We consider a parametric modelling approach for survival data where covariates are allowed to enter the model through multiple distributional parameters (i.e., scale and shape). This is in contrast with the standard c...
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We consider a parametric modelling approach for survival data where covariates are allowed to enter the model through multiple distributional parameters (i.e., scale and shape). This is in contrast with the standard convention of having a single covariate-dependent parameter, typically the scale. Taking what is referred to as a multi-parameter regression (MPR) approach to modelling has been shown to produce flexible and robust models with relatively low model complexity cost. However, it is very common to have clustered data arising from survival analysis studies, and this is something that is under developed in the MPR context. The purpose of this article is to extend MPR models to handle multivariate survival data by introducing random effects in both the scale and the shape regression components. We consider a variety of possible dependence structures for these random effects (independent, shared and correlated), and estimation proceeds using a h-likelihood approach. The performance of our estimation procedure is investigated by a way of an extensive simulation study, and the merits of our modelling approach are illustrated through applications to two real data examples, a lung cancer dataset and a bladder cancer dataset.
Standard survival models such as the proportional hazards model contain a single regression component, corresponding to the scale of the hazard. In contrast, we consider the so-called "multi-parameter regression&...
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Standard survival models such as the proportional hazards model contain a single regression component, corresponding to the scale of the hazard. In contrast, we consider the so-called "multi-parameter regression" approach whereby covariates enter the model through multiple distributional parameters simultaneously, for example, scale and shape parameters. This approach has previously been shown to achieve flexibility with relatively low model complexity. However, beyond a stepwise type selection method, variable selection methods are underdeveloped in the multi-parameter regression survival modeling setting. Therefore, we propose penalized multi-parameter regression estimation procedures using the following penalties: least absolute shrinkage and selection operator, smoothly clipped absolute deviation, and adaptive least absolute shrinkage and selection operator. We compare these procedures using extensive simulation studies and an application to data from an observational lung cancer study;the Weibull multi-parameter regression model is used throughout as a running example.
It is standard practice for covariates to enter a parametric model through a single distributional parameter of interest, for example, the scale parameter in many standard survival models. Indeed, the well-known propo...
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It is standard practice for covariates to enter a parametric model through a single distributional parameter of interest, for example, the scale parameter in many standard survival models. Indeed, the well-known proportional hazards model is of this kind. In this article, we discuss a more general approach whereby covariates enter the model through more than one distributional parameter simultaneously (e.g., scale and shape parameters). We refer to this practice as multi-parameter regression (MPR) modeling and explore its use in a survival analysis context. We find that multi-parameter regression leads to more flexible models which can offer greater insight into the underlying data generating process. To illustrate the concept, we consider the two-parameter Weibull model which leads to time-dependent hazard ratios, thus relaxing the typical proportional hazards assumption and motivating a new test of proportionality. A novel variable selection strategy is introduced for such multi-parameter regression models. It accounts for the correlation arising between the estimated regression coefficients in two or more linear predictorsa feature which has not been considered by other authors in similar settings. The methods discussed have been implemented in the mpr package in R.
Orthotropic steel deck (OSD) has been widely employed in the bridge engineering owing to its superiorities of light-weight and high strength. However, the fatigue damage of rib-to-deck welded joint in OSD is one of th...
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Orthotropic steel deck (OSD) has been widely employed in the bridge engineering owing to its superiorities of light-weight and high strength. However, the fatigue damage of rib-to-deck welded joint in OSD is one of the most challenging issues. The notch stress intensity factors (NSIFs) that characterize the local mechanical properties of notch tips are major parameters for fatigue evaluation of rib-to-deck welded joint. This paper proposes formulae of the NSIFs of weld root for rib-to-deck welded joint under deck loading modes. First, parametric studies are conducted using a finite element model to establish a holistic understanding of the effects of the geometrical parameters on the NSIFs. The investigated parameters include the weld penetration rate, relative weld height, deck toe flank angle, and plate thickness ratio. Then, multi-parameter analysis is carried out based on the data generated from the parametric study. Finally, the proposed formulae of the NSIFs are evaluated and applied to evaluate the stress distribution and the averaged strain energy density of single-weld specimens for rib-to-deck welded joints. The maximum error of 9.5% indicates that the NSIFs predicted using the proposed formulae are in good agreement with the finite element analysis results. The proposed formulae provide useful tools for determining the stress distributions and the averaged strain energy density of single-weld rib-to-deck welded joint specimens.
The melting points of ionic liquids (ILs) of imidazolium bromides and imidazolium chlorides have been investigated by means of quantitative structure-activity relationship (QSAR) approach in order to develop predictio...
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The melting points of ionic liquids (ILs) of imidazolium bromides and imidazolium chlorides have been investigated by means of quantitative structure-activity relationship (QSAR) approach in order to develop prediction models for predicting the melting points of ionic liquid salts. The cationic structures of these ILs were optimized by means of Hyperchem software and MOPAC program. QSAR module of Materials Studio software and Genetic Algorithm (GA) programs were employed to calculate and select the structure descriptors of ILs, then prediction models correlating the selected structure descriptors and melting points of ionic liquids were set up by using the multiple linear regressions (MLR) method and the back-propagation artificial neural network (BP ANN) method, separately. Finally, the obtained QSAR models, including MLR model and BP ANN model, were validated by external test sets. In this work, three data sets, which were 30 imidazolium bromides, 20 imidazolium chlorides and the merging of above two data sets, respectively, were used to investigate the QSAR correlation of the melting points of ILs. The results demonstrated that the prediction mean absolute errors (MAEs) of MLR models for test sets of those three data sets were in the order of 20.52K, 13.59K and 21.95K, and the prediction MAEs of BP ANN models were 8.77K, 4.98 K and 9.31 K, respectively. It indicated that the predictions of two models for all melting points of ILs were reliable, and the prediction precision of BP ANN model was higher than that of MLR model. (C) 2010 Elsevier B.V. All rights reserved.
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