On average derivative quantile regression

Background: Numerous researches have been undertaken to delineate the significant risk factors linked to miscarriage. The etiology of miscarriage has presented challenges in its elucidation, necessitating a comprehensive understanding of the elements that are linked to this phenomenon. The examination of these aspects has been conducted utilizing diverse methodological techniques and analytical procedures. The Cox's proportional hazards model and the accelerated failure time models are commonly utilized in the field of survival analysis. While these models provide a certain level of flexibility, they do not allow for the differentiation of predictor indicators between high-risk and low-risk subpopulations. In contrast, quantile regression allows for the assessment of separate effects of covariates at different quantiles of the conditional distribution of miscarriage. Objective: This study assessed the risk factors for miscarriage using the censored quantile regression model and compared the results to that of Cox proportional hazard model. Methodology: A secondary data from 6077 records of pregnant women with recognized pregnancy and enrolled in the pre-natal care in Kakamega County General Teaching and Referral Hospital (KCGTRH) in Kakamega county, western Kenya during the period from 1 January, 2019 up to 31 October, 2020 were recruited into the study. The study used chi-squared tests for descriptive analysis. Cox proportional hazards and censored quantile regression were used for modeling. Analysis was done using the R package and 5% was the level of significance. Results: Censored quantile regressions were conducted to estimate the parameters for the quantiles, \(\tau\) = 0.05, 0.1, 0.15, 0.2. The results showed that ethnicity had a positive effect and was statistically significant at \(\tau\) = 0.1 (p = 0.0023) and number of previous stillbirths had a negative effect and was significant at \(\tau\) = 0.15 (p = 0.032) and at \(\tau\) = 0.2 (p = 0.036). Graphical comparison of censored quantile model effects to that of cox PH model revealed that the variables; prior miscarriages, prior stillbirths, place of residence, and number of ANC visits have a statistically significant adverse effect on the survival time of miscarriages in the initial phases of pregnancy, contrary to cox PH model. Conclusion: No variable had a statistically significant influence across all quantiles. The results depicts that at a certain moment in the monitoring procedure, they will have a significant impact on the length of survival for miscarriages. A quantile regression model have the capacity to incorporate cross-over effects, whereby the influence of a covariate can manifest as either positive or negative. In contrast, Cox estimates do not allow for the potential scenario when a covariate initially increases the hazard for a specific time period and subsequently decreases it.

One of the most important endpoints in haematopoietic cell transplant research is survival. A common objective is to interrogate which, if any, co-variates correlate with these endpoints. The most common statistical approach uses the Cox proportional hazards model. However, there are several problems and limitations of using this model including assumptions of proportional hazards and homogenous effects. In contrast, results of transplant studies often show non-proportional hazards because of early transplant-related mortality such that there is a survival disadvantage to transplants early on followed by a benefit. Even when a transplant proves better than a comparator not all transplant recipients benefit equally and some may be disadvantaged. Also, the favourable or unfavourable impact of a co-variate may vary in different time intervals. The accelerated failure time model which directly evaluates the association between survival and co-variates has similar limitations. Also, these models confer only a static view of the treatment effect. Several articles in our statistics series such as that by Zhen-Huan Hu and us (Bone Marrow Transplant. 2021 Aug 19. doi: 10.1038/s41409-021-01435-2), by Zhen-Huan Hu, Hai-Lin Wang and us and forthcoming articles by Megan Othus and by Liesbeth C. de Wreede, Johannes Schetelig and Hein Putter discuss issues in proper analyses of survival data from transplant studies including observational databases and randomized controlled trials. Are there better alternatives? A new popular model is quantile regression. In this typescript Bo Wei concisely introduce the quantile regression model for right censored data. He uses data from a Center for International Blood and Marrow Transplant Research (CIBMTR) registry study to show how to use the quantile regression and interpret the results. He also discusses use of quantile regression in complex survival analyses such as competing risk data or non-compliant data. Quantile regression is a natural, powerful approach for analyzing censored data with heterogenous co-variate effects. It has advantages compared with other survival models in depicting the dynamic association between survival outcome and co-variates. It can be applied to other transplant outcomes such as cumulative incidence of relapse, event-free and relapse-free survivals. There is an equation, but only one. Remember: The only thing to fear is fear itself (FDR). Please stick with it and you will be rewarded.Robert Peter Gale MD, PhD, DSc(hc), FACP, FRCP, FRCPI(hon), LHD, DPS, Mei-Jie Zhang PhD.

PurposeThe purpose of this paper is to investigate proprietary data from customers of a Southern Louisiana credit union. It analyzes the factors that contribute to an accelerated failure time (AFT) using information from customers’ credit applications as well as information provided in their credit report.Design/methodology/approachThis paper investigates the factors that affect credit risk using survival analysis by employing two primary models – the AFT model and the Cox proportional hazard (PH) model. While several studies employ the Cox PH model, few use the AFT model. However, this paper concludes that the AFT model has superior predictive qualities.FindingsThis paper finds that the factors specific to borrowers and local factors play an important role in the duration of a loan.Practical implicationsThis paper offers an easily interpretable model for determining the duration of a potential borrower. The marketing department of credit unions can then use this information to predict when a customer will default, thus allowing the credit union to intervene in a timely manner to prevent defaults. Further, the credit union can use this information to seek out customers who are less likely to default.Originality/valueThis study is different from the previous research due to its focus on credit unions, which have distinct characteristics. Compared to similar lending institutions, the charter of the credit union does not allow management to sell off loans to other investors.

A general class of semiparametric hazards regression models for survival data is proposed and studied. This general class includes some popular classes of models as subclasses, such as Cox's proportional hazards model, the accelerated failure time model and a recently proposed class of models called the accelerated hazards model. In the general class of models, a covariate's effect is identified as having two separate components, namely a time-scale change on hazard progression and a relative hazards ratio. The new model is flexible in modelling survival data and may yield more accurate prediction of an individual's survival process. By way of the nested structure that includes the proportional hazards model, the accelerated failure time model and the accelerated hazards model, the general class of models may provide a numerical tool for determining which of them is more appropriate for a given dataset.

Introduction: Quantile regression is a valuable alternative for survival data analysis, enabling flexible evaluations of covariate effects on survival outcomes with intuitive interpretations. It offers practical computation and reliability. However, challenges arise when applying quantile regression to censored data, particularly for upper quantiles. The minimum distance approach, utilizing dual-kernel estimation and the inverse cumulative distribution function, shows promise in addressing these challenges, especially with higher-dimensional covariates. Methods: This study contrasts two methods within the realm of quantile linear regression for survival analysis: check-based modeling and the minimum distance approach. Effectiveness is assessed across various scenarios through comprehensive simulation. Results: The simulation results showed that using the quantile regression model with the minimum distance approach reduces the percentage of root mean square error in parameter estimation compared to the quantile regression models based on the check loss function. Additionally, a larger sample size and reduced censoring percentage led to decreased root mean square error in parameter estimation. Conclusion: The research highlights the benefits of using the minimum distance approach for quantile regression. It reduces errors, improves model predictions, captures patterns, and optimizes parameters even with complete data. However, this approach has limitations. The accuracy of estimated quantiles can be influenced by the choice of distance metric and weighting scheme. The assumption of independence between censoring mechanism and survival time may not hold in real-world scenarios. Additionally, dealing with large datasets can be computationally complex.

A Bayesian network interpretation of the Cox's proportional hazard model

Goodness-of-fit tests for Cox's proportional hazards model and Aalen's additive risk model, in which each model is compared on an equal footing with the best fitting fully nonparametric model, are developed. The goodness-of-fit statistics are based on differences each model, with a fully nonparametric estimator of d recently introduced by the authors. Here A( , z) denotes the conditional hazard function of the survival time of an individual with covariate vector z. Comparison of the results of the tests makes it possible to decide whether Cox's proportional hazards or Aalen's additive risk model gives a better fit to the data. In addition, a goodness-of-fit test for Cox's model within the family of all proportional hazards models A(t, z) = AO(t)r(z), where AO is a baseline hazard function and r is a general relative risk function, is developed. Additive hazards and proportional hazards regression models used in the analysis of censored survival data can give substantially different results. For instance, in connection with a study of cancer mortality among Japanese atomic bomb survivors, Muirhead & Darby (1987) have noted that the two models give substantially different estimates of the age-spe- cific probability that an individual will develop radiation induced cancer. Muirhead & Darby (see also Aranda-Ordaz, 1983) introduced a generalized parametric model which contains parametric additive hazards and proportional hazards models as special cases. The goodness- of-fit of each model is then obtained by comparing with the best fitting model within the generalized family, allowing the two special models to be treated on an equal footing. Beyond the parametric setting, much effort has been devoted to the development of goodness-of-fit tests for Cox's (1972) proportional hazards model

Quantile regression is an important statistical tool for statistical modeling. It has been widely used in various fields including econometrics, medicine, and bioinformatics. Despite its popularity in practice, individually estimated quantile regression functions often cross each other and consequently violate the basic properties of quantiles. In this paper we propose a new method for estimating multiple quantile regression functions without crossing. Both linear and kernel quantile regression models are considered. Several numerical examples are presented to illustrate competitive performance of the proposed method.

Accelerated failure model with empirical analysis and application to colon cancer data: Testing and validation

We propose a notion of conditional vector quantile function and a vector quantile regression. A conditional vector quantile function (CVQF) of a random vector Y, taking values in ℝd given covariates Z=z, taking values in ℝk, is a map u↦QY∣Z(u,z), which is monotone, in the sense of being a gradient of a convex function, and such that given that vector U follows a reference non-atomic distribution FU, for instance uniform distribution on a unit cube in ℝd, the random vector QY∣Z(U,z) has the distribution of Y conditional on Z=z. Moreover, we have a strong representation, Y=QY∣Z(U,Z) almost surely, for some version of U. The vector quantile regression (VQR) is a linear model for CVQF of Y given Z. Under correct specification, the notion produces strong representation, Y=β(U)⊤f(Z), for f(Z) denoting a known set of transformations of Z, where u↦β(u)⊤f(Z) is a monotone map, the gradient of a convex function, and the quantile regression coefficients u↦β(u) have the interpretations analogous to that of the standard scalar quantile regression. As f(Z) becomes a richer class of transformations of Z, the model becomes nonparametric, as in series modelling. A key property of VQR is the embedding of the classical Monge-Kantorovich's optimal transportation problem at its core as a special case. In the classical case, where Y is scalar, VQR reduces to a version of the classical QR, and CVQF reduces to the scalar conditional quantile function. Several applications to diverse problems such as multiple Engel curve estimation, and measurement of financial risk, are considered.

The impact of covariate measurement error on quantile regression functions is investigated using a small variance approximation. The approximation shows how the error contaminated and error free quantile regression functions are related, a key factor being the distribution of the error free covariate. Exact calculations probe the accuracy of the approximation. The order of the approxiamtion error is unchanged if the error free covariate density is replaced by the error contaminated density. It is then possible to use the approximation to investigate the sensitivity of estimates to varying amounts of measurement error.

Optimal Duration of Imatinib Treatment / Deep Molecular Response for Treatment-Free Remission after Imatinib Discontinuation from a Canadian Tyrosine Kinase Inhibitor Discontinuation Trial

Simulation program for estimating statistical power of Cox's proportional hazards model assuming no specific distribution for the survival time

Background: The Cox proportional hazard (Cox PH) model is the most common and widely used method for analyzing time-to-event data. This approach, however, has been criticized for predicting patient outcomes since it assumes that the outcome is a linear combination of covariates and a constant hazard ratio over time, which is invalid in many cases and may not always be fulfilled, and thus Random Survival Forest (RSF) for time-to-event data has been proposed as an alternative to Cox PH. By considering non-linearity and interrelated covariates, the RSF is recognized as a way to correct bias in Cox proportional hazard models. Methods: The Cox PH model was compared to the Random Survival Forest by a relaxed proportional hazard (PH) assumption in this retrospective cohort study, which included 189 patients who underwent a new algorithmic treatment of an advanced human immunodeficiency virus clinical trial proposed by the World Health Organization from January to December 2018 at Kibong'oto infectious diseases hospital. Results: The study results show that the Random Survival Forest outperforms the Cox PH model in time-to-event data analysis by integrating covariates that do not meet proportional hazard assumptions based on predictive error curves, concordance indices, Brier scores, and integrated Brier scores as predictive indicators. Despite the fact that the PH assumption was relaxed for all covariates in the dataset, the Cox PH model selected only a few, and all deselected covariates were highly significant in the RSF, implying that the Cox PH model was inbuilt with the proportional hazard assumption. Conclusions: As a result, only covariates that satisfied the PH inbuilt assumption were chosen, regardless of whether the assumption was tested or not, rendering it ineffective when compared to a random survival forest. Therefore, having a dataset free from non-linearity and interrelated variables is impossible in the real world; hence, the RSF model outperforms the Cox PH model in predictive accuracy and covariate selection performance.

Objective: To compare the prognostic factors of mortality among melioidosis patients between lognormal accelerated failure time (AFT), Cox proportional hazards (PH), and Cox PH with time-varying coefficient (TVC) models. Methods: A retrospective study was conducted from 2014 to 2019 among 453 patients who were admitted to Hospital Sultanah Bahiyah, Kedah and Hospital Tuanku Fauziah, Perlis in Northern Malaysia due to confirmed-cultured melioidosis. The prognostic factors of mortality from melioidosis were obtained from AFT survival analysis, and Cox’s models and the findings were compared by using the goodness of fit methods. The analyses were done by using Stata SE version 14.0. Results: A total of 242 patients (53.4%) survived. In this study, the median survival time of melioidosis patients was 30.0 days (95% CI 0.0-60.9). Six significant prognostic factors were identified in the Cox PH model and Cox PH-TVC model. In AFT survival analysis, a total of seven significant prognostic factors were identified. The results were found to be only a slight difference between the identified prognostic factors among the models. AFT survival showed better results compared to Cox’s models, with the lowest Akaike information criteria and best fitted Cox-snell residuals. Conclusions: AFT survival analysis provides more reliable results and can be used as an alternative statistical analysis for determining the prognostic factors of mortality in melioidosis patients in certain situations.