Quantile regression has emerged as a useful and effective tool in modeling survival data, especially for cases where noises demonstrate heterogeneity. Despite recent advancements, non‐smooth ...components involved in censored quantile regression estimators may often yield numerically unstable results, which, in turn, lead to potentially self‐contradicting conclusions. We propose an estimating equation‐based approach to obtain consistent estimators of the regression coefficients of interest via the induced smoothing technique to circumvent the difficulty. Our proposed estimator can be shown to be asymptotically equivalent to its original unsmoothed version, whose consistency and asymptotic normality can be readily established. Extensions to handle functional covariate data and recurrent event data are also discussed. To alleviate the heavy computational burden of bootstrap‐based variance estimation, we also propose an efficient resampling procedure that reduces the computational time considerably. Our numerical studies demonstrate that our proposed estimator provides substantially smoother model parameter estimates across different quantile levels and can achieve better statistical efficiency compared to a plain estimator under various finite‐sample settings. The proposed method is also illustrated via four survival datasets, including the HMO (health maintenance organizations) HIV (human immunodeficiency virus) data, the primary biliary cirrhosis (PBC) data, and so forth.
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
This article discusses an extension of censored quantile regression to a distributed setting. With the growing availability of massive datasets, it is oftentimes an arduous task to analyze all the ...data with limited computational facilities efficiently. Our proposed method, which attempts to overcome this challenge, is comprised of two key steps, namely: (i) estimation of both Kaplan-Meier estimator and model coefficients in a parallel computing environment; (ii) aggregation of coefficient estimations from individual machines. We study the upper limit of the order of the number of machines for this computing environment, which, if fulfilled, guarantees that the proposed estimator converges at a comparable rate to that of the oracle estimator. In addition, we also provide two further modifications for distributed systems including (i) a communication-facilitated adaptation in the sense of Chen, Liu, and Zhang and (ii) a nonparametric counterpart along the direction of Kong and Xia for censored quantile regression. Numerical experiments are conducted to compare the proposed and the existing estimators. The promising results demonstrate the computation efficiency of the proposed methods. Finally, for practical concerns, a cross-validation procedure is also developed which can better select the hyperparameters for the proposed methodologies.
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Conventionally, censored quantile regression stipulates a specific, pointwise conditional quantile of the survival time given covariates. Despite its model flexibility and straightforward ...interpretation, the pointwise formulation oftentimes yields rather unstable estimates across neighboring quantile levels with large variances. In view of this phenomenon, we propose a new class of quantile-based regression models with time-dependent covariates for censored data. The models proposed aim to capture the relationship between the failure time and the covariate processes of a target population that falls within a specific quantile bracket. The pooling of information within a homogeneous neighborhood facilitates more efficient estimates hence, more consistent conclusion on statistical significances of the variables concerned. This new formulation can also be regarded as a generalization of the accelerated failure time model for survival data in the sense that it relaxes the assumption of global homogeneity for the error at all quantile levels. By introducing a class of weighted rank-based estimation procedure, our framework allows a quantile-based inference on the covariate effect with a less restrictive set of assumptions. Numerical studies demonstrate that the proposed estimator outperforms existing alternatives under various settings in terms of smaller empirical biases and standard deviations. A perturbation-based resampling method is also developed to reconcile the asymptotic distribution of the parameter estimates. Finally, consistency and weak convergence of the proposed estimator are established via empirical process theory.
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Quantile regression is a flexible and effective tool for modeling survival data and its relationship with important covariates, which often vary over time. Informative right censoring of data from ...the prevalent cohort within the population often results in length‐biased observations. We propose an estimating equation‐based approach to obtain consistent estimators of the regression coefficients of interest based on length‐biased observations with time‐dependent covariates. In addition, inspired by Zeng and Lin 2008, we also develop a more numerically stable procedure for variance estimation. Large sample properties including consistency and asymptotic normality of the proposed estimator are established. Numerical studies presented demonstrate convincing performance of the proposed estimator under various settings. The application of the proposed method is demonstrated using the Oscar dataset.
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BFBNIB, DOBA, FSPLJ, FZAB, GIS, IJS, IZUM, KILJ, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBMB, UILJ, UKNU, UL, UM, UPUK
Objectives To assess preferences of health care workers (HCWs) and parents of term and preterm infants to adverse health outcomes, and how perceived surgical mortality influences decision-making. ...Study design A total of 536 participants (157 HCWs, 201 parents of term infants, and 178 parents of preterm infants) were recruited to take part in a structured interview. Preferences related to treatment of a critically ill preterm infant with necrotizing enterocolitis were measured by health state rank permutation analysis and pivotal risk analysis. Between-group and subgroup comparisons were performed. Results HCWs rank adverse health states less favorably than parents of preterm infants, consistently ranking 2 of the most adverse health states worse than death. Pivotal risk values of HCWs for all health states were consistently the lowest of the 3 groups. High operative mortality was associated uniformly with reduction in pivotal risks for all groups both in favorable and adverse health states. Subgroup analyses revealed significant discrepancies in preferences between fathers and mothers as well as doctors and nurses. Regular religious practice was significantly associated with increased pivotal risks in parental subgroups. Conclusions As discrepancies in health state preferences existed between subgroups (ie, doctors vs nurses, mothers vs fathers) and perceived operative mortality consistently biased parental and HCW health state preferences, we recommend that HCWs should first identify differences regarding patient management before interviewing the parents together. HCWs should be aware of inadvertently biasing parents when discussing the risks and outcomes of surgery in conjunction with the overall long-term prognosis of the underlying condition.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
Censored quantile regression (CQR) has received growing attention in survival analysis because of its flexibility in modeling heterogeneous effect of covariates. Advances have been made in developing ...various inferential procedures under different assumptions and settings. Under the conditional independence assumption, many existing CQR methods can be characterized either by stochastic integral-based estimating equations (see, e.g., Peng and Huang) or by locally weighted approaches to adjust for the censored observations (see, for instance, Wang and Wang). While there have been proposals of different apparently dissimilar strategies in terms of formulations and the techniques applied for CQR, the inter-relationships amongst these methods are rarely discussed in the literature. In addition, given the complicated structure of the asymptotic variance, there has been limited investigation on improving the estimation efficiency for censored quantile regression models. This article addresses these open questions by proposing a unified framework under which many conventional approaches for CQR are covered as special cases. The new formulation also facilitates the construction of the most efficient estimator for the parameters of interest amongst a general class of estimating functions. Asymptotic properties including consistency and weak convergence of the proposed estimator are established via the martingale-based argument. Numerical studies are presented to illustrate the promising performance of the proposed estimator as compared to existing contenders under various settings.
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In adolescent idiopathic scoliosis (AIS), the continuous search for effective prognostication of significant curve progression at the initial clinical consultation to inform decision for timely ...treatment and to avoid unnecessary overtreatment remains a big challenge as evidence of the multifactorial etiopathogenic nature is increasingly reported. This study aimed to formulate a composite model composed of clinical parameters and circulating markers in the prediction of curve progression.
This is a two-phase study consisting of an exploration cohort (120 AIS, mean Cobb angle of 25°± 8.5 at their first clinical visit) and a validation cohort (51 AIS, mean Cobb angle of 23° ± 5.0° at the first visit). Patients with AIS were followed-up for a minimum of six years to formulate a composite model for prediction. At the first visit, clinical parameters were collected from routine clinical practice, and circulating markers were assayed from blood.
We constructed the composite predictive model for curve progression to severe Cobb angle > 40° with a high HR of 27.9 (95% CI of 6.55 to 119.16). The area under curve of the composite model is higher than that of individual parameters used in current clinical practice. The model was validated by an independent cohort and achieved a sensitivity of 72.7% and a specificity of 90%.
This is the first study proposing and validating a prognostic composite model consisting of clinical and circulating parameters which could quantitatively evaluate the probability of curve progression to a severe curvature in AIS at the initial consultation. Further validation in clinic will facilitate application of composite model in assisting objective clinical decision.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
We propose a class of power-transformed linear quantile regression models for time-to-event observations subject to censoring. By introducing a process of power transformation with different ...transformation parameters at individual quantile levels, our framework relaxes the assumption of logarithmic transformation on survival times and provides dynamic estimation of various quantile levels. With such formulation, our proposal no longer requires the potentially restrictive global linearity assumption imposed on a class of existing inference procedures for censored quantile regression. Uniform consistency and weak convergence of the proposed estimator as a process of quantile levels are established via the martingale-based argument. Numerical studies are presented to illustrate the outperformance of the proposed estimator over existing contenders under various settings.
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BFBNIB, GIS, IJS, KISLJ, NUK, PNG, UL, UM, UPUK
Value-at-risk (VaR) has been playing the role of a standard risk measure since its introduction. In practice, the delta-normal approach is usually adopted to approximate the VaR of portfolios with ...option positions. Its effectiveness, however, substantially diminishes when the portfolios concerned involve a high dimension of derivative positions with nonlinear payoffs; lack of closed form pricing solution for these potentially highly correlated, American-style derivatives further complicate the problem. This paper proposes a generic simulation-based algorithm for VaR estimation that can be easily applied to any existing procedures. Our proposal leverages cross-sectional information and applies variable selection techniques to simplify the existing simulation framework. Asymptotic properties of the new approach demonstrate faster convergence due to the additional model selection component introduced. We have also performed sets of numerical results that verify the effectiveness of our approach in comparison with some existing strategies.
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This paper proposes a distributionally robust multi-period portfolio model with ambiguity on asset correlations with fixed individual asset return mean and variance. The correlation matrix bounds can ...be quantified via corresponding confidence intervals based on historical data. We employ a general class of coherent risk measures namely the spectral risk measure, which includes the popular measure conditional value-at-risk (CVaR) as a particular case, as our objective function. Specific choices of spectral risk measure permit flexibility for capturing risk preferences of different investors. A semi-analytical solution is derived for our model. The prominent stochastic dual dynamic programming (SDDP) algorithm adapted with intricate modifications is developed as a numerical method under the discrete distribution setting. In particular, our new formulation accounts for the unknown worst-case distribution in each iteration. We verify the convergence property of this algorithm under the setting of finite scenarios. Our results show that the optimal solution favours a certain degree of anti-diversification due to dependence ambiguity and exhibits its protection ability during the financial crisis period.
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CEKLJ, DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, ODKLJ, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
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