Flexible boosting of accelerated failure time models

Accelerated Failure Time (AFT) models are viable alternatives to the Cox proportional hazard model, where failure times are explicitly modelled with respect to covariates. A major problem with parametric AFT models in practice is that statistical distribution used there often have a limited range of shapes, which may be inadequate to cope with real-life data. This paper presents an AFT model algorithm involving generalised lambda distributions (GLD) using maximum likelihood estimation, by extending and adapting existing work on GLD regression model and estimation, which would enhance the capabilities of AFT models owing to the rich shapes of GLDs. The proposed method is demonstrated to achieve parameter consistency and is very robust against outliers. A real-life example demonstrating the use of GLD AFT models compared to more established methods such as semi-parametric models of Buckley James regression, Accelerated Failure Time GEE model and Cox proportional hazard model is also given.

The accelerated failure time (AFT) model is a linear model under the log-transformation of survival time that has been introduced as a useful alternative to the proportional hazards (PH) model. In this paper we propose variable-selection procedures of fixed effects in a parametric AFT model using penalized likelihood approaches. We use three popular penalty functions, least absolute shrinkage and selection operator (LASSO), adaptive LASSO and smoothly clipped absolute deviation (SCAD). With these procedures we can select important variables and estimate the fixed effects at the same time. The performance of the proposed method is evaluated using simulation studies, including the investigation of impact of misspecifying the assumed distribution. The proposed method is illustrated with a primary biliary cirrhosis (PBC) data set.

With the rapid urbanization of geographical spaces worldwide, pedestrian safety is a major concern on urban roads. In developing economies like India, an unprecedented increase in accidents involving pedestrians has been observed at intersections. The present study focuses on pedestrian behavior, specifically, violation of red signals while crossing at signalized intersections. With the help of hazard-based duration models, the waiting duration of red-light violators has been analyzed. In addition, the response time of pedestrians during conflict has also been modeled with the help of a hazard-based duration approach. Four signalized intersections from Nagpur City in India were selected for the survival analysis. Kaplan–Meier survival curves have been plotted for both waiting time and response time. With the help of the semi-parametric Cox proportional hazard model, various factors have been identified to describe the survival function of the pedestrians’ crossing. However, the model results were found to be unsatisfactory since the explanatory variables failed in the proportional hazard assumption. Therefore, the parametric accelerated failure time model was utilized to determine the various covariates that affected the waiting time and the response time. The Weibull model was found to be the best fit for waiting duration analysis, while the log-logistic model was considered for the study of response time. The developed models can help understand the external factors and personal features of pedestrians in relation to the risk involved during violation crossings.

7668 Background: Concurrent chemoradiation is standard treatment against stage III NSCLC. HOG LUN 01–24 examines whether consolidation therapy with D improves overall survival. We present an analysis investigating the association of patient characteristics with overall survival from patients on this study. Methods: Eligible patients had untreated stage III NSCLC, FEV1 ≥ 1 liter, PS of 0–1, and weight loss < 5%. Patients received P 50 mg/m2 days 1, 8, 29, 36 with E 50 mg/m2 days 1–5, 29–33, and concurrent 5,940 cGy XRT. Patients with non-progressive disease were randomized to D 75 mg/m2 q3wk X 3 cycles vs observation. A multivariable parametric accelerated failure time model was performed to identify factors that affected survival and to estimate the treatment effect adjusting for these factors. Results: A multivariate analysis was performed on 203 patients who were the subject of a DSMB interim analysis. Median follow up was 25.6 months. Variables analyzed included age (<70 vs ≥ 70), sex, race, body mass index, PS (0 vs 1), FEV-1 (> 2 vs ≤ 2), smoking status, hemoglobin (≥12 vs <12), and stage. A multivariable parametric accelerated failure time model demonstrated the association of age <70 vs =70 years (p=0.0447), FEV1 >2 vs =2 (p=0.0153), and pre-treatment hemoglobin values (p=0.0083) as independent prognostic factors for overall survival. The median survival for hemoglobin <12 was 16.8 vs 21.5 months for hemoglobin ≥12 (p=0.0432). Similarly, the median survival with FEV >2L was 21.6 vs 18.9 months for FEV =2 L. Survival was not significantly influenced by smoking status, sex, race, PS, stage, or BMI. Conclusions: This analysis suggests that age <70, FEV-1 >2L and higher pre-treatment hemoglobin values are associated with improved overall survival in patients with stage III NSCLC. No significant financial relationships to disclose.

Recently, in order to get closer agreement at the extremes, skewed distributions are playing an important role in various research studies. The generalized logistic distribution (GLD) of Type II, which is indexed by one shape parameter, is introduced here to extend the scope of this distribution in some asymmetrical studies. Several properties of this distribution in relation to other probability distributions are stated. Furthermore, the maximum-likelihood (ML) method and an approximate ML method are used to derive the point estimators of the parameters based on progressive Type II censoring. A wide range of sample sizes and progressive-censoring schemes are considered in a simulation study to see the performance of estimates of location and scale parameters of the Type II GLD. The coverages probability of the pivotal quantities (for location and scale parameters) based on asymptotic normality are shown to be unsatisfactory, especially when the effective sample size is small. To improve the coverage probabilities, we suggest the use of unconditional simulated percentage points for the construction of confidence intervals. Two numerical examples are presented to illustrate the methods of estimation discussed here.

Abstract. The increasing availability of synthetic aperture radar (SAR) data from a range of different sensors necessitates efficient methods for semi-automated information extraction at multiple spatial scales for different fields of application. The focus of the presented study is two-fold: 1) to evaluate the applicability of multi-temporal TerraSAR-X imagery for multiresolution segmentation, and 2) to identify suitable Scale Parameters through different weighing of different homogeneity criteria, mainly colour variance. Multiresolution segmentation was used for segmentation of multi-temporal TerraSAR-X imagery, and the ESP (Estimation of Scale Parameter) tool was used to identify suitable Scale Parameters for image segmentation. The validation of the segmentation results was performed using very high resolution WorldView-2 imagery and a reference map, which was created by an ecological expert. The results of multiresolution segmentation revealed that in the context of object-based image analysis the TerraSAR-X images are applicable for generating optimal image objects. Furthermore, ESP tool can be used as an indicator for estimation of Scale Parameter for multiresolution segmentation of TerraSAR-X imagery. Additionally, for more reliable results, this study suggests that the homogeneity criterion of colour, in a variance based segmentation algorithm, needs to be set to high values. Setting the shape/colour criteria to 0.005/0.995 or 0.00/1 led to the best results and to the creation of adequate image objects.

This study examines the estimation of the scale parameter of the Weibull-Power Function Distribution (WPFD) using both maximum likelihood and Bayesian approaches. Bayesian estimation is conducted under one informative Gamma prior with hyperparameters , as well as two non-informative priors: the uniform prior and Jeffreys’ prior. For each prior specification, Bayes estimators are derived under squared error, quadratic, and precautionary loss functions. Closed-form expressions for the posterior distributions and corresponding Bayes estimators are obtained. The finite-sample performance of the competing estimators is evaluated through a Monte Carlo simulation study based on 1000 replications. Estimator performance is assessed using mean squared error (MSE), bias, and coverage probability. The results indicate that all estimators are consistent, with bias and MSE decreasing as sample size increases. Across different prior specifications and parameter settings, the Bayesian estimator under the quadratic loss function consistently attains the lowest MSE, yielding reductions of approximately 10-20% relative to the maximum likelihood estimator in small and moderate samples. These findings suggest that Bayesian estimation under quadratic loss provides improved finite-sample efficiency for estimating the WPFD scale parameter, while maintaining asymptotic comparability with the maximum likelihood approach.

Semiparametric accelerated failure time (AFT) models are a useful alternative to Cox proportional hazards models, especially when the assumption of constant hazard ratios is untenable. However, rank-based criteria for fitting AFT models are often nondifferentiable, which poses a computational challenge in high-dimensional settings. In this article, we propose a new alternating direction method of multipliers algorithm for fitting semiparametric AFT models by minimizing a penalized rank-based loss function. Our algorithm scales well in both the number of subjects and number of predictors, and can easily accommodate a wide range of popular penalties. To improve the selection of tuning parameters, we propose a new criterion which avoids some common problems in cross-validation with censored responses. Through extensive simulation studies, we show that our algorithm and software is much faster than existing methods (which can only be applied to special cases), and we show that estimators which minimize a penalized rank-based criterion often outperform alternative estimators which minimize penalized weighted least squares criteria. Application to nine cancer datasets further demonstrates that rank-based estimators of semiparametric AFT models are competitive with estimators assuming proportional hazards in high-dimensional settings, whereas weighted least squares estimators are often not. A software package implementing the algorithm, along with a set of auxiliary functions, is available for download at github.com/ajmolstad/penAFT.

Cox-McFadden Partial and Marginal Likelihoods for the Proportional Hazard Model with Random Effects

Improved point and interval estimation of the smallest scale parameter of n independent populations following two-parameter exponential distributions are studied. The model is formulated in such a way that allows for treating the estimation of the smallest scale parameter as a problem of estimating an unrestricted scale parameter in the presence of a nuisance parameter. The classes of improved point and interval estimators are enriched with Stein-type, Brewster and Zidek-type, Maruyama-type and Strawderman-type improved estimators under both quadratic and entropy losses, whereas using as a criterion the coverage probability, with Stein-type, Brewster and Zidek-type, and Maruyama-type improved intervals. The sampling framework considered incorporates important life-testing schemes such as i.i.d. sampling, type-II censoring, progressive type-II censoring, adaptive progressive type-II censoring, and record values.

A note on universal admissibility of scale parameter estimators

1 Order statistics in exponential distribution

The unimodal distributions are frequently used in the theorical statistical studies. But in applied statistics, there are many situations in which the unimodal distributions can not be fitted to the data. For example, the distribution of the data outside the control zone in quality control or outlier observations in linear models and time series may require to be a bimodal. These situations, occur when the recorded data have the probability proportional to an increasing function of absolute value of deviations. In this paper a new family of distributions called double normal family of distribution is introduced and characterized. This symmetric family is a subclass of the univariate Kotz type distributions. The normal distribution is a special case of this family. Estimation of location and scale parameters by moment and maximum likelihood methods are given. Some pivotal quantity are introduced. Confidence intervals for some parameters by numerical methods are given.

A broad class of rank‐based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations. The corresponding estimators can be obtained via linear programming, and are shown to be consistent and asymptotically normal. The limiting covariance matrices can be estimated by a resampling technique, which does not involve nonparametric density estimation or numerical derivatives. The new estimators represent consistent roots of the non‐monotone estimating equations based on the familiar weighted log‐rank statistics. Simulation studies demonstrate that the proposed methods perform well in practical settings. Two real examples are provided.

Right-censored time-to-event data are sometimes observed from a (sub)cohort of patients whose survival times can be subject to outcome-dependent sampling schemes. In this paper, we propose a unified estimation method for semiparametric accelerated failure time models under general biased estimating schemes. The proposed estimator of the regression covariates is developed upon a bias-offsetting weighting scheme and is proved to be consistent and asymptotically normally distributed. Large sample properties for the estimator are also derived. Using rank-based monotone estimating functions for the regression parameters, we find that the estimating equations can be easily solved via convex optimization. The methods are confirmed through simulations and illustrated by application to real datasets on various sampling schemes including length-bias sampling, the case-cohort design and its variants.