Survival Analysis With Quantile Regression Models

Peng, Limin; Huang, Yijian

doi:10.1198/016214508000000355

Cited by 265 publications

(486 citation statements)

References 3 publications

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“…For the MLE estimation, we have chosen to run three optimization methods with quite different internal characteristics (BFGS, Nelder-Mead and Rsolnp), from which the TBS estimation method automatically chooses the best (for each test case). The error distribution has been defined as normal in all test cases, so we expected that estimated values from the TBS model should have lower bias and MSE when compared to values estimated with Portnoy (2003) and Peng and Huang (2008), which in fact has happened. The results are shown in Table 4.…”

Section: Simulation Studymentioning

confidence: 99%

“…In a second simulation study, we compared the performance of the TBS model against the estimators of Portnoy (2003) and Peng and Huang (2008), using the implementation available in the R package quantreg. We have generated data from the TBS model with normal error distribution, one binary covariate, twenty different combinations of the parameters (λ = {0.5, 1.5}, ξ = {0.5, 1.5}, β = {(−1, 1), (1, −1), (−0.5, 0.5), (0.5, −0.5), (0.5, 0.5)}), and two sample sizes (n = 100, 1000).…”

Section: Simulation Studymentioning

confidence: 99%

“…Several authors, including Ying et al (1995), gave compelling arguments in favor of focusing on the quantiles of the survival time for modeling and reporting data analysis results. The many semi-parametric and non-parametric approaches are mostly based on self-consistency and martingales, which estimate equations for the median regression (Cheng et al, 1997;Portnoy, 2003;Peng and Huang, 2008). Carroll and Ruppert (1984), and Fitzmaurice et al (2007) propose parametric versions of a Box-Cox transform-both-sides regression model, considering only uncensored continuous responses, the original Box-Cox transformation, and the normal distribution for the error.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Transform both sides model: A parametric approach

Polpo

Campos

Sinha

et al. 2014

Computational Statistics & Data Analysis

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A parametric regression model for right-censored data with a log-linear median regression function and a transformation in both response and regression parts, named parametric Transform-Both-Sides (TBS) model, is presented. The TBS model has a parameter that handles data asymmetry while allowing various different distributions for the error, as long as they are unimodal symmetric distributions centered at zero. The discussion is focused on the estimation procedure with five important error distributions (normal, double-exponential, Student's t, Cauchy and logistic) and presents properties, associated functions (that is, survival and hazard functions) and estimation methods based on maximum likelihood and on the Bayesian paradigm. These procedures are implemented in TBSSurvival, an open-source fully documented R package. The use of the package is illustrated and the performance of the model is analyzed using both simulated and real data sets.

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Section: Simulation Studymentioning

confidence: 99%

Section: Simulation Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Transform both sides model: A parametric approach

Polpo

Campos

Sinha

et al. 2014

Computational Statistics & Data Analysis

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show abstract

“…More references about quantile regression estimation and interpretation can be found in the seminal book of Koenker (2005). Further extension of quantile regression to various model and data structures can be found in the literature, e.g., Machado and Silva (2005) for count data, Mu and He (2007) for power transformed data, Peng and Huang (2008) and Wang and Wang (2009) for survival analysis, He and Liang (2000) and Wei and Carroll (2009) for regression with measurement errors, Ando and Tsay (2011) for regression with augmented factors, and Kai et al (2011) for semiparametric varying-coefficient partially linear models, among others.…”

Section: Introductionmentioning

confidence: 99%

Quantile Correlations and Quantile Autoregressive Modeling

Li¹,

Li²,

Tsai³

2015

Journal of the American Statistical Association

118

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In this paper, we propose two important measures, quantile correlation (QCOR) and quantile partial correlation (QPCOR). We then apply them to quantile autoregressive (QAR) models, and introduce two valuable quantities, the quantile autocorrelation function (QACF) and the quantile partial autocorrelation function (QPACF). This allows us to extend the Box-Jenkins three stage procedure (model identification, model parameter estimation, and model diagnostic checking) from classical autoregressive models to quantile autoregressive models. Specifically, the QPACF of an observed time series can be employed to identify the autoregressive order, while the QACF of residuals obtained from the fitted model can be used to assess the model adequacy. We not only demonstrate the asymptotic properties of QCOR, QPCOR, QACF, and PQACF, but also show the large sample results of the QAR estimates and the quantile version of the Ljung-Box test. Moreover, we obtain the bootstrap approximations to the distributions of parameter estimator and proposed measures. Simulation studies indicate that the proposed methods perform well in finite samples, and an empirical example is presented to illustrate usefulness.

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“…The Portnoy (2003) method is of particular interest, as it essentially extends the Kaplan-Meier estimator to the regression setting. A similar generalization of the Nelson-Aalen estimator was also recently proposed by Peng and Huang (2008). The models developed in the rest of this paper are based on the Portnoy estimator.…”

mentioning

confidence: 99%

Partially linear censored quantile regression

Neocleous

Portnoy

2009

Lifetime Data Anal

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Censored Regression Quantile (CRQ) methods provide a powerful and flexible approach to the analysis of censored survival data when standard linear models are felt to be appropriate. In many cases however, greater flexibility is desired to go beyond the usual multiple regression paradigm. One area of common interest is that of partially linear models: one (or more) of the explanatory covariates are assumed to act on the response through a nonlinear function. Here the CRQ approach (Portnoy (2003)) is extended to this partially linear setting. Basic consistency results are presented. A simulation experiment and unemployment example justify the value of the partially linear approach over methods based on the Cox proportional hazards model and on methods not permitting nonlinearity.

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Survival Analysis With Quantile Regression Models

Cited by 265 publications

References 3 publications

Transform both sides model: A parametric approach

Transform both sides model: A parametric approach

Quantile Correlations and Quantile Autoregressive Modeling

Partially linear censored quantile regression

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