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Two-piece distribution based semi-parametric quantile regression for right censored data

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Abstract

Widely used methods such as Cox proportional hazards, accelerated failure time, and Bennet proportional odds models do not model the quantiles directly, but rather allow to assess the influence of the covariates only on the location of the distribution. Quantile regression allows to assess the effects of covariates, not only on a location parameter (such as a mean or median) but also on specific percentiles of the conditional distribution. In recent years, a large family of flexible two-piece asymmetric distributions where the location parameter coincides with a specific quantile of the distribution has been studied. In a conditional (regression) setting the use of such a family of two-piece asymmetric distributions has only been investigated in the complete data case in the literature. In this paper, we propose a semi-parametric procedure to estimate the conditional quantile curves of two-piece asymmetric distributions based on right censored survival data. We use a local likelihood estimation technique in a multi-parameter functional form, via which the effect of a covariate on the location, scale, and index of the conditional survival distribution can be assessed. The finite sample performance of the estimators is investigated via simulations, and the methodology is illustrated on real data examples.

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References

  • Aerts M, Claeskens G (1997) Local polynomial estimation in multi-parameter likelihood models. J Am Stat Assoc 92(440):1536–1545

    Article  MATH  Google Scholar 

  • Anderson KM (1991) A nonproportional hazards Weibull accelerated failure time regression model. Biometrics 47(1):281–288

    Article  Google Scholar 

  • Antoniadis A, Gijbels I, Lambert-Lacroix S, Poggi J-M (2016) Joint estimation and variable selection for mean and dispersion in proper dispersion models. Electron J Stat 10(1):1630–1676

    Article  MathSciNet  MATH  Google Scholar 

  • Bennett S (1983) Analysis of survival data by the proportional odds model. Stat Med 2(2):273–277

    Article  Google Scholar 

  • Bottai M, Zhang J (2010) Laplace regression with censored data. Biom J 52(4):487–503

    Article  MathSciNet  MATH  Google Scholar 

  • Bravo F (2018) Semiparametric quantile regression with random censoring. Ann Inst Stat Math 72(1):265–295

    Article  MathSciNet  MATH  Google Scholar 

  • Burke K, MacKenzie G (2017) Multi-parameter regression survival modeling: an alternative to proportional hazards. Biometrics 73(2):678–686

    Article  MathSciNet  MATH  Google Scholar 

  • Chen S, Khan S (2001) Semiparametric estimation of a partially linear censored regression model. Econom Theory 17(3):567–590

    Article  MathSciNet  MATH  Google Scholar 

  • Christou E, Akritas MG (2019) Single index quantile regression for censored data. Stat Methods Appl 28(4):655–678

    Article  MathSciNet  MATH  Google Scholar 

  • Cox DR (1972) Regression models and life-tables. J R Stat Soc Ser B 34(2):187–202

    MathSciNet  MATH  Google Scholar 

  • De Backer M, El Ghouch A, Van Keilegom I (2020) Linear censored quantile regression: a novel minimum-distance approach. Scand J Stat 47(4):1275–1306

    Article  MathSciNet  MATH  Google Scholar 

  • Ding Y (2010) Some new insights about the accelerated failure time model. Doctoral dissertation, University of Michigan

  • Ewnetu WB, Gijbels I, Verhasselt A (2023) Flexible two-piece distributions for right censored survival data. Lifetime Data Anal 29:34–65

    Article  MathSciNet  MATH  Google Scholar 

  • Fan J, Gijbels I (1994) Censored regression: local linear approximations and their applications. J Am Stat Assoc 89(426):560–570

    Article  MathSciNet  MATH  Google Scholar 

  • Fan J, Gijbels I (1996) Local polynomial modelling and its applications. CRC Press, Boca Raton

  • Fechner G (1897) Kollektivmasslehre. Engelmann, Leipzig

    Google Scholar 

  • Fleming TR, Harrington DP (1991) Counting processes and survival analysis. Wiley, New York

    MATH  Google Scholar 

  • Gannoun A, Saracco J, Yuan A, Bonney GE (2005) Non-parametric quantile regression with censored data. Scand J Stat 32(4):527–550

    Article  MathSciNet  MATH  Google Scholar 

  • Gijbels I, Prosdocimi I, Claeskens G (2010) Nonparametric estimation of mean and dispersion functions in extended generalized linear models. Test 19(3):580–608

    Article  MathSciNet  MATH  Google Scholar 

  • Gijbels I, Karim R, Verhasselt A (2019) On quantile-based asymmetric family of distributions: properties and inference. Int Stat Rev 87(3):471–504

    Article  MathSciNet  Google Scholar 

  • Gijbels I, Karim R, Verhasselt A (2021) Semiparametric quantile regression using quantile-based asymmetric family of densities. Comput Stat Data Anal 157:107129

    Article  MATH  Google Scholar 

  • Huang J, Ma S, Xie H (2007) Least absolute deviations estimation for the accelerated failure time model. Stat Sin 17(4):1533–1548

    MathSciNet  MATH  Google Scholar 

  • Jin Z, Lin DY, Wei LJ, Ying Z (2003) Rank-based inference for the accelerated failure time model. Biometrika 90(2):341–353

    Article  MathSciNet  MATH  Google Scholar 

  • Kim HT, Truong YK (1998) Nonparametric regression estimates with censored data: local linear smoothers and their applications. Biometrics 54(4):1434–1444

    Article  MathSciNet  MATH  Google Scholar 

  • Kleinbaum DG, Klein M (2012) Survival analysis. A self learning text, 3rd edn. Springer, New York

    Book  MATH  Google Scholar 

  • Kneib T, Silbersdorff A, Säfken B (2023) Rage against the mean: a review of distributional regression approaches. Econom Stat 26:99–123

    MathSciNet  Google Scholar 

  • Koenker R (2015) Quantile regression. Int Encycl Soc Behav Sci 19(2):712–718

    Google Scholar 

  • Lee S (2003) Efficient semi-parametric estimation of a partially linear quantile regression model. Econom Theory 19(1):1–31

    Article  MathSciNet  MATH  Google Scholar 

  • Li G, Datta S (2001) A bootstrap approach to non-parametric regression for right censored data. Ann Inst Stat Math 53(4):708–729

    Article  MATH  Google Scholar 

  • Peng L, Huang Y (2008) Survival analysis with quantile regression models. J Am Stat Assoc 103(482):637–649

    Article  MathSciNet  MATH  Google Scholar 

  • Portnoy S (2003) Censored regression quantiles. J Am Stat Assoc 98(464):1001–1012

    Article  MathSciNet  MATH  Google Scholar 

  • Powell JL (1984) Least absolute deviations estimation for the censored regression model. J Econom 25(3):303–325

    Article  MathSciNet  MATH  Google Scholar 

  • Powell JL (1986) Censored regression quantiles. J Econom 32(1):143–155

    Article  MathSciNet  MATH  Google Scholar 

  • Rubio FJ, Hong Y (2016) Survival and lifetime data analysis with a flexible class of distributions. J Appl Stat 43(10):1794–1813

    Article  MathSciNet  MATH  Google Scholar 

  • Rubio FJ, Yu K (2017) Flexible objective Bayesian linear regression with applications in survival analysis. J Appl Stat 44(5):798–810

    Article  MathSciNet  MATH  Google Scholar 

  • Stasinopoulos MD, Rigby RA, Heller GZ, Voudouris V, De Bastiani F (2017) Flexible Regression and Smoothing: using GAMLSS in R. CRC Press, Boca Raton

    Book  Google Scholar 

  • Tibshirani R, Hastie T (1987) Local likelihood estimation. J Am Stat Assoc 82(398):559–567

    Article  MathSciNet  MATH  Google Scholar 

  • Wallis KF (2014) The two-piece normal, binormal, or double Gaussian distribution: its origin and rediscoveries. Stat Sci 29(1):106–112

    Article  MathSciNet  MATH  Google Scholar 

  • Wang HJ, Wang L (2009) Locally weighted censored quantile regression. J Am Stat Assoc 104(487):1117–1128

    Article  MathSciNet  MATH  Google Scholar 

  • Wei LJ (1992) The accelerated failure time model: a useful alternative to the Cox regression model in survival analysis. Stat Med 11(14–15):1871–1879

    Article  Google Scholar 

  • Ying Z, Jung SH, Wei LJ (1995) Survival analysis with median regression models. J Am Stat Assoc 90(429):178–184

    Article  MathSciNet  MATH  Google Scholar 

  • Yu K, Jones M (1998) Local linear quantile regression. J Am Stat Assoc 93(441):228–237

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou M, Kim MO, Bathke AC (2012) Empirical likelihood analysis for the heteroscedastic accelerated failure time model. Stat Sin 22(1):295–316

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors are grateful to an Associate Editor and two reviewers for their comments which led to an improvement of the manuscript. We thank the authors of Christou and Akritas (2019) to provide us with the R code to calculate their estimator in the SIQR model. The second author gratefully acknowledges support from Research Grant FWO G0D6619N of the Flemish Science Foundation, and from the C16/20/002 project of the Research Fund KU Leuven. The resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation - Flanders (FWO) and the Flemish Government.

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Authors and Affiliations

  1. Center of Statistics, Data Science Institute, Hasselt University, Agoralaan D, Diepenbeek, 3590, Belgium

    Worku Biyadgie Ewnetu & Anneleen Verhasselt

  2. Department of Mathematics, KU Leuven, Celestijnenlaan 200 B, Leuven, 3001, Belgium

    Irène Gijbels

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  1. Worku Biyadgie Ewnetu
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  2. Irène Gijbels
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  3. Anneleen Verhasselt
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Correspondence to Anneleen Verhasselt.

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Ewnetu, W.B., Gijbels, I. & Verhasselt, A. Two-piece distribution based semi-parametric quantile regression for right censored data. Stat Papers (2023). https://doi.org/10.1007/s00362-023-01475-4

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