival data with censoring,recently.About regression analysis of the proportional hazards model with parameter constraints,the Modified MM algorithm was proposed,but the algorithm can not be applied to other models.To overcome this difficulty,ant colony algorithm and particle swarm optimization are applied for the calculation of the constrained estimator.
引文
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[4]Hamood R,Hamood H,Merhasin I,et al.Diabetes after Hormone therapy in breast cancer survivors:A case-cohort study[J].Journal of Clinical Oncology,2018,36(20):2061-2069.
[5]Liu S L,Tang L Q,Chen Q Y,et al.The prognosis of neck residue nasopharyngeal carcinoma(NPC)patients:Results from a case-cohort study[J].Journal of Cancer,2018,9(10):1765-1772.
[6]Pan Y,Cai J,Longnecker M P,et al.Secondary outcome analysis for data from an outcome-dependent sampling design[J].Statistics in Medicine,2018,37(15):2321-2337.
[7]Mugenyi L,Herzog S A,Hens N,et al.Modelling longitudinal binary outcomes with outcome-dependent observation times:An application to a malaria cohort study[J].2018,http://dx.doi.org/10.1101/252411.
[8]Fan J,Lv J,Qi L.Sparse high-dimensional models in economics[J].Annual Review of Economics,2011,3:291-317.
[9]Hoerl E,Kennard R W.Ridge regression:Applications to nonorthogonal problems[J].Technometrics,1970,12(1):69-82.
[10]Tibshirani R.Regression shrinkage and selection via the lasso[J].Journal of the Royal Statistical Society,Series B,1996,58:267-288.
[11]Fan J,Li R.Variable selection via nonconcave penalized likelihood and its oracle properties[J].Journal of the American Statistical Association,2001,96:1348-1360.
[12]Zhang C H.Nearly unbiased variable selection under minimax concave penalty[J].The Annals of Statistics,2010,38:894-942.
[13]Kohavi R.A study of cross-validation and bootstrap for accuracy estimation and model selection[J].IEEE,1995,1137-1145.
[14]Fan J,Li R.Variable selection via nonconcave penalized likelihood andits oracle properties[J].Journal of the American Statistical Association,2001,96:1348-1360.
[15]Fan J,Li R.Variable selection for Cox′s proportional hazards model and frailty model[J].The Annals of Statistics,2002,30:74-99.
[16]Akaike H.A new look at the statistical model identification[J].IEEE,1974,19:716-723.
[17]Schwarz G.Estimating the dimension of a model[J].The Annals of Statistics,1978,6(2):461-464.
[18]Houwelingen H C V,Bruinsma T,Hart A A M,et al.Cross-validated Cox regression on microarray gene expression data[J].Statisticsin Medicine,2006,25:3201-3216.
[19]Fan J,Lv J.Sure independence screening for ultrahigh dimensional feature space[J].Journal of the Royal Statistical Society,Series B,2008,70:849-911.
[20]Fan J,Song R.Sure independence screening in generalized linear models with NP-dimensionality[J].Journal of the American Statistical Association,2010,38:3567-3604.
[21]Fan J,Feng Y,Song R.Nonparametric independence screening in sparseultra-high-dimensional additive models[J].Journal of the American Statistical Association,2011,106:544-557.
[22]Stone C.Additive regression and other nonparametric models[J].The Annals of Statistics,1985,13:689-705.
[23]Zhu L P,Li L,Li R,et al.Model-free feature screening for ultrahigh-dimensional data[J].Journal of the American Statistical Association,2011,106:1464-1475.
[24]Li R,Zhong W,Zhu L P.Feature screening via distance correlation learning[J].Journal of the American Statistical Association,2012,107:1129-1139.
[25]Mai Q,Zou H.The fused Kolmogorov filter:A nonparametric model-free screening method[J].The Annals of Statistics,2015,43:1471-1497.
[26]Drosou K,Koukouvinos C.Sure independence screening for analyzing supersaturated designs[J].Communication in Statistics-Simulation and Computation,2018(455):1-17.
[27]Ni A,Cai J W.A regularized variable selection procedure in additive hazards model with stratified case-cohort design[J].Lifetime Data Analysis,2018,24:443-463.
[28]Aalen O.A model for nonparametric regression analysis of counting processes.Lecture notes in statistics 2[M].New York:Springer,1980.
[29]Cox D R.Regression models and life tables[J].Journal of the Royal Statistical Society,Series B,1972,34:187-220.
[30]Lin D Y,Ying Z L.Semiparametric analysis of general additive-multiplicative hazard models for counting processes[J].The Annals of Statistics,1995,23:1712-1734.
[31]Stoker T M.Consistent estimation of scaled coefficients[J].Econometrica,1986,54:1461-1481.
[32]Wang J.Asymptotics of least-squares estimation for constrained nonlinear regression[J].The Annals of Statistics,1996,24:1316-1326.
[33]Wang J.Approximate representation of estimators in constrained regression problems[J].Scandinavian Journal of Statistics,2000,27:21-33.
[34]Moore T J,Sadler B M.Maximum-likelihood estimation and scoring under parametric constrains[J].Army Research Laboratory,ARL-TR-3805,2006.
[35]Moore T J,Sadler B M,Kozick R J.Maximum-likelihood estimation,the Cramér-Rao bound,and the method of scoring with parameter constraints[J].IEEE Trans.Signal Process,2008,56:895-908.
[36]Ding J,Tian G,Yuen K C.A new MM algorithm for constrained estimation in the proportional hazards model[J].Computational Statistics and Data Analysis,2015,84:135-151.
[37]Gorst-Rasmussen A,Scheike T.Independent screening for single-index hazard rate models with ultrahigh dimensional features[J].Journal of the Royal Statistical Society,2013,Series B,75:217-245.
[38]Boyd S,Vandenberghe L.Convex optimization[M].Cambridge:Cambridge University Press,2004.
[39]Holland J H.Adaptation in natural and artificial systems[M].Ann Arbor:University of Michigan Press,1975.
[40]Kennedy J,Eberhart R C.Particle swarm optimization[M].Proc.IEEE.Intl.Conf.on Neural Networks,IEEE Service Center,Piscataway,NJ,1995,IV:1942-1948.