Personalized medicine has received increasing attention among statisticians, computer scientists, and clinical practitioners. A major component of personalized medicine is the estimation of ...individualized treatment rules (ITRs). Recently, Zhao et al. proposed outcome weighted learning (OWL) to construct ITRs that directly optimize the clinical outcome. Although OWL opens the door to introducing machine learning techniques to optimal treatment regimes, it still has some problems in performance. (1) The estimated ITR of OWL is affected by a simple shift of the outcome. (2) The rule from OWL tries to keep treatment assignments that subjects actually received. (3) There is no variable selection mechanism with OWL. All of them weaken the finite sample performance of OWL. In this article, we propose a general framework, called residual weighted learning (RWL), to alleviate these problems, and hence to improve finite sample performance. Unlike OWL which weights misclassification errors by clinical outcomes, RWL weights these errors by residuals of the outcome from a regression fit on clinical covariates excluding treatment assignment. We use the smoothed ramp loss function in RWL and provide a difference of convex (d.c.) algorithm to solve the corresponding nonconvex optimization problem. By estimating residuals with linear models or generalized linear models, RWL can effectively deal with different types of outcomes, such as continuous, binary, and count outcomes. We also propose variable selection methods for linear and nonlinear rules, respectively, to further improve the performance. We show that the resulting estimator of the treatment rule is consistent. We further obtain a rate of convergence for the difference between the expected outcome using the estimated ITR and that of the optimal treatment rule. The performance of the proposed RWL methods is illustrated in simulation studies and in an analysis of cystic fibrosis clinical trial data. Supplementary materials for this article are available online.
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BFBNIB, GIS, IJS, INZLJ, KISLJ, NMLJ, NUK, PNG, SAZU, UL, UM, UPUK, ZRSKP
This article investigates the performance of several residuals for the Cox proportional hazards regression model to diagnose the influential observations. The standardized and adjusted forms of ...residuals are proposed for Cox proportional hazards regression model. In addition, Cook's distance is proposed for both standardized and adjusted residuals. The assessment of different residuals for the identification of influential observations is made through the Monte Carlo simulation. A real dataset of bone marrow transplant Leukaemia is analyzed to show the benefit of the proposed methods. Simulation and application results show that the standardized and adjusted residuals based on the Cox-Snell method perform best for the detection of influential points. Furthermore, the standardized, and adjusted Martingale and deviance residuals work better when the sample size is large.
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Summary
A primary goal of ecology is to understand the fundamental processes underlying the geographic distributions of species. Two major strands of ecology – habitat modelling and community ecology ...– approach this problem differently. Habitat modellers often use species distribution models (SDMs) to quantify the relationship between species’ and their environments without considering potential biotic interactions. Community ecologists, on the other hand, tend to focus on biotic interactions and, in observational studies, use co‐occurrence patterns to identify ecological processes. Here, we describe a joint species distribution model (JSDM) that integrates these distinct observational approaches by incorporating species co‐occurrence data into a SDM.
JSDMs estimate distributions of multiple species simultaneously and allow decomposition of species co‐occurrence patterns into components describing shared environmental responses and residual patterns of co‐occurrence. We provide a general description of the model, a tutorial and code for fitting the model in R. We demonstrate this modelling approach using two case studies: frogs and eucalypt trees in Victoria, Australia.
Overall, shared environmental correlations were stronger than residual correlations for both frogs and eucalypts, but there were cases of strong residual correlation. Frog species generally had positive residual correlations, possibly due to the fact these species occurred in similar habitats that were not fully described by the environmental variables included in the JSDM. Eucalypt species that interbreed had similar environmental responses but had negative residual co‐occurrence. One explanation is that interbreeding species may not form stable assemblages despite having similar environmental affinities.
Environmental and residual correlations estimated from JSDMs can help indicate whether co‐occurrence is driven by shared environmental responses or other ecological or evolutionary process (e.g. biotic interactions), or if important predictor variables are missing. JSDMs take into account the fact that distributions of species might be related to each other and thus overcome a major limitation of modelling species distributions independently.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
The two-variable orthogonal least squares procedure was developed independently by Julius Ludwig Weisbach (1806-1871) and Robert Jackson Adcock (1826-1895). In this article we discuss aspects of two ...recent articles concerned with the contributions of these individuals. We also identify a prototype of the orthogonal minimax fitting procedure due to August Beyer (1677-1753).
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8.
Diagnostics for the Cox model Xue, Yishu; Schifano, Elizabeth D
Communications for statistical applications and methods,
11/2017, Volume:
24, Issue:
6
Journal Article
Peer reviewed
Open access
The most popular regression model for the analysis of time-to-event data is the Cox proportional hazards model. While the model specifies a parametric relationship between the hazard function and the ...predictor vari-ables, there is no specification regarding the form of the baseline hazard function. A critical assumption of the Cox model, however, is the proportional hazards assumption: when the predictor variables do not vary over time, the hazard ratio comparing any two observations is constant with respect to time. Therefore, to perform cred-ible estimation and inference, one must first assess whether the proportional hazards assumption is reasonable. As with other regression techniques, it is also essential to examine whether appropriate functional forms of the predictor variables have been used, and whether there are any outlying or influential observations. This article reviews diagnostic methods for assessing goodness-of-fit for the Cox proportional hazards model. We illus-trate these methods with a case-study using available R functions, and provide complete R code for a simulated example as a supplement.
Linear dependence of variables is a commonly used assumption in most diagnostic systems for which many robust methodologies have been developed over the years. In case the system nonlinearities are ...relevant, fault diagnosis methods, relying on the assumption of linearity, might potentially provide unsatisfactory results in terms of false alarms and missed detections. In recent years, many authors have proposed machine learning (ML) techniques to improve fault diagnosis performance to mitigate this problem. Although very powerful, these techniques require faulty data samples that are representative of any fault scenario. Additionally, ML techniques suffer from issues related to overfitting and unpredictable performance in regions which are not fully explored in the training phase. This paper proposes a non-linear additive model to characterize the non-linear redundancy relationships among the system signals. Using the multivariate adaptive regression splines (MARS) algorithm, these relationships are identified directly from the data. Next, the non-linear redundancy relationships are linearized to derive a local time-dependent fault signature matrix. The faulty sensor can then be isolated by measuring the angular distance between the column vectors of the fault signature matrix and the primary residual vector. A quantitative analysis of fault isolation and fault estimation performance is performed by exploiting real data from multiple flights of a semi-autonomous aircraft, thus allowing a detailed quantitative comparison with state-of-the-art machine-learning-based fault diagnosis algorithms.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
In this study, response surface methodology (RSM)–artificial neural network (ANN) approach was used to optimise/model disperse dye removal by adsorption using water treatment residuals (WTR). RSM was ...first applied to evaluate the process using three controllable operating parameters, namely WTR dose, initial pH (pHinitial) and dye concentration, and optimal conditions for colour removal were determined. In the second step, the experimental results of the design data of RSM were used to train the neural network along with a non-controllable parameter, the final pH (pHfinal). The trained neural networks were used for predicting the colour removal. A colour removal of 52.6 ± 2.0% obtained experimentally at optimised conditions (pHinitial 3.0, adsorbent dose 30 g/L and dye concentration 75 mg/L) was comparable to 52.0% and 52.2% predicted by RSM and RSM-ANN, respectively. This study thus shows that optimising/predicting the colour removal process using the RSM–ANN approach is possible, and it also indicates that adsorption onto WTR could be used as a primary treatment for removal of colour from dye wastewater.
•Water treatment residual (WTR) is a potential sorbent for colour removal.•Up to 52% colour removal can be obtained with WTR at optimum conditions.•Optimisation with RSM-ANN approach is possible.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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