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Variable Selection for Stratified Sampling Designs in Semiparametric Accelerated Failure Time Models with Clustered Failure Times

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A penalized weighted GEE achieves the oracle property for clustered survival data under stratified sampling.

desk verdict First penalized selection for stratified clustered AFT data with convincing selection simulations, but the oracle inference claim is not supported because the variance matrix omits within-cluster dependence. read the letter →

arxiv 2507.14689 v1 pith:4XQKRMRL submitted 2025-07-19 stat.ME

Ying Chen , Chuan-Fa Tang , Sy Han Chiou , Min Chen This is my paper · ORCID
classification stat.ME MSC 62N0162N0262J07
keywords acceleratedfailuretimemodelBuckley–JamesestimatorgeneralizedestimatingequationinverseprobabilityweightsKaplan–Meieroraclepropertystratifiedcase-cohortsamplingwithin-clusterdependence
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper builds a variable-selection and inference tool for semiparametric accelerated failure time (AFT) models when data come from stratified sampling designs, case-cohort studies being the main example, and failure times are clustered. It claims that a weighted penalized estimating equation, built from Buckley–James imputation of censored responses through a weighted pooled Kaplan–Meier estimator, recovers the true set of predictors and yields asymptotically normal coefficient estimates, meaning it has the oracle property. This matters because existing penalized survival methods either assume a full cohort, ignore the sampling weights or the within-cluster correlation, or rely on the proportional hazards assumption. If the theory holds, applied analysts gain a principled way to choose risk factors and construct confidence intervals when the AFT scale is appropriate and only a biased subsample was measured.

What carries the argument

The load-bearing object is the penalized weighted estimating equation (6), whose censored responses are imputed by the Buckley–James mechanism: each censored log-failure time is replaced by the conditional expectation computed under the pooled weighted Kaplan–Meier estimator $\hat{F}_{n,\omega}^\beta$ of the common marginal error distribution $F$ (equations (3)–(4)). Inverse-probability weights $\omega_i$ correct the stratified sampling bias, the working covariance matrix $\Omega(\alpha)$ absorbs within-cluster dependence (its estimate is asymptotically negligible under condition C8), and the SCAD penalty drives sparsity. The inner–outer iterative algorithm (Algorithm 1) linearizes the discontinuous Buckley–James estimating function by fixing imputed responses at a current estimate $b$, solving a penalized weighted GEE by minorization–maximization plus Newton–Raphson, then updating $b$, following the iterative scheme of [18] and the penalized GEE updates of [43]. The limiting distribution is governed by two slope matrices: $A_\omega$, the asymptotic slope of the imputed estimating function, and $D_\omega$, the weighted least-squares curvature; their difference feeds the bias term in the oracle expansion (14).

What would settle it

Simulate clustered AFT data under the same stratified design but give different members of a cluster different marginal error distributions (for example, one member standard normal and another heavy-tailed), keeping conditions C1–C9 otherwise intact; if the coverage of the 95% Wald intervals for active coefficients drops substantially below nominal or the correct-model selection rate fails to improve with sample size, the consistency claim for the pooled weighted Kaplan–Meier imputation is contradicted.

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Extended reading notes

Core claim

The paper's central claim is Theorem 2: under regularity conditions C1–C9, with tuning parameter $\lambda_n \to 0$ and $\sqrt{n}\,\lambda_n \to \infty$, the approximate solution $\hat{\beta}_{\omega}$ of the penalized weighted GEE (equation (6)) is an oracle estimator. Zero coefficients are estimated as exactly zero with probability tending to one, and the active coefficients satisfy an asymptotic normality expansion (equation (14)) centered on $\beta_{10}$ with covariance $B_\omega$, after subtraction of the penalty-induced bias $q_{01}$. The authors position this as the first formal treatment of penalized variable selection under stratified sampling in the semiparametric AFT framework with clustered failure times, carried by inverse-probability sampling weights, a pooled weighted Kaplan–Meier imputation for censored responses, and a working covariance matrix that absorbs within-cluster dependence.

Load-bearing premise

The pooled weighted Kaplan–Meier estimator must consistently estimate one common marginal error distribution shared by every member of every cluster — a premise the authors themselves flag in Section 7 as open — so if cluster members' error distributions differ, or censoring depends on unmeasured cluster-level factors, the imputation is inconsistent and the oracle theory collapses.

Editorial extensions

If this is right

  • When the AFT scale is appropriate, the estimator gives a stratification-aware alternative to penalized Cox regression: sampling weights remove the bias that unweighted variable selection incurs under unequal selection probabilities.
  • Confidence intervals obtained from refitting the selected model plus the multiplier-resampling variance step reach near-nominal coverage in simulations once weights are used, in contrast to unweighted approaches.
  • The method is robust to misspecification of the within-cluster correlation structure: an exchangeable working covariance helps at low to moderate censoring, while an independence working structure is a safe fallback at high censoring.
  • Stratified cross-validation, which splits within strata and aggregates folds, preserves case–control balance and is needed for reliable tuning-parameter selection in heavy-censoring designs.
  • The oracle property holds at each outer-layer iteration, so the theoretical guarantees apply even if the iterative algorithm has not fully converged.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same inverse-probability weighting scheme should transfer to nested case–control and length-biased sampling designs; a decisive test would be whether the oracle expansion (14) survives those mechanisms, since the paper only sketches them as future work.
  • Because the common-marginal assumption is load-bearing, a cheap diagnostic for practitioners would compare member-specific Kaplan–Meier curves within clusters before pooling, since the theory gives no guidance on how much disagreement is tolerable.
  • For $p$ larger than the number of clusters, the Newton–Raphson inner loop is expected to break down; the boosting-style estimating-equation updates the paper points to are the plausible route, but their oracle behavior is untested.
  • The multiplier-resampling variance estimator assumes that perturbation of the weighted Kaplan–Meier imputation propagates correctly; a small-sample comparison against a strata-respecting bootstrap would show when the Wald intervals can be relied on.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This paper proposes a penalized weighted generalized estimating equation (GEE) approach to Buckley–James estimation for the semiparametric accelerated failure time model with clustered failure times under stratified sampling. The estimator solves the penalized estimating equation (6) via a two-layer iterative algorithm: an inner Newton–Raphson loop for the penalized GEE at fixed imputed responses, and an outer loop that updates the imputed responses through a weighted pooled Kaplan–Meier estimator. The authors state consistency and oracle properties in Theorems 1 and 2, including asymptotic normality of the active coefficients in (14). They use stratified cross-validation for tuning and SCAD penalties, and estimate standard errors by perturbation resampling after refitting the selected model. Simulation studies with 80–90% censoring compare weighted and unweighted estimators under three error distributions and working independence/exchangeable correlation, and a dental case-cohort application illustrates the methods.

Significance. If the theoretical results held, this would be a valuable contribution: it fills a real gap by combining variable selection, inverse-probability-of-sampling weights, and GEE-type within-cluster correlation in a semiparametric AFT model, with an algorithm that appears to converge in the reported settings. The simulation study is reasonably extensive and the structured cross-validation suggestion for stratified designs is sensible. However, the inference half of Theorem 2 is not established as written: the covariance formula (13) ignores within-cluster dependence, and the proof transplants an independent-data theorem. The selection-consistency and linearization parts are plausible, but the paper needs to supply the missing cluster-level covariance argument or revise the theorem. The manuscript does not appear to ship code or a reproducibility supplement, and several proof steps defer to 'similar arguments' in Lai and Ying [28,29].

major comments (3)
  1. [Section 3.3, Eq. (13) and Theorem 2(3)] The matrix Bω in Eq. (13) is a marginal variance formula built from the limits Γ0, Γ1, Γω,ℓ_1, and Γω,ℓ_2 in condition (C9), all of which are sums of marginal probabilities Pr(C_ij − X_ijβ0 ≥ t). The estimating function U_{n,ω}(β0) in Eq. (5) is a sum over clusters of K-dimensional residual vectors, so its asymptotic variance necessarily includes cross-member terms Cov(U_{ik}, U_{ik′}) coming from the joint law of (ε_i, C_i). The proof of Theorem 2(3) simply states 'we follow Theorem 2 of Lai and Ying [29]' and transplants an independent-data covariance; no argument shows that the within-cluster cross terms vanish. This is load-bearing because the abstract's 'reliable inference' claim rests on the normality statement (14). Since the simulation standard errors are obtained by perturbation resampling (Section 4.1) rather than from (13), Tables 2–4 do not validate the formula; the authors should derive the correct cluster-level covariance or state Theorem 2(3) with a covariance matrix that is estimable and prove the corresponding convergence.
  2. [Section 3.3, Lemma 2 and its proof] Lemma 2 is stated with an 'almost surely' remainder, but the proof establishes only Op bounds (20)–(21) for each marginal counting process and then sums the per-member expansions U^{(k)}_{n,ω}. Summing over k does not yield a joint central limit theorem or a correct covariance for clustered data; the decomposition in (36)–(37) can give the slope matrix Aω but not the variance Bω without a joint-cluster analysis of the estimating function. Please state the exact mode of convergence and supply the joint representation used for inference.
  3. [Section 3.3, Condition (C9)] The limits in (C9) involve only marginal survivor probabilities for each cluster member. Even if the errors have common marginal F, the asymptotic covariance of a cluster-level estimating equation depends on second-order joint features such as Pr(C_ij − X_ijβ0 ≥ s, C_ij′ − X_ij′β0 ≥ t) or the joint influence functions of the pooled Kaplan–Meier estimator. Unless such quantities are included in the conditions, the asserted covariance matrix in (13) is not identified from the assumptions; condition (C9) should be expanded or the covariance should be left generic.
minor comments (6)
  1. [Theorem 2(1)] Theorem 2(1) states 'with probability tending to 1, lim_{n→∞} Pr(...)' which is redundant; it should simply read Pr(β̂_{2,ω}=0)→1.
  2. [Lemma 1] The displayed statement of (16) omits the constraint ∥β−β′∥≤n^{-r} that is used in the proof; the statement and proof should be aligned.
  3. [Algorithm 1, lines 8–9] Line 8 computes α̂(β̂^{(s)}_ω) but line 9 uses H_{n,ω}(α̂(b)); please clarify which value of α enters the Hessian in the update.
  4. [Section 5] There are several typos: 'standard Gumble' should be 'standard Gumbel', 'donated' should be 'denoted', and 'tunning' should be 'tuning'.
  5. [Table 4] At 90% censoring, the averaged resampling standard errors in the SCAD rows are 30–45% below the empirical standard errors (e.g., 7.78 vs 11.28 for weighted-EX SCAD1); the text comments only on the 50% censoring rows and should acknowledge this discrepancy.
  6. [Section 2, Eq. (2)] Equation (2) and the surrounding text contain minor typographical issues: 'n ˆYi(β)' lacks a multiplication sign and 'replaced' should be 'replaces'.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity; Theorem 2(3)'s variance import is an unsupported correctness claim, not a by-construction reduction.

full rationale

The derivation chain is not circular: the penalized estimator is defined through equations (6) and (8), the oracle zero-coefficient property follows from the SCAD penalty's behavior near zero under conditions C1–C9 and a sqrt(n)-consistent initial estimator, and the asymptotic linearity is derived in Lemma 2 rather than assumed. The only imported result is the covariance formula for the clustered score in Theorem 2(3), taken from Lai and Ying [29]; this is a genuine correctness risk because the paper itself notes in Section 3.3 that 'the assumption of independent failure times, which is essential in Lai and Ying [29] and Johnson et al. [21], is not satisfied in the present of correlated failure times within the GEE framework,' and then the proof states only 'We follow the Theorem 2 of Lai and Ying [29] and obtain that...' without deriving the within-cluster covariance. This gap is an unproven transplant, not a circular reduction: B_omega is asserted to be the limiting covariance rather than constructed to equal the score's variance by definition. Self-citations to Chiou et al. [8,10] appear when crediting the GEE-BJ framework and an initial estimator, but they are not load-bearing; the oracle theorems do not reduce to these citations. The simulation design includes an external oracle benchmark, so the comparisons do not manufacture their own target. Overall, no step exhibits the required by-construction equivalence between input and claimed output, so the paper receives a low circularity score with the noted caveat about Theorem 2(3).

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the standard BJ+GEE machine: the pooled KM imputation with a common marginal F, the C1-C9 conditions, and established oracle proofs from Fan-Li and Wang et al. The genuinely new pieces (stratified-sampling weights in the penalized estimating equation and the double-loop algorithm) do not introduce new entities. Free parameters are conventional: SCAD a = 3.7, tuning via CV, moment estimator of alpha, and numerical tolerances. No invented physical or structural entities appear.

free parameters (6)
  • SCAD tuning parameter lambda_n = Not fixed; selected by stratified CV (lambda_CV) or 1-SE rule (lambda_1SE) over a grid
    Controls sparsity; selected using the imputed-response prediction error mu_omega(lambda_n) in Section 3.2.
  • SCAD constant a = 3.7
    Conventional value from Fan and Li (2001), used in simulations and the dental analysis.
  • Working correlation parameter alpha = Estimated by weighted moments from residuals (Section 4.2)
    Nuisance parameter; the theory treats it as asymptotically ignorable (C8) but efficiency depends on it.
  • Zeroing cutoff = 10^-3
    Coefficients below the cutoff are treated as zero, following Wang et al. (2011); affects reported FP and C rates.
  • Convergence tolerance gamma and stabilization zeta = gamma = 10^-3, zeta = 10^-6
    Numerical settings of Algorithm 1; results may vary with these choices.
  • Perturbation resampling size B = 200
    Bootstrap sample size for variance estimation in Section 4.1.
assumptions (6)
  • domain assumption Conditions C1-C9 (Section 3.3): bounded covariates, smooth error density, finite exponential moments, bounded nonrandom weights, consistent initial value, converging working covariance, limit functions
    C7 (initial estimator consistency) and C6 (nonrandom bounded weights) are the most load-bearing; C9 defines the limit objects in the asymptotic expansions.
  • domain assumption Common marginal error distribution F and equal cluster size K
    Section 2: 'we assume that Ki = K and eps_i have the same marginal distribution F'; required for the pooled weighted KM estimator (4) to be consistent.
  • domain assumption Conditional independence of failure and censoring times given covariates
    Section 2: 'Tik and Cik are conditionally independent given Xik'; needed for the KM imputation to be valid.
  • standard math Tail modification of estimating functions from Lai and Ying
    The proofs of Lemmas 1-2 adopt the tail modification pn(x) = p(n^gamma(x - c n^-gamma)) from Lai and Ying (1988, 1991); treated as established technique.
  • standard math Asymptotic templates of Lai-Ying, Fan-Li, Jin-Lin-Ying, and Wang-Zhou-Qu
    Theorems borrow the local-minimizer proof of Fan and Li (2001), the BJ linearity results of Lai and Ying, the iterative stabilization of Jin et al. (2006), and the MM/Newton-Raphson penalized GEE algorithm of Wang et al. (2011).
  • domain assumption Known inclusion probabilities (nonrandom weights)
    Condition C6 treats omega_i as fixed and bounded; in the dental application weights come from design probabilities, but in general inclusion probabilities are estimated from data.

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Pith. "Pith review of Variable Selection for Stratified Sampling Designs in Semiparametric Accelerated Failure Time Models with Clustered Failure Times." pith.science (2026). https://pith.science/paper/4XQKRMRL

@misc{pith2026250714689,
  author       = {Pith},
  title        = {Pith review of: Variable Selection for Stratified Sampling Designs in Semiparametric Accelerated Failure Time Models with Clustered Failure Times},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4XQKRMRL}},
  note         = {Machine review of arXiv:2507.14689}
}
read the original abstract

In large-scale epidemiological studies, statistical inference is often complicated by high-dimensional covariates under stratified sampling designs for failure times. Variable selection methods developed for full cohort data do not extend naturally to stratified sampling designs, and appropriate adjustments for the sampling scheme are necessary. Further challenges arise when the failure times are clustered and exhibit within-cluster dependence. As an alternative of Cox proportional hazards (PH) model when the PH assumption is not valid, the penalized Buckley-James (BJ) estimating method for accelerated failure time (AFT) models can potentially handle within-cluster correlation in such setting by incorporating generalized estimating equation (GEE) techniques, though its practical implementation remains hindered by computational instability. We propose a regularized estimating method within the GEE framework for stratified sampling designs, in the spirit of the penalized BJ method but with a reliable inference procedure. We establish the consistency and asymptotic normality of the proposed estimators and show that they achieve the oracle property. Extensive simulation studies demonstrate that our method outperforms existing methods that ignore sampling bias or within-cluster dependence. Moreover, the regularization scheme effectively selects relevant variables even with moderate sample sizes. The proposed methodology is illustrated through applications to a dental study.

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Works this paper leans on

55 extracted references · 55 canonical work pages

  1. [29]

    T. Lai, Z. Ying, Large sample theory of a modified Buckley-James estimator for regression analysis with censored data, The Annals of Statistics 62 (1991) 1370–1402

    work page 1991

  2. [1]

    Borgan, B

    O. Borgan, B. Langholz, S. Samuelsen, L. Goldstein, J. Pogoda, Exposure stratified case-cohort designs, Lifetime Data Analysis 6 (2000) 39–58

    work page 2000

  3. [2]

    Buckley, I

    J. Buckley, I. James, Linear regression with censored data, Biometrika 66 (1979) 429–436

    work page 1979

  4. [3]

    J. Cai, J. Fan, R. Li, H. Zhou, Variable selection for multivariate failure time data, Biometrika 92 (2005) 303–316

    work page 2005

  5. [4]

    T. Cai, J. Huang, L. Tian, Penalized estimation for the accelerated failure time model, Biometrics 65 (2009) 394–404

    work page 2009

  6. [5]

    Calhoun, X

    P. Calhoun, X. Su, M. Nunn, J. Fan, Constructing multivariate survival trees: The MST package for R, Journal of Statistical Software 83 (2018)

    work page 2018

  7. [6]

    Caplan, J

    D. Caplan, J. Cai, G. Yin, B. White, Root canal filled versus non-root canal filled teeth: A retrospective comparison of survival times, Journal of Public Health Dentistry 65 (2005) 90–96

    work page 2005

  8. [7]

    Chen, De-noising boosting methods for variable selection and estimation subject to error-prone variables, Statistics and Computing 33 (2023) 38

    L. Chen, De-noising boosting methods for variable selection and estimation subject to error-prone variables, Statistics and Computing 33 (2023) 38

    work page 2023

Show all 55 references
  1. [8]

    Chiou, S

    S. Chiou, S. Kang, J. Kim, J. Yan, Marginal semiparametric multivariate accelerated failure time model with generalized estimating, Lifetime Data Analysis 20 (2014) 599–618

    2014

  2. [9]

    Chiou, S

    S. Chiou, S. Kang, J. Yan, Fast accelerated failure time modeling for case-cohort data, Statistics and Computing 24 (2014) 559–568

    2014

  3. [10]

    Chiou, S

    S. Chiou, S. Kang, J. Yan, Rank-based estimating equations with general weight for accelerated failure time models: An induced smoothing approach, Statistics in Medicine 34 (2015) 1495–1510

    2015

  4. [11]

    Chiou, S

    S. Chiou, S. Kang, J. Yan, Semiparametric accelerated failure time modeling for clustered failure times from stratified sampling, Journal of the American Statistical Association 110 (2015) 621–629

    2015

  5. [12]

    Chiou, G

    S. Chiou, G. Xu, Rank-based estimation for semiparametric accelerated failure time model under length-biased sampling, Statistics and Computing 27 (2015) 483–500

    2015

  6. [13]

    Cox, Regression models and life-tables (with discussion), Journal of the Royal Statistical Society 34 (1972) 187–220

    D. Cox, Regression models and life-tables (with discussion), Journal of the Royal Statistical Society 34 (1972) 187–220

    1972

  7. [14]

    J. Fan, R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, Journal of the American Statistical Association 96 (2001) 1348–1360

    2001

  8. [15]

    J. Fan, R. Li, Variable selection for Cox’s proportional hazards model and frailty model, The Annals of Statistics 30 (2002) 74–99

    2002

  9. [16]

    Hastie, R

    T. Hastie, R. Tibshirani, J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer, New York (2001)

    2001

  10. [17]

    Hunter, R

    D. Hunter, R. Li, Variable selection using MM algorithms, Annals of Statistics 33 (2005) 1617

    2005

  11. [18]

    Z. Jin, D. Lin, Z. Ying, On least-squares regression with censored data, Biometrika 93 (2006) 147–161

    2006

  12. [19]

    Johnson, Variable selection in semiparametric linear regression with censored data, Journal of the Royal Statistical Society: Series B (Methodological) 70 (2008) 351–370

    B. Johnson, Variable selection in semiparametric linear regression with censored data, Journal of the Royal Statistical Society: Series B (Methodological) 70 (2008) 351–370

    2008

  13. [20]

    Johnson, R

    L. Johnson, R. Strawderman, Induced smoothing for the semiparametric accelerated failure time model: Asymptotics and extensions to clustered data, Biometrika 96 (2009) 577–590

    2009

  14. [21]

    Johnson, D

    B. Johnson, D. Lin, D. Zeng, Penalized estimating functions and variable selection in semiparametric regression models, Journal of the American Statistical Association 103 (2008) 672–680

    2008

  15. [22]

    Kang, Fitting semiparametric accelerated failure time models for nested case-control data, Journal of Statistical Computation and Simula- tion 87 (2017) 652–663

    S. Kang, Fitting semiparametric accelerated failure time models for nested case-control data, Journal of Statistical Computation and Simula- tion 87 (2017) 652–663

    2017

  16. [23]

    S. Kang, J. Cai, Marginal hazards model for case-cohort studies with multiple disease outcomes, Biometrika 96 (2009) 887–901

    2009

  17. [24]

    S. Kang, J. Cai, Marginal hazards regression for retrospective studies within cohort with possibly correlated failure time data, Biometrics 65 (2009) 405–414

    2009

  18. [25]

    S. Kim, J. Cai, W. Lu, More e fficient estimators for case-cohort studies, Biometrika 100 (2013) 695–708

    2013

  19. [26]

    L. Kong, J. Cai, Case-cohort analysis with accelerated failure time model, Biometrics 65 (2009) 135–142

    2009

  20. [27]

    Kulich, D

    M. Kulich, D. Lin, Improving the e fficiency of relative-risk estimation in case-cohort studies, Journal of the American Statistical Association 99 (2004) 832–844

    2004

  21. [28]

    T. Lai, Z. Ying, Stochastic integrals of empirical-type processes with applications to censored regression, Journal of multivariate analysis 27 (1988) 334–358

    1988

  22. [30]

    Liang, S

    K. Liang, S. Zeger, Longitudinal data analysis using generalized linear models, Biometrika 73 (1986) 13–22

    1986

  23. [31]

    J. Liu, R. Zhang, W. Zhao, Y . Lv, Variable selection in semiparametric hazard regression for multivariate survival data, Journal of Multivariate Analysis 142 (2015) 26–40

    2015

  24. [32]

    T. Lu, S. Kang, H. Zhou, Semiparametric accelerated failure time modeling for multivariate failure times under multivariate outcome- dependent sampling designs, Statistics and Its Interface 13 (2020) 373–383

    2020

  25. [33]

    Miller, J

    R. Miller, J. Halpern, Regression with censored data, Biometrika 69 (1982) 521–531

    1982

  26. [34]

    B. Nan, M. Yu, J. Kalbfleisch, Censored linear regression for case-cohort studies, Biometrika 93 (2006) 747–762

    2006

  27. [35]

    B. Nan, J. Kalbfleisch, M. Yu, Asymptotic theory for the semiparametric accelerated failure time model with missing data, The Annals of Statistics 37 (2009) 2351–2376

    2009

  28. [36]

    A. Ni, J. Cai, D. Zeng, Variable selection for case-cohort studies with failure time outcome, Biometrika 103 (2016) 547–562

    2016

  29. [37]

    Prentice, A case-cohort design for epidemiologic cohort studies and disease prevention trials, Biometrika 73 (1986) 1–11

    R. Prentice, A case-cohort design for epidemiologic cohort studies and disease prevention trials, Biometrika 73 (1986) 1–11

    1986

  30. [38]

    Ritov, Estimation in a linear regression model with censored data, The Annals of Statistics (1990) 303–328

    Y . Ritov, Estimation in a linear regression model with censored data, The Annals of Statistics (1990) 303–328

    1990

  31. [39]

    Samuelsen, H

    S. Samuelsen, H. Ånestad, A. Skrondal, Stratified case-cohort analysis of general cohort sampling designs, Scandinavian Journal of Statistics 34 (2007) 103–119

    2007

  32. [40]

    Tibshirani, Regression shrinkage and selection via the Lasso, Journal of the Royal Statistical Society: Series B (Methodological) 58 (1996) 267–288

    R. Tibshirani, Regression shrinkage and selection via the Lasso, Journal of the Royal Statistical Society: Series B (Methodological) 58 (1996) 267–288. 22

    1996

  33. [41]

    Tibshirani, The Lasso method for variable selection in the Cox model, Statistics in Medicine 16 (1997) 385–395

    R. Tibshirani, The Lasso method for variable selection in the Cox model, Statistics in Medicine 16 (1997) 385–395

    1997

  34. [42]

    Tsiatis, Estimating regression parameters using linear rank tests for censored data, The Annals of Statistics 18 (1990) 354–372

    A. Tsiatis, Estimating regression parameters using linear rank tests for censored data, The Annals of Statistics 18 (1990) 354–372

    1990

  35. [43]

    L. Wang, J. Zhou, A. Qu, Penalized generalized estimating equations for high-dimensional longitudinal data analysis, Biometrics 68 (2011) 353–360

    2011

  36. [44]

    S. Wang, B. Nan, J. Zhu, D. Beer, Doubly penalized Buckley–James method for survival data with high-dimensional covariates, Biometrics 64 (2008) 132–140

    2008

  37. [45]

    L. Wang, S. Wang, G. Wang, Variable selection and estimation for longitudinal survey data, Journal of Multivariate Analysis 130 (2014) 409–424

    2014

  38. [46]

    Wei, The accelerated failure time model: a useful alternative to the Cox regression model in survival analysis, Statistics in Medicine 11 (1992) 1871–1879

    L. Wei, The accelerated failure time model: a useful alternative to the Cox regression model in survival analysis, Statistics in Medicine 11 (1992) 1871–1879

    1992

  39. [47]

    Williams, A note on robust variance estimation for cluster-correlated data, Biometrics 56 (2000) 645–646

    R. Williams, A note on robust variance estimation for cluster-correlated data, Biometrics 56 (2000) 645–646

    2000

  40. [48]

    Wolfson, EEBoost: A general method for prediction and variable selection based on estimating equations, Journal of the American Statis- tical Association 106 (2011) 296–305

    J. Wolfson, EEBoost: A general method for prediction and variable selection based on estimating equations, Journal of the American Statis- tical Association 106 (2011) 296–305

    2011

  41. [49]

    Y . Yan, H. Zhou, J. Cai, Improving e fficiency of parameter estimation in case-cohort studies with multivariate failure time data, Biometrics 73 (2017) 1042–1052

    2017

  42. [50]

    Yang, A generalization of the product-limit estimator with an application to censored regression, The Annals of Statistics 25 (1997) 1088–1108

    S. Yang, A generalization of the product-limit estimator with an application to censored regression, The Annals of Statistics 25 (1997) 1088–1108

    1997

  43. [51]

    M. Yu, B. Nan, A hybrid Newton-type method for censored survival data using double weights in linear models, Lifetime data analysis 12 (2006) 345–364

    2006

  44. [52]

    Q. Yu, G. Wong, M. Yu, Buckley–James-type of estimators under the classical case cohort design, Annals of the Institute of Statistical Mathematics 59 (2007) 675–695

    2007

  45. [53]

    Yu, Buckley–James type estimator for censored data with covariates missing by design, Scandinavian Journal of Statistics 38 (2011) 252–267

    M. Yu, Buckley–James type estimator for censored data with covariates missing by design, Scandinavian Journal of Statistics 38 (2011) 252–267

    2011

  46. [54]

    Zou, The adaptive Lasso and its oracle properties, Journal of the American Statistical Association 101 (2006) 1418–1429

    H. Zou, The adaptive Lasso and its oracle properties, Journal of the American Statistical Association 101 (2006) 1418–1429

    2006

  47. [55]

    H. Zou, T. Hastie, Regularization and variable selection via the elastic net, Journal of the Royal Statistical Society Series B: Statistical Methodology 67 (2005) 301–320. 23

    2005

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