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Abstract Understanding the combined effects of risk factors on all-cause mortality is crucial for implementing effective risk stratification and designing targeted interventions, but such combined effects are understudied. We aim to use survival-tree based machine learning models as more flexible nonparametric techniques to examine the combined effects of multiple physiological risk factors on mortality. More specifically, we (1) study the combined effects between multiple physiological factors and all-cause mortality, (2) identify the five most influential factors and visualize their combined influence on all-cause mortality, and (3) compare the mortality cut-offs with the current clinical thresholds. Data from the 1999–2014 NHANES Survey were linked to National Death Index data with follow-up through 2015 for 17,790 adults. We observed that the five most influential factors affecting mortality are the tobacco smoking biomarker cotinine, glomerular filtration rate (GFR), plasma glucose, sex, and white blood cell count. Specifically, high mortality risk is associated with being male, active smoking, low GFR, elevated plasma glucose levels, and high white blood cell count. The identified mortality-based cutoffs for these factors are mostly consistent with relevant studies and current clinical thresholds. This approach enabled us to identify important cutoffs and provide enhanced risk prediction as an important basis to inform clinical practice and develop new strategies for precision medicine.

With the availability of massive amounts of data from electronic health records and registry databases, incorporating time-varying patient information to improve risk prediction has attracted great attention. To exploit the growing amount of predictor information over time, we develop a unified framework for landmark prediction using survival tree ensembles, where an updated prediction can be performed when new information becomes available. Compared to conventional landmark prediction with fixed landmark times, our methods allow the landmark times to be subject-specific and triggered by an intermediate clinical event. Moreover, the nonparametric approach circumvents the thorny issue of model incompatibility at different landmark times. In our framework, both the longitudinal predictors and the event time outcome are subject to right censoring, and thus existing tree-based approaches cannot be directly applied. To tackle the analytical challenges, we propose a risk-set-based ensemble procedure by averaging martingale estimating equations from individual trees. Extensive simulation studies are conducted to evaluate the performance of our methods. The methods are applied to the Cystic Fibrosis Foundation Patient Registry (CFFPR) data to perform dynamic prediction of lung disease in cystic fibrosis patients and to identify important prognosis factors.

Simple Summary: Up to 50% of patients diagnosed with advanced melanoma develop brain metastases during the course of their disease. The prognosis of melanoma patients is heavily affected by the presence of brain metastases. Unfortunately, there is a lack of data on prognostic factors for these patients. Many of these patients are treated with immune checkpoint inhibitors. Therefore, the aim of our study was to identify prognostic factors in melanoma patients with brain metastases treated with immune checkpoint inhibitors. In a population of 1278 advanced melanoma patients, we found that serum lactate dehydrogenase levels were the strongest clinical parameter associated with survival. This information is useful for both doctors and patients to provide more insight into patients' prognoses. The efficacy of immune checkpoint inhibitors (ICIs) in patients with advanced melanoma that develop brain metastases (BM) remains unpredictable. In this study, we aimed to identify prognostic factors in patients with melanoma BM who are treated with ICIs. Data from advanced melanoma patients with BM treated with ICIs in any line between 2013 and 2020 were obtained from the Dutch Melanoma Treatment Registry. Patients were included from the time of the treatment of BM with ICIs. Survival tree analysis was performed with clinicopathological parameters as potential classifiers and overall survival (OS) as the response variable. In total, 1278 patients were included. Most patients were treated with ipilimumab–nivolumab combination therapy (45%). The survival tree analysis resulted in 31 subgroups. The median OS ranged from 2.7 months to 35.7 months. The strongest clinical parameter associated with survival in advanced melanoma patients with BM was the serum lactate dehydrogenase (LDH) level. Patients with elevated LDH levels and symptomatic BM had the worst prognosis. The clinicopathological classifiers identified in this study can contribute to optimizing clinical studies and can aid doctors in giving an indication of the patients' survival based on their baseline and disease characteristics. [ABSTRACT FROM AUTHOR]

Interval-censored failure time data as a general type of survival data often arises in medicine and other applied fields. Survival tree is a flexible predictive method for survival data because no specific assumptions are required. Generalized Log-Rank Test have good power with parameters for interval-censored failure time data. We construct a special test statistic of Generalized Log-Rank Tests, and propose a new survival tree with hyper-parameter by combining the test statistic with Conditional Inference Framework for interval-censored failure time data. The effect of tuning hyper-parameter are discussed and hyper-parameter tuning allows the tree method to be more general and flexible. Thus the tree method either improve upon or remain competitive with existing tree method for interval-censored failure time data-ICtree, which is a special case of ours. An extensive simulation is executed to assess the predictive performance of our tree methods. Finally, the tree methods are applied to a tooth emergence data.

ABSTRACT: Studies of dairy cow longevity usually focus on the animal life after first calving, with few studies considering early life conditions and their effects on longevity. The objective was to evaluate the effect of birth conditions routinely collected by Dairy Herd Improvement agencies on offspring longevity measured as length of life and length of productive life. Lactanet provided 712,890 records on offspring born in 5,425 Quebec dairy herds between January 1999 and November 2015 for length of life, and 506,066 records on offspring born in 5,089 Quebec dairy herds between January 1999 and December 2013 for length of productive life. Offspring birth conditions used in this study were calving ease (unassisted, pull, surgery, or malpresentation), calf size (small, medium, or large), and twinning (yes or no). Observations were considered censored if the culling reason was “exported,” “sold for dairy production,” or “rented out” as well as if the animals were not yet culled at the time of data extraction. If offspring were not yet culled when the data were extracted, the last test-day date was considered the censoring date. Conditional inference survival trees were used in this study to analyze the effect of offspring birth conditions on offspring longevity. The hazard ratio of culling between the groups of offspring identified by the survival trees was estimated using a Cox proportional hazard model with herd-year-season as a frailty term. Five offspring groups were identified with different length of life based on their birth condition. Offspring with the highest length of life [median = 3.61 year; median absolute deviation (MAD) = 1.86] were those classified as large or medium birth size and were also the result of an unassisted calving. Small offspring as a result of a twin birth had the lowest length of life (median = 2.20 year; MAD = 1.69) and were 1.52 times more likely to be culled early in life. Six groups were identified with different length of productive life. Offspring that resulted from an unassisted or surgery calving and classified as large or medium when they were born were in the group with the highest length of productive life (median = 2.03 year; MAD = 1.63). Offspring resulting from a malpresentation or pull in a twin birth were in the group with the lowest length of productive life (median = 1.15 year; MAD = 1.11) and were 1.70 times more likely to be culled early in life. In conclusion, birth conditions of calving ease, calf size, and twinning greatly affected offspring longevity, and such information could be used for early selection of replacement candidates.

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. 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. 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. 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 and Purpose: Survival tree model is a nonparametric method which can be used to identify the affecting factors from a specific time to the onset of an event. In this method, the categories are selected according to the most important factors. The purpose of this study was to determine the factors affecting the duration of breastfeeding in mothers and introduce the homogeneous subgroups using a survival tree model. Methods: It was a historical cohort study analyzing the survival data of mothers with healthy single childbirths referring to the rural and urban health centers of Agh-Ghala County since 2011 until 2014. Data analyses and groupings of breastfeeding survival were performed using survival tree model with conditional inference algorithm in R Software. A separation criterion (SEP) confirmed the relevance of the model. Results: Survival tree model results revealed that the type of consumed milk with the complementary nutrition, ethnicity and the time interval between current childbirth and the previous delivery were the most important factors affecting the duration of breastfeeding. The SEPchr('39')s criterion was 2.082. Thus, due to the significant difference between the subgroups and the value of more than 1 for SEP criterion, the efficiency of the model was confirmed. Conclusions: Survival tree model could be introduced as a suitable and powerful method for ranking the duration of breastfeeding rate which presents four homogeneous subgroups for analysis in addition to identifying the predictive variables.

Studies of dairy cow longevity usually focus on the animal life after first calving, with few studies considering early life conditions and their effects on longevity. The objective was to evaluate the effect of birth conditions routinely collected by Dairy Herd Improvement agencies on offspring longevity measured as length of life and length of productive life. Lactanet provided 712,890 records on offspring born in 5,425 Quebec dairy herds between January 1999 and November 2015 for length of life, and 506,066 records on offspring born in 5,089 Quebec dairy herds between January 1999 and December 2013 for length of productive life. Offspring birth conditions used in this study were calving ease (unassisted, pull, surgery, or malpresentation), calf size (small, medium, or large), and twinning (yes or no). Observations were considered censored if the culling reason was "exported," "sold for dairy production," or "rented out" as well as if the animals were not yet culled at the time of data extraction. If offspring were not yet culled when the data were extracted, the last test-day date was considered the censoring date. Conditional inference survival trees were used in this study to analyze the effect of offspring birth conditions on offspring longevity. The hazard ratio of culling between the groups of offspring identified by the survival trees was estimated using a Cox proportional hazard model with herd-year-season as a frailty term. Five offspring groups were identified with different length of life based on their birth condition. Offspring with the highest length of life [median = 3.61 year; median absolute deviation (MAD) = 1.86] were those classified as large or medium birth size and were also the result of an unassisted calving. Small offspring as a result of a twin birth had the lowest length of life (median = 2.20 year; MAD = 1.69) and were 1.52 times more likely to be culled early in life. Six groups were identified with different length of productive life. Offspring that resulted from an unassisted or surgery calving and classified as large or medium when they were born were in the group with the highest length of productive life (median = 2.03 year; MAD = 1.63). Offspring resulting from a malpresentation or pull in a twin birth were in the group with the lowest length of productive life (median = 1.15 year; MAD = 1.11) and were 1.70 times more likely to be culled early in life. In conclusion, birth conditions of calving ease, calf size, and twinning greatly affected offspring longevity, and such information could be used for early selection of replacement candidates. [ABSTRACT FROM AUTHOR]

Survival analysis of right‐censored data often arises in many areas of research including medical research. The effect of covariates (and their interactions) on survival distribution can be studied through existing methods that require pre‐specifying the functional form of the covariates including their interactions. Survival trees offer a relatively flexible approach when the form of covariates' effects is unknown. We have proposed the SurvCART algorithm to construct a survival tree. There are two features that distinguish the SurvCART algorithm from the rest. First, most of the currently available survival tree construction techniques are not based on a formal test of significance and, hence, prone to spurious findings. The proposed SurvCART algorithm utilizes the "conditional inference" framework that selects splitting variable via parameter instability test and subsequently finds the optimal split based on some maximally chosen statistic. We used likelihood score‐based parameter instability tests that converge to distribution with known distribution function so that the p‐value can be obtained easily without any approximation. Second, the SurvCART algorithm has the flexibility to extend the concept of heterogeneity to the censoring time distribution as well, a feature that can be useful when censoring distribution is influenced by baseline covariates. We evaluated the operating characteristics of the parameter instability test and compared the performance of the SurvCART algorithm with other survival tree algorithms via simulation. Finally, the SurvCART algorithm was applied to a real data setting. The proposed method is implemented in R package LongCART available on CRAN. [ABSTRACT FROM AUTHOR]

As the COVID-19 pandemic is spreading around the world, increasing evidence highlights the role of cardiometabolic risk factors in determining the susceptibility to the disease. The fragmented data collected during the initial emergency limited the possibility of investigating the effect of highly correlated covariates and of modeling the interplay between risk factors and medication. The present study is based on comprehensive monitoring of 576 COVID-19 patients. Different statistical approaches were applied to gain a comprehensive insight in terms of both the identification of risk factors and the analysis of dependency structure among clinical and demographic characteristics. The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus enters host cells by binding to the angiotensinconverting enzyme 2 (ACE2), but whether or not renin-angiotensin-aldosterone system inhibitors (RAASi) would be beneficial to COVID-19 cases remains controversial. The survival tree approach was applied to define a multilayer risk stratification and better profile patient survival with respect to drug regimens, showing a significant protective effect of RAASi with a reduced risk of in-hospital death. Bayesian networks were estimated, to uncover complex interrelationships and confounding effects. The results confirmed the role of RAASi in reducing the risk of death in COVID-19 patients. De novo treatment with RAASi in patients hospitalized with COVID-19 should be prospectively investigated in a randomized controlled trial to ascertain the extent of risk reduction for in-hospital death in COVID-19. [ABSTRACT FROM AUTHOR]

In treating patients diagnosed with early Stage I non-small-cell lung cancer (NSCLC), doctors must choose surgery alone, Adjuvant Cisplatin-Based Chemotherapy (ACT) alone or both. For patients with resected stages IB to IIIA, clinical trials have shown a survival advantage from 4-15% with the adoption of ACT. However, due to the inherent toxicity of chemotherapy, it is necessary for doctors to identify patients whose chance of success with ACT is sufficient to justify the risks. This research seeks to use gene expression profiling in the development of a statistical decision-making algorithm to identify patients whose survival rates will improve from ACT treatment. Using the data from the National Cancer Institute, the lasso method in the Cox-Proportional-Hazards regression model is used as the main method to determine a feasible number of genes that are strongly associated with the treatment-related patient survival. Considering treatment groups separately, the patients are assigned a risk category based on the estimation of survival times. These risk categories are used to develop a Random Forests classification model to identify patients who are likely to benefit from chemotherapy treatment. This model allows the prediction of a new patient’s prognosis and the likelihood of survival benefit from ACT treatment based on a feasible number of genomic biomarkers. The proposed methods are evaluated using a simulation study. [ABSTRACT FROM AUTHOR]

Increasing demand on hospital resources by an ageing population is impacting significantly on the number of beds available and, in turn, the length of time that elderly patients must wait for a bed before being admitted to hospital. This research presents a new methodology that models patient pathways and allows the accurate prediction of patient length of stay in hospital, using a phase-type survival tree to cluster patients based on their covariates and length of stay in hospital. A type of Markov model, called the conditional Coxian phase-type distribution is then implemented, with the probability density function for the time spent at a particular stage of care, for example, the first community discharge, conditioned on the length of stay experienced at the previous stage, namely the initial hospital admission. This component of the methodology is subsequently applied to each cohort of patients over a number of hospital and community stages in order to build up the profile of patient readmissions and associated timescales for each cohort. It is then possible to invert the methodology, so that the length of stay for an observation representing a new patient admission may be estimated at each stage of care, based on the assigned cohort at the initial hospital stage. This approach provides hospital managers with an accurate understanding of the rates with which different groups of patients move between hospital and community care, which may be used to reduce the negative effects of bed-blocking and the premature discharge of patients without a required period of convalescence. This has the benefit of assisting hospital managers with the effective allocation of vital healthcare resources. The approach presented is different to previous research in that it allows the inclusion of patient covariate information into the methodology describing patient transitions between hospital and community care stages in an aggregate Markov process. A data set containing hospital readmission data for elderly patients from the Abruzzo region of Italy is used as a case study in the application of the presented methodology. [ABSTRACT FROM AUTHOR]

Interval-censored data, in which the event time is only known to lie in some time interval, arise commonly in practice, for example, in a medical study in which patients visit clinics or hospitals at prescheduled times and the events of interest occur between visits. Such data are appropriately analyzed using methods that account for this uncertainty in event time measurement. In this paper, we propose a survival tree method for interval-censored data based on the conditional inference framework. Using Monte Carlo simulations, we find that the tree is effective in uncovering underlying tree structure, performs similarly to an interval-censored Cox proportional hazards model fit when the true relationship is linear, and performs at least as well as (and in the presence of right-censoring outperforms) the Cox model when the true relationship is not linear. Further, the interval-censored tree outperforms survival trees based on imputing the event time as an endpoint or the midpoint of the censoring interval. We illustrate the application of the method on tooth emergence data. [ABSTRACT FROM AUTHOR]

Background and purpose The burden of stroke is increasing in low to middle income countries. Identifying risk patterns for ischemic stroke (IS) can help develop individualized preventive measures for at risk populations. Methods The study population included 3088 Iranian subjects (1426 men) aged ≥50 years, free of cardiovascular diseases at baseline. The risk factors for ischemic stroke were identified by multivariate Cox analysis. A survival tree model was used to explore interactions between risk factors. Results During 12 years of follow-up, 106 cases of IS occurred. Age (hazard ratio (HR): 1.08), male gender (HR: 1.69), diastolic blood pressure (DBP) (HR: 1.04), fasting plasma glucose (HR: 1.10), waist circumference (WC) (HR: 1.03) and smoking (HR: 1.96), were associated with increased risk and estimated glomerular filtration rate (eGFR) (HR: 0.97) and wrist circumference (HR: 0.68) decreased the risk of IS (all P -values <0.05). The survival tree identified six risk patterns. The highest and lowest risks were related to subjects ≥60.5 years with DBP ≥100 mmHg and subjects <60.5 years with DBP<97 mmHg, respectively. In subjects ≥60.5 years with DBP <100 mmHg, risk of ischemic stroke was determined by WC ≥96.5 cm or (eGFR) <60.87 ml/min/1.73 m 2 . Conclusion By applying survival tree as a complementary method to the conventional Cox-analysis, for the first time, we identified risk patterns of ischemic stroke and explored the interactions between risk factors of the disease. DBP was the most important predictor of ischemic stroke in middle-aged and old subjects. In elderly subjects with DBP <100 mmHg, abdominal obesity was associated with high risk; however, among non-obese subjects, kidney dysfunction increased the risk of ischemic stroke. Wrist circumference was reported as a novel predictor. [ABSTRACT FROM AUTHOR]

Tree methods (recursive partitioning) are a popular class of nonparametric methods for analyzing data. One extension of the basic tree methodology is the survival tree, which applies recursive partitioning to censored survival data. There are several existing survival tree methods in the literature, which are mainly designed for right-censored data. We propose two new survival trees for left-truncated and right-censored (LTRC) data, which can be seen as a generalization of the traditional survival tree for right-censored data. Further, we show that such trees can be used to analyze survival data with time-varying covariates, essentially building a time-varying covariates survival tree. Implementation of the methods is easy, and simulations and real data analysis results show that the proposed methods work well for LTRC data and survival data with time-varying covariates, respectively. [ABSTRACT FROM AUTHOR]

Objective: Recursive partitioning is a common, assumption-free method of survival data analysis. It focuses mainly on univariate trees, which use splits based on a single variable in each internal node. In this paper, I provide an extension of an oblique survival tree induction technique, in which axis-parallel splits are replaced by hyperplanes, dividing the feature space into areas with a homogeneous survival experience.Method and Materials: The proposed tree induction algorithm consists of two steps. The first covers the induction of a large tree with internal nodes represented by hyperplanes, whose positions are calculated by the minimization of a piecewise-linear criterion function, the dipolar criterion. The other phase uses a split-complexity algorithm to prune unnecessary tree branches and a 10-fold cross-validation technique to choose the best tree. The terminal nodes of the final tree are characterised by Kaplan-Meier survival functions. A synthetic data set was used to test the performance, while seven real data sets were exploited to validate the proposed method.Results: The evaluation of the method was focused on two features: predictive ability and tree size. These were compared with two univariate tree models: the conditional inference tree and recursive partitioning for survival trees, respectively. The comparison of the predictive ability, expressed as an integrated Brier score, showed no statistically significant differences (p=0.486) among the three methods. Similar results were obtained for the tree size (p=0.11), which was calculated as a median value over 20 runs of a 10-fold cross-validation.Conclusions: The predictive ability of trees generated using piecewise-linear criterion functions is comparable to that of univariate tree-based models. Although a similar conclusion may be drawn from the analysis of the tree size, in the majority of the studied cases, the number of nodes of the dipolar tree is one of the smallest among all the methods. [ABSTRACT FROM AUTHOR]

In many scenarios, a patient in medical research is treated as a statistical unit. However, in some scenarios, we are interested in treating aggregate data as a statistical unit. In such situations, each set of aggregated data is considered to be a concept in a symbolic representation, and each concept has a hyperrectangle or multiple points in the variable space. To construct a tree-structured model from these aggregate survival data, we propose a new approach, where a datum can be included in several terminal nodes in a tree. By constructing a model under this condition, we expect to obtain a more flexible model while retaining the interpretive ease of a hierarchical structure. In this approach, the survival function of concepts that are partially included in a node is constructed using the Kaplan-Meier method, where the number of events and risks at each time point is replaced by the expectation value of the number of individual descriptions of concepts. We present an application of this proposed model using primary brain tumor patient data. As a result, we obtained a new interpretation of the data in comparison to the classical survival tree modeling methods. [ABSTRACT FROM AUTHOR]

Background: For 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. Results: We 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. Conclusions: In 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

Objective: This study aims at comparing the performances of supervised principal component analysis (SPCA) which is used for dimension reduction and an alternatively proposed approach of nonlinear principal component analysis using artificial neural networks performed by gene selection with survival tree (survival tree based NLPCA- NN). Material and Methods: Gene expression data set from Rosenwald et al.(2002) pertaining to 240 patients with diffuse large B-cell lymphoma (DLBCL) is used. While Cox scores are used for determining important genes from high dimensional gene expression data in SPCA, in survival tree based NLPCA-NN approach, importance values of the survival tree are used. Important genes according to the Cox scores are reduced to three principal components by singular value decomposition. Important genes determined by the survival tree are taken as input variables in neural networks and reduced to three principal components. The performances of SPCA and survival tree based NLPCA-NN are compared by using Cox regression models (CRM). C index is calculated to compare obtained Cox regression models. Results: According to Cox scores, 121 genes are determined; according to importance values of survival tree 114 genes are determined. The percentages of variances explained by SPCA and survival tree based NLPCA-NN were 18.2% and 35.1% respectively. Harrell's C indexes are calculated as 0.726 for CRM-1, 0.687 for CRM-2. Conclusion: As a result, while SPCA takes only the linear relationships into consideration, survival tree based NLPCA-NN also takes non-linear relationships into account and has more variance explanation and NLPCA-NN can be evaluated as an alternative method to SPCA. [ABSTRACT FROM AUTHOR]

We compare splitting methods for constructing survival trees that are used as a model of survival time based on covariates. A number of splitting criteria on the classification and regression tree (CART) have been proposed by various authors, and we compare nine criteria through simulations. Comparative studies have been restricted to criteria that suppose the survival model for each terminal node in the final tree as a non-parametric model. As the main results, the criteria using the exponential log-likelihood loss, log-rank test statistics, the deviance residual under the proportional hazard model, or square error of martingale residual are recommended when it appears that the data have constant hazard with the passage of time. On the other hand, when the data are thought to have decreasing hazard with passage of time, the criterion using the two-sample test statistic, or square error of deviance residual would be optimal. Moreover, when the data are thought to have increasing hazard with the passage of time, the criterion using the exponential log-likelihood loss, or impurity that combines observed times and the proportion of censored observations would be the best. We also present the results of an actual medical research to show the utility of survival trees. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Aim: To determine 2 different prognostic indexes (PI) for the differentiation of subgroups of nonmetastatic breast cancer patients with the Cox regression analysis and survival tree (ST) methods and the additional usage of the Kaplan-Meier estimates to investigate the predictive power of these methods. Materials and methods: Prognostic factors data were collected for 410 patients. The Cox regression analysis examines the relationship of the survival distribution and covariates. The ST method is a tree-structured survival analysis based on a recursive partitioning algorithm. In this study, Harrell's concordance indexes of models for training and test sets were computed. Furthermore, survival curves were estimated by the Kaplan-Meier method. Disease-free survival (DFS) was calculated from the time of initial diagnosis (initiation of the first treatment) to the first recurrence of disease. Results: After a median follow-up of 48 months, 100 (24.4%) patients have had at least 1 of the DFS events. In Cox regression analysis, we proposed the simple PI, which is a sum of axillary nodal and HER2/neu status. In the ST method, we identified 3 variables: HER2/neu, axillary nodal, and estrogen receptor status. The axillary nodal status was the most important determining factor for recurrence. Conclusion: We found that the PI of the ST and Cox regression methods had similar performance levels in predicting DFS, and the error rates of the models were close to each other in the training and test sets. Furthermore, we determined that the axillary nodal status and HER2/neu were the most important determining factors for prediction of DFS in breast cancer patients. [ABSTRACT FROM AUTHOR]

Tissue microarrays(TMAs) are a new high-throughput tool for the study of protein expression patterns in tissues and are increasingly used to evaluate the diagnostic and prognostic importance of biomarkers. TMA data are rather challenging to analyze. Covariates are highly skewed, non-normal, and may be highly correlated. We present statistical methods for relating TMA data to censored time-to-event data. We review methods for evaluating the predictive power of Cox regression models and show how to test whether biomarker data contain predictive information above and beyond standard pathology covariates. We use nonparametric bootstrap methods to validate model fitting indices such as the concordance index. We also present data mining methods for characterizing high risk patients with simple biomarker rules. Since researchers in the TMA community routinely dichotomize biomarker expression values, survival trees are a natural choice. We also use bump hunting(patient rule induction method), which we adapt to the use with survival data. The proposed methods are applied to a kidney cancer tissue microarray data set. [ABSTRACT FROM AUTHOR]