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We treat the situations that the effect of covariates on hazard is differed in subgroups of patients. To handle this situation, we can consider the hybrid model of the Cox model and tree-structured model. Through simulation studies, we compared several splitting criteria for constructing this hybrid model. As a result, the criterion using the degree of the improvement in the negative maximum partial log-likelihood obtained by splitting showed a good performance for many situations. We also present the results obtained by applying this tree model in an actual medical research study to show its utility.

Study objectives Sleep is multidimensional, with domains including duration, timing, continuity, regularity, rhythmicity, quality, and sleepiness/alertness. Individual sleep characteristics representing these domains are known to predict health outcomes. However, most studies consider sleep characteristics in isolation, resulting in an incomplete understanding of which sleep characteristics are the strongest predictors of health outcomes. We applied three multivariable approaches to robustly determine which sleep characteristics increase mortality risk in the osteoporotic fractures in men sleep study. Methods In total, 2,887 men (mean 76.3 years) completed relevant assessments and were followed for up to 11 years. One actigraphy or self-reported sleep characteristic was selected to represent each of seven sleep domains. Multivariable Cox models, survival trees, and random survival forests were applied to determine which sleep characteristics increase mortality risk. Results Rhythmicity (actigraphy pseudo-F statistic) and continuity (actigraphy minutes awake after sleep onset) were the most robust sleep predictors across models. In a multivariable Cox model, lower rhythmicity (hazard ratio, HR [95%CI] =1.12 [1.04, 1.22]) and lower continuity (1.16 [1.08, 1.24]) were the strongest sleep predictors. In the random survival forest, rhythmicity and continuity were the most important individual sleep characteristics (ranked as the sixth and eighth most important among 43 possible sleep and non-sleep predictors); moreover, the predictive importance of all sleep information considered simultaneously followed only age, cognition, and cardiovascular disease. Conclusions Research within a multidimensional sleep health framework can jumpstart future research on causal pathways linking sleep and health, new interventions that target specific sleep health profiles, and improved sleep screening for adverse health outcomes.

Background Patients with lung cancer often present with recurrence, even after resection. The identification of risk factors for recurrence after resection is useful. Methods Among 1,338 patients with lung cancer who underwent a complete resection, 277 developed recurrences post surgery. Data regarding the TNM factors, histologic subtype, and presence/absence of vessel invasion were analyzed retrospectively using the survival tree method to identify groups with a high risk of recurrence after resection. Results The results revealed that the T factor, the N factor, and lymphatic (ly) and blood (v) vessel invasion were related to the risk of recurrence, and six combinations of these factors were identified using the survival tree method: group A: v = 0, T ≤ 1b, ly = 0; group B: v = 0, T ≤ 1b, ly ≥ 1; group C: v = 0, T ≥ 2a; group D: v ≥ 1, N ≤ 1, T ≤ 2b; group E: v ≥ 1, N ≤ 1, T ≥ 3; and group F: v ≥ 1, N ≥ 2. The six groups were then further classified into three groups: a low-risk group (group A), a moderate-risk group (groups B, C, and D), and a high-risk group (groups E and F). The 5-year recurrence-free survival rate was approximately 98% for the low-risk group, 75% for the moderate-risk group, and 30% for the high-risk group. Conclusions Combining the T, N, v, and ly factors allowed the precise identification of a group with a high risk of recurrence after resection.

Mixture distribution survival trees are constructed by approximating different nodes in the tree by distinct types of mixture distributions to improve within node homogeneity. Previously, we proposed a mixture distribution survival tree-based method for determining clinically meaningful patient groups from a given dataset of patients’ length of stay. This article extends this approach to examine the interrelationship between length of stay in hospital, outcome measures, and other covariates. We describe an application of this approach to patient pathway and examine the relationship between length of stay in hospital and/or treatment outcome using five-years’ retrospective data of stroke patients.

Patients with hepatocellular carcinoma (HCC) satisfying the Milan criteria are candidates for liver transplantation (LT), but locoregional therapies could be another options for them. A total of 1859 treatment-naïve HCC patients fulfilling the Milan criteria were analyzed. Survival tree analysis was performed to generate survival nodes with similar survival risks in 1729 non-LT group, and compared with the survival of 130 patients who received LT. Among patients who did not receive LT, survival tree analysis classified patients into 6 nodes according to Child-Pugh (CP) score, serum alphafetoprotein (AFP) levels, tumor size, and age, with different mortality risks (5-year survival rate of 87.3%, 77.5%, 65.8%, 64.7%, 44.0%, and 28.7% for nodes 1–6, respectively; P 0.05), but the survival rates of patients in nodes 3 to 6 were worse than that of LT (P

Introduction: The M component and TNM stage groupings for malignant pleural mesothelioma (MPM) have been empirical. The International Association for the Study of Lung Cancer developed a multinational database to propose evidence-based revisions for the eighth edition of the TNM classification of MPM. Methods: Data from 29 centers were submitted either electronically or by transfer of existing institutional databases. The M component as it currently stands was validated by confirming sufficient discrimination (by Kaplan-Meier analysis) with respect to overall survival (OS) between the clinical MO (cM0) and cM1 categories. Candidate stage groups were developed by using a recursive partitioning and amalgamation algorithm applied to all cM0 cases. Results: Of 3519 submitted cases, 2414 were analyzable and 84 were cM1 cases. Median OS for cM1 cases was 9.7 months versus 13.4 months (p = 0.0013) for the locally advanced (T4 or N3) cM0 cases, supporting inclusion of only cM1 in the stage IV group. Exploratory analyses suggest a possible difference in OS for single- versus multiple-site cM1 cases. A recursive partitioning and amalgamation generated survival tree on the OS outcomes restricted to cM0 cases with the newly proposed (eighth edition) T and N components indicates that optimal stage groupings for the eighth edition will be as follows: stage IA (T1N0), stage IB (T2-3N0), stage II (T1-2N1), stage IIIA (T3N1), stage IIIB (T1-3N2 or any T4), and stage IV (any M1). Conclusions: This first evidence-based revision of the TNM classification for MPM leads to substantial changes in the T and N components and the stage groupings. (C) 2016 International Association for the Study of Lung Cancer. Published by Elsevier Inc. All rights reserved.

International audience; AbstractBackgroundFor clinical genomic studies with high-dimensional datasets, tree-based ensemble methods offer a powerful solution for variable selection and prediction taking into account the complex interrelationships between explanatory variables. One of the key component of the tree-building process is the splitting criterion. For survival data, the classical splitting criterion is the Logrank statistic. However, the presence of a fraction of nonsusceptible patients in the studied population advocates for considering a criterion tailored to this peculiar situation.ResultsWe propose a bagging survival tree procedure for variable selection and prediction where the survival tree-building process relies on a splitting criterion that explicitly focuses on time-to-event survival distribution among susceptible patients.A simulation study shows that our method achieves good performance for the variable selection and prediction. Different criteria for evaluating the importance of the explanatory variables and the prediction performance are reported. Our procedure is illustrated on a genomic dataset with gene expression measurements from early breast cancer patients.ConclusionsIn the presence of nonsusceptible patients among the studied population, our procedure represents an efficient way to select event-related explanatory covariates with potential higher-order interaction and identify homogeneous groups of susceptible patients.

Health care providers continue to feel the pressure in providing adequate care for an increasing elderly population. If length of stay patterns for elderly patients in care can be captured through analytical modelling, then accurate predictions may be made on when they are expected to leave hospital. The Discrete Conditional Phase-type (DC-Ph) model is an effective technique through which length of stay in hospital can be modelled and consists of both a conditional and a process component. This research expands the DC-Ph model by introducing a survival tree as the conditional component, whereby covariates are used to partition patients into cohorts based on their distribution of length of stay in hospital. The Coxian phase-type distribution is then used to model the length of stay for patients belonging to each cohort. A demonstration of how patient length of stay may be predicted for new admissions using this methodology is then given. This tool has the benefit of providing an aid to the decision making processes undertaken by hospital managers and has the potential to result in the more effective allocation of hospital resources. Hospital admission data from the Lombardy region of Italy is used as a case-study.

The aim of this paper is to propose a new survival tree method for discrete-time survival data with time-varying covariates. This method can accommodate simultaneously time-varying covariates and time-varying effects. The method is then used for bankruptcy analysis of US firms that conducted an Initial Public Offerings between 1990 and 1999 using accounting and financial ratios.

Minimal depth is a dimensionless order statistic that measures the predictiveness of a variable in a survival tree. It can be used to select variables in high-dimensional problems using Random Survival Forests (RSF), a new extension of Breiman's Random Forests (RF) to survival settings. We review this methodology and demonstrate its use in high-dimensional survival problems using a public domain R-language package randomSurvivalForest . We discuss effective ways to regularize forests and discuss how to properly tune the RF parameters ‘nodesize’ and ‘mtry’. We also introduce new graphical ways of using minimal depth for exploring variable relationships. © 2011 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 4: 115–132 2011 © 2011 Wiley Periodicals, Inc.

It is important to predict osteoporotic fracture risk accurately in order to select high-risk patients for treatment. Previous tree-structured survival analysis (TSSA) methods focused on optimization in statistical performance in construction of survival trees. However, they did not take into account the cost of the predictive variables. Because of the high cost of some predictors, the derived algorithm may have only limited application in practice. In this article, the authors consider the cost-effectiveness in TSSA and propose a cost-saving TSSA (denoted as CSTSSA) to construct the survival tree for identifying subjects at high risk of hip fracture based on the data from Study of Osteoporotic Fractures. The new rule is compared with the optimum classification based on log-rank test statistics using the noninferiority test by Lu and others. The comparison results suggest that, for identifying patients at high risk of hip fracture, the CSTSSA is a good alternative to the optimum classification.

Tree-based methods are frequently used in studies with censored survival time. Their structure and ease of interpretability make them useful to identify prognostic factors and to predict conditional survival probabilities given an individual's covariates. The existing methods are tailor-made to deal with a survival time variable that is measured continuously. However, survival variables measured on a discrete scale are often encountered in practice. The authors propose a new tree construction method specifically adapted to such discrete-time survival variables. The splitting procedure can be seen as an extension, to the case of right-censored data, of the entropy criterion for a categorical outcome. The selection of the final tree is made through a pruning algorithm combined with a bootstrap correction. The authors also present a simple way of potentially improving the predictive performance of a single tree through bagging. A simulation study shows that single trees and bagged-trees perform well compared to a parametric model. A real data example investigating the usefulness of personality dimensions in predicting early onset of cigarette smoking is presented. The Canadian Journal of Statistics 37: 17-32; 2009 © 2009 Statistical Society of Canada Arbres de survie a temps discret Les methodes d'arbres sont frequemment utilisees lors d'etudes impliquant des donnees censurees. La structure d'un arbre ainsi que la facilite avec laquelle il peut etre interprete font de lui un outil utile afin d'identifier des facteurs de pronostique et de predire les probabilites de survie conditionnelles d'un individu etant donne ses covariables. Les methodes existantes ont ete developpees pour traiter une variable temporelle continue. En pratique, il arrive frequemment que la variable mesurant le temps de survie soit mesuree selon une echelle discrete. Les auteurs proposent une nouvelle methode pour construire un arbre qui est specialement adaptee aux variables de survie a temps discret. Le critere de division peut etre vu comme etant une extension, au cas de censure a droite, du critere d'entropie pour une variable categorielle. La selection de l'arbre final est basee sur une methode d'elagage combinee avec une correction bootstrap. Les auteurs presentent egalement une methode simple pour ameliorer, potentiellement, la performance d'un seul arbre avec le bagging. Une etude par simulation montre que des arbres seuls et des arbres “bagges” performent bien comparativement a un modele parametrique. Les auteurs presentent aussi une illustration de la nouvelle methode avec des vraies donnees qui investiguent l'utilite d'utiliser des dimensions de la personnalite afin de prevoir le debut de l'utilisation de la cigarette. La revue canadienne de statistique 37: 17-32; 2009 © 2009 Societe statistique du Canada

Objective: Various immunohistochemical studies have been performed regarding intrahepatic cholangiocarcinoma (ICC), including the cell cycle-related proteins (p27, cyclin D1, 14-3-3σ, p53, cyclin B1 and Ki-67), the proto-oncogenes (c-erbB-2 and c-Met), the extracellular matrix proteins (tenascin and laminin) and others (β-catenin, epidermal growth factor receptor, osteopontin, aquaporin 1, MUC5AC and fascin). Nevertheless, none of these have been proven to be a predictive power of the prognosis with high specificity and sensitivity for ICC. Methods: Sixty-one patients with ICC were selected and ICC specimens were immunohistochemically stained with the above 16 markers, as previously reported. Results: The immunoreactivity of osteopontin, tenascin and Ki-67 divided the patients with ICC into 4 subgroups by the survival tree model. There was a significant relationship between the location of the tumor, TNM classification, histological differentiation, tumor size, lymphatic permeation, perineural invasion, lymph node metastasis, intrahepatic metastasis and viral infection among the 4 subgroups. In addition, there was a significant difference in survival among the 4 subgroups. Conclusion: In this study, the subgrouping by the survival tree model might be helpful for predicting the patients’ prognosis in ICC.

Predicted survival probability functions of censored event free survival are improved by bagging survival trees. We suggest a new method to aggregate survival trees in order to obtain better predictions for breast cancer and lymphoma patients. A set of survival trees based on B bootstrap samples is computed. We define the aggregated Kaplan-Meier curve of a new observation by the Kaplan-Meier curve of all observations identified by the B leaves containing the new observation. The integrated Brier score is used for the evaluation of predictive models. We analyse data of a large trial on node positive breast cancer patients conducted by the German Breast Cancer Study Group and a smaller 'pilot' study on diffuse large B-cell lymphoma, where prognostic factors are derived from microarray expression values. In addition, simulation experiments underline the predictive power of our proposal.

In the paper the comparison of ensemble based methods applied to censored survival data was conducted. Bagging survival trees, dipolar survival tree ensemble and random forest were taken into consideration. The prediction ability was evaluated by the integrated Brier score, the prediction measure developed for survival data. Two real datasets with different percentage of censored observations were examined.

In the paper the ensemble of dipolar trees for analysis of competing risks is proposed. The tool is build on the base of the learning sets, which contain the data from clinical studies following patients response for a given treatment. In case of competing risks many types of response are investigated. The proposed method is able to cope with incomplete (censored) observations and as a result, for a given set of covariates and a type of event, returns the aggregated cumulative incidence function.

We propose recursively imputed survival tree (RIST) regression for right-censored data. This new nonparametric regression procedure uses a novel recursive imputation approach combined with extremely randomized trees that allows significantly better use of censored data than previous tree-based methods, yielding improved model fit and reduced prediction error. The proposed method can also be viewed as a type of Monte Carlo EM algorithm, which generates extra diversity in the tree-based fitting process. Simulation studies and data analyses demonstrate the superior performance of RIST compared with previous methods.

Purpose Survival after neuroblastoma relapse is poor. Understanding the relationship between clinical and biologic features and outcome after relapse may help in selection of optimal therapy. Our aim was to determine which factors were significantly predictive of postrelapse overall survival (OS) in patients with recurrent neuroblastoma—particularly whether time from diagnosis to first relapse (TTFR) was a significant predictor of OS. Patients and Methods Patients with first relapse/progression were identified in the International Neuroblastoma Risk Group (INRG) database. Time from study enrollment until first event and OS time starting from first event were calculated. Cox regression models were used to calculate the hazard ratio of increased death risk and perform survival tree regression. TTFR was tested in a multivariable Cox model with other factors. Results In the INRG database (N = 8,800), 2,266 patients experienced first progression/relapse. Median time to relapse was 13.2 months (range, 1 day to 11.4 years). Five-year OS from time of first event was 20% (SE, ± 1%). TTFR was statistically significantly associated with OS time in a nonlinear relationship; patients with TTFR of 36 months or longer had the lowest risk of death, followed by patients who relapsed in the period of 0 to less than 6 months or 18 to 36 months. Patients who relapsed between 6 and 18 months after diagnosis had the highest risk of death. TTFR, age, International Neuroblastoma Staging System stage, and MYCN copy number status were independently predictive of postrelapse OS in multivariable analysis. Conclusion Age, stage, MYCN status, and TTFR are significant prognostic factors for postrelapse survival and may help in the design of clinical trials evaluating novel agents.

Survival tree based analysis is a powerful method of prognostication and determining clinically meaningful patient groups from a given dataset of patients' length of stay. In our previous work [1, 2] we proposed a phase type survival tree method for clustering patients into homogeneous groups with respect to their length of stay where partitioning is based on covariates representing patient characteristics such as gender, age at the time of admission, and primary diagnosis code. This paper extends this approach to examine the relationship between LOS in hospital and destination on discharge among these patient groups. An application of this approach is illustrated using 5 year retrospective data of patients admitted to Belfast City Hospital with a diagnosis of stroke (hemorrhagic stroke, cerebral infarction, transient ischaemic attack TIA, and stroke unspecified).

One of the main objectives in survival analysis is prediction the time of failure occurrence. It is done on a base of learning sets, which contain incomplete (censored) information on patients failure times. Proposed predictors should allow to cope with censored data. In the paper the influence of censoring for the performance of dipolar tree ensemble was investigated. The prediction ability of the model was verified by several measures, such as direct and indirect estimators of absolute predictive errors: DS,x, Dx and explained variation. The analysis is conducted on the base of artificial data, generated with different values of censoring rate.

We elucidated in Chapter 4 the usefulness of the recursive partitioning technique for the analysis of binary outcomes. Not only can this technique be extended to the analysis of censored data, but also, as pointed out by Gordon and Olshen (1985), tree-based regression is applicable to more general situations than that of the proportional hazard regression described previously. As a matter of fact, the most popular use of the tree-based methods is in the area of survival analysis.

We introduce random survival forests, a random forests method for the analysis of right-censored survival data. New survival splitting rules for growing survival trees are introduced, as is a new missing data algorithm for imputing missing data. A conservation-of-events principle for survival forests is introduced and used to define ensemble mortality, a simple interpretable measure of mortality that can be used as a predicted outcome. Several illustrative examples are given, including a case study of the prognostic implications of body mass for individuals with coronary artery disease. Computations for all examples were implemented using the freely available R-software package, randomSurvivalForest., Published in at http://dx.doi.org/10.1214/08-AOAS169 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Background: Many authors have described MELD as a predictor of short-term mortality in the liver transplantation waiting list. However MELD score accuracy to predict long term mortality has not been statistically evaluated. Objective: The aim of this study is to analyze the MELD score as well as other variables as a predictor of long-term mortality using a new model: the Survival Tree analysis. Study Design and Setting: The variables obtained at the time of liver transplantation list enrollment and considered in this study are: sex, age, blood type, body mass index, etiology of liver disease, hepatocellular carcinoma, waiting time for transplant and MELD. Mortality on the waiting list is the outcome. Exclusion, transplantation or still in the transplantation list at the end of the study are censored data. Results: The graphical representation of the survival trees showed that the most statistically significant cut off is related to MELD score at point 16. Conclusion: The results are compatible with the cut off point of MELD indicated in the clinical literature.

Survival trees are a useful regression tool to model the relationship between a survival time and a set of covariates. Survival or censored data are particularly common in medical research, and they also arise from many different areas of scientific and clinical research. For example, in the social sciences, we may be interested in the school drop-out rates and the turnover in a labor market. Tree based methods, due to their nonparametric nature and flexibility, have become very popular in the last two decades as an alternative to the traditional proportional hazard model. In this chapter we present the XploRe stree quantlet in the XploRequantlib hazreg Grund and Yang (2000, Chapter 5), which represent the XploRe implementation of the methodology decribed by Zhang (1995) and Zhang and Singer (1999).

We elucidated in Chapter 4 the usefulness of the recursive partitioning technique for the analysis of binary outcomes. Not only can this technique be extended to the analysis of censored data, but also, as pointed out by Gordon and Olshen (1985), tree-based regression is applicable to more general situations than that of the proportion hazard regression described previously. As a matter of fact, the most popular use of the tree-based methods is in the area of survival analysis.

Background RADIANT-3 was a phase III study investigating the effect of the mammalian target of rapamycin inhibitor everolimus on progression-free survival (PFS) in patients with advanced pancreatic neuroendocrine tumors (pNET; Yao et al, NEJM, 2011). Everolimus significantly improved PFS compared with placebo (11 vs 4.6 months, P Methods Baseline plasma levels of VEGF-A, PlGF, sVEGFR1, and sVEGFR2 were determined by ELISA using multiplexed MSD platform. The optimal cutoffs for these markers were explored using the “survival tree analysis” method. Interaction of treatment and baseline marker status ( Results PFS was significantly improved to a similar extent in patients receiving everolimus compared with patients who received placebo, regardless of baseline levels of markers (P Conclusions These exploratory analyses demonstrated consistent everolimus efficacy in all patients with advanced pNET irrespective of their baseline VEGF pathway biomarker levels. However, levels of VEGF-A, PlGP, and sVEGFR1 are potential prognostic factors for pNET. Marker Cutoff (pg/mL) Median PFS Prognostic effect HR [95% CI]; P value Treatment effect P value VEGF-A 246.1 8.3 vs 5.5 1.50 [1.17-1.92]; PlGF 32.06 8.0 vs 4.2 1.52 [1.14-2.02]; .004 SVEGFR1 226.2 8.3 vs 5.5 1.62 [1.27-2.07]; SVEGFR2 24503.1 10.8 vs 5.7 1.30 [0.96-1.76]; .090 Disclosure J.C. Yao: Consultant/advisory role for Novartis, Ipsen, Pfizer, Endo; Honoraria from Novartis; Research funding from Novartis, Genentech. M. Shah: Honoraria for presentations and participation in Advisory Board Meetings: Novartis, Ipsen, Pfizer Research grant: Novartis. A. Panneerselvam: Novartis employee. S. Stergiopoulos: Novartis employee. D. Chen: Novartis employee. M. Pavel: Honoraria for presentations and participation in Advisory Board Meetings: Novartis, Ipsen, Pfizer Research grant: Novartis. All other authors have declared no conflicts of interest.

The regression-tree methodology is extended to right-censored response variables by replacing the conventional splitting rules with rules based on the Tarone-Ware or Harrington-Fleming classes of two-sample statistics. New pruning strategies for determining desirable tree size are also devised. Properties of this approach are developed and comparisons with existing procedures, in terms of practical problems, are discussed. Illustrative, real-world performances of the technique are presented.