Joint lifetime modeling with matrix distributions

Quantile regression has emerged as a powerful tool in survival analysis as it directly links the quantiles of patients' survival times to their demographic and genomic profiles, facilitating the identification of important prognostic factors. In view of limited work on variable selection in the context, we develop a new adaptive-lasso-based variable selection procedure for quantile regression with censored outcomes. To account for random censoring for data with multivariate covariates, we employ the ideas of redistribution-of-mass and e ective dimension reduction. Asymptotically our procedure enjoys the model selection consistency, that is, identifying the true model with probability tending to one. Moreover, as opposed to the existing methods, our new proposal requires fewer assumptions, leading to more accurate variable selection. The analysis of a real cancer clinical trial demonstrates that our procedure can identify and distinguish important factors associated with patient sub-populations characterized by short or long survivals, which is of particular interest to oncologists.

BackgroundPrognostic genes or gene signatures have been widely used to predict patient survival and aid in making decisions pertaining to therapeutic actions. Although some web-based survival analysis tools have been developed, they have several limitations.ObjectiveTaking these limitations into account, we developed ESurv (Easy, Effective, and Excellent Survival analysis tool), a web-based tool that can perform advanced survival analyses using user-derived data or data from The Cancer Genome Atlas (TCGA). Users can conduct univariate analyses and grouped variable selections using multiomics data from TCGA.MethodsWe used R to code survival analyses based on multiomics data from TCGA. To perform these analyses, we excluded patients and genes that had insufficient information. Clinical variables were classified as 0 and 1 when there were two categories (for example, chemotherapy: no or yes), and dummy variables were used where features had 3 or more outcomes (for example, with respect to laterality: right, left, or bilateral).ResultsThrough univariate analyses, ESurv can identify the prognostic significance for single genes using the survival curve (median or optimal cutoff), area under the curve (AUC) with C statistics, and receiver operating characteristics (ROC). Users can obtain prognostic variable signatures based on multiomics data from clinical variables or grouped variable selections (lasso, elastic net regularization, and network-regularized high-dimensional Cox-regression) and select the same outputs as above. In addition, users can create custom gene signatures for specific cancers using various genes of interest. One of the most important functions of ESurv is that users can perform all survival analyses using their own data.ConclusionsUsing advanced statistical techniques suitable for high-dimensional data, including genetic data, and integrated survival analysis, ESurv overcomes the limitations of previous web-based tools and will help biomedical researchers easily perform complex survival analyses.

There is an increasing demand to determine the clinical implication of experimental findings in molecular biomedical research. Survival (or failure time) analysis methodologies have been adapted to the analysis of genomics data to link molecular information with clinical outcomes of interest. Genome-wide molecular profiles have served as sources for discovery of predictive/prognostic biomarkers as well as therapeutic targets in the past decade. In this review, we overview currently available software, web applications, and databases specifically developed for survival analysis in genomics research and discuss issues in assessing clinical utility of molecular features derived from genomic profiling.

Phase-type (PH) distributions are being used to model a wide range of phenomena in performance and dependability evaluation. The resulting models may be employed in analytical as well as in simulation-driven approaches. Simulations require the efficient generation of random variates from PH distributions. PH distributions have different representations and different associated computational costs for pseudo random-variate generation (PRVG). In this paper we study the problem of efficient representation and efficient generation of PH distributed variates. We introduce various PH representations of different sizes and optimize them according to different cost functions associated with PRVG.

Phase-type (PH) fitting is a technique to approximate any general distribution as a PH distribution, which is a probability distribution representing an absorbing time of a Markov chain. Since the PH distribution is described as a discrete- or continuous-time Markov chain (CTMC), the PH fitting can provide approximate Markov models to any non-exponential stochastic models. Thus, the PH fitting is helpful for model-based performance evaluation. On the other hand, from the statistical point of view, the PH fitting is categorized as parameter estimation from data. Some efficient PH fitting techniques are based on the maximum-likelihood principle. Therefore, it is crucial to evaluate statistical errors, i.e., the variance and covariance of estimators. In maximum-likelihood estimation, the Fisher information matrix is a well-known method to compute the variance and covariance of estimators, and is obtained as the second derivative of the log-likelihood function (LLF). In this article, we propose an algorithm for efficiently computing the Fisher information matrix in PH fitting. By applying the uniformization technique to a CTMC, we design the algorithm for computing the second derivatives of LLF in PH fitting.

Effective and efficient emergency medical services (EMS) are a critical part of a national healthcare system. This paper describes research to model EMS by better capturing ambulance service times using Coxian phase-type (PH) distributions. Distributions are fitted to both the overall cycle time for different classes of patient priorities, as well as to sub-cycles. Sub-cycles are the distinct identifiable parts of the ambulance cycle time, such as travel times, time on scene and turnaround time at the hospital. The Coxian PH fits have then been used within a priority simulation model to provide guidance on the number of ambulances required to meet response time targets. Results from using various numbers of phases from the fitted Coxian distributions are compared. The proposed benefit of using sub-cycle fits is that it more readily permits scenario modelling within the simulation, such as evaluating the impact of reducing the turnaround time on the overall response times in the ambulance system.

In this paper, the sensitivity of the handoff dwell time (HDT) model on wireless mobile network performance is studied. We present an approach on the basis of the universal approximation property of phase-type (PH) distribution in order to address the intractable numerical issue caused by HDT. We first obtain the steady state probability under the general HDT. The performance metrics from the perspective of base station (BS) as well as from the point view of call are developed. The PH-type HDT is then assumed to derive the numerically tractable expressions for the performance metrics. Finally, the truncated Gaussian HDT is approximately fitted by the PH distribution via expectation maximization algorithm to reuse the closed form analytical expression. The comparison shows that, in terms of the BS performance, the handoff blocking probability exhibits a significant discrepancy whenever one uses the exponential or truncated Gaussian HDT distribution, while the new call blocking probability is less sensitive to different HDT. In addition, HDT has little impact on the call performance with respect to the call completion probability and total waiting time. Both the analytical model and the approximation approach are verified by simulation.

In this paper, we investigate a wear and mixed shock model in which the system can fail due to internal aging or external shocks. The lifetime of the system, due to internal wear, follows continuous phase-type (PH) distributions. The external random shocks arrive at the system according to a PH renewal process. The system will fail when the internal failure occurs or k1 consecutive external shocks, the size of at least d1 or k2 consecutive external shocks the size of at least d2 occur, where d1<d2, k1>k2. The failed system can be repaired immediately, and the repair times of the system are governed by continuous PH distributions. The system can be replaced by a new and identical one based on a bivariate replacement policy (L,N). The long-run average profit rate for the system is obtained by employing the closure property of the PH distribution. Finally, a numerical example is also given to determine the optimal replacement policy.

This paper studies a series repairable system with a single repair facility in which the component lifetime and repair time are subject to general distribution that can be represented as Phase-type (PH) distribution. Based on the basic assumption, the proposed model is more suitable to characterize the real situation. The process of solving system steady-state probability is provided, and the analytical expressions for system stationary availability, mean time between failures (MTBF), mean down time (MDT), reliability and failure rate functions are expressed. Finally, the validity and applicability of the model are illustrated with a numerical example.

e21557 Background: High-risk melanoma pts treated with ipi had a more favorable outcome than those treated with interferon-α2b (IFN) in phase III adjuvant trial E1609. We hypothesized that further profiling of circulating immune cells and cytokines would inform underlying mechanisms associated with immune response vs. resistance to CTLA4 blockade. Methods: Multiparameter flow cytometry was used to compare surface protein expression on PBMC collected at baseline, focusing on Treg, MDSC and effector T cells (N = 210 ipi, N = 119 IFN). Multiplex Luminex assays were used to test baseline serum for concentrations of candidate cytokines, chemokines and growth factors. A survival analysis tool, DRPPM-PATH-SURVEIOR, was then used to perform a univariate screening of these analytes using a Cox proportional hazards (PH) model. A median cut-point was derived for each marker, and pts were split into above or below median cohorts. The dichotomized scores were then processed through a Cox regression analysis. Features were ranked based on p-values calculated by a likelihood test for overall survival (OS) and recurrence-free survival (RFS). A Lasso Cox regression model was further developed using Glmnet by optimizing lambda at minimum mean cross-validated error. Pts were randomly and evenly split into training and testing datasets. Results: Initial univariate Cox PH regression model screening identified 6 cellular and 2 serum protein biomarkers associated with OS and RFS. Enriched populations of CTLA4+ Treg (CD3+/CD4+/CD25hi+/CD152+) and monocytic (M)-MDSC (Lin-CD33+/HLA-DRlo+/CD14+/CD15+) were identified as being associated with poor outcome, while enriched populations of CXCR3+/CD4+ T cells, CXCR3+/CD8+ T cells, CTLA4+/INFg+/CD8+ T cells and CD39+ Treg (CD3+/CD4+/CD25hi+/CD39+) were associated with better outcome. Higher levels of CCL3 and CXCL11 chemokines in serum were associated with improved OS and RFS. To develop a prognostic model predictive of ipi treatment benefits, we focused on top ranked biomarkers and generated and tested a Lasso Cox regression model based on CTLA4+ Treg, M-MDSC and CXCR3+/CD8+ T cell populations using a training subset (N = 105 ipi pts). This model was predictive of pt OS and RFS in the testing subset (N = 105) with C-index = 0.67. To examine broader applicability of our Lasso Cox model, we analyzed an additional 119 pts treated on the IFN control arm. By incorporating treatment arm as an interaction term with our 3 biomarker Lasso Cox score, our model was determined to be predictive of risk in pts treated with ipi but not IFN. Conclusions: Our analysis confirms the predictive value of a 3 biomarker Lasso Cox score predicated on CTLA4+ Treg, M-MDSC and CXCR3+/CD8+ T cell content in patient blood at baseline as it relates to adjuvant ipi treatment outcomes.

Considering maintenance resources assignments of the large-scale complex equipment, the policy that single repairman has multiple vacations is utilized to analyze a warm standby repairable system. The former models that the known conditions are usually assumed to follow exponential distribution or other typical distributions have many constraint conditions. It is assumed that the online component lifetime, standby components lifetime, repair time and repairman vacation time are subject to different continuous Phase-type (PH) distribution, respectively. The reliability model with high versatile is acquired. The reliability features, such as system reliability function, system stationary availability, stationary failure frequency and mean time between failures (MTBF), are provided by the model. Finally, the applicability of the model is implemented by numerical application, and the influences of standby components counts and vacations or non-vacation of a repairman on the system reliability laws are demonstrated.

In this paper, we study a multi-server queueing system with retrials and an infinite orbit. The arrival of primary customers is described by a batch Markovian arrival process (BMAP), and the service times have a phase-type (PH) distribution. Previously, in the literature, such a system was mainly considered under the strict assumption that the intervals between the repeated attempts from the orbit have an exponential distribution. Only a few publications dealt with retrial queueing systems with non-exponential inter-retrial times. These publications assumed either the rate of retrials is constant regardless of the number of customers in the orbit or this rate is constant when the number of orbital customers exceeds a certain threshold. Such assumptions essentially simplify the mathematical analysis of the system, but do not reflect the nature of the majority of real-life retrial processes. The main feature of the model under study is that we considered the classical retrial strategy under which the retrial rate is proportional to the number of orbital customers. However, in this case, the assumption of the non-exponential distribution of inter-retrial times leads to insurmountable computational difficulties. To overcome these difficulties, we supposed that inter-retrial times have a phase-type distribution if the number of customers in the orbit is less than or equal to some non-negative integer (threshold) and have an exponential distribution in the contrary case. By appropriately choosing the threshold, one can obtain a sufficiently accurate approximation of the system with a PH distribution of the inter-retrial times. Thus, the model under study takes into account the realistic nature of the retrial process and, at the same time, does not resort to restrictions such as a constant retrial rate or to rough truncation methods often applied to the analysis of retrial queueing systems with an infinite orbit. We describe the behavior of the system by a multi-dimensional Markov chain, derive the stability condition, and calculate the steady-state distribution and the main performance indicators of the system. We made sure numerically that there was a reasonable value of the threshold under which our model can be served as a good approximation of the BMAP/PH/N queueing system with the PH distribution of inter-retrial times. We also numerically compared the system under consideration with the corresponding queueing system having exponentially distributed inter-retrial times and saw that the latter is a poor approximation of the system with the PH distribution of inter-retrial times. We present a number of illustrative numerical examples to analyze the behavior of the system performance indicators depending on the system parameters, the variance of inter-retrial times, and the correlation in the input flow.

Efficient and accurate methods are indispensible in the evaluation of complex systems. Methods of various abstraction levels may be applied, ranging from measurements in test-beds over simulation to analytical approaches. These methods vary in their efficiency and accuracy. In order to obtain realistic results, methods from all abstraction levels should be applied. Furthermore, real-world phenomena must be represented in a suitable way at all abstraction levels. This approach requires the use of stochastic models for the faults that may affect a system. This thesis explores several important issues of system evaluation using stochastic fault models. The first part of the thesis provides a survey of stochastic fault-models for system evaluation. We survey a broad range of existing fault-models and provide a new classification scheme for fault models in service-oriented systems. In the second part of the thesis we address the use of phase-type (PH) distributions as fault models in system evaluation. We study algorithms for random-variate generation and discuss their computational costs. An optimisation method for reducing the cost of random-variate generation by transformation of the representation is presented and an optimality result for the sub-class of acyclic phase-type distributions is derived. We then develop a new algorithm for efficient and user-friendly fitting of PH distributions to data sets using clustering. The algorithm is implemented as part of the HyperStar tool. We additionally illustrate application of HyperStar as a graphical user interface for prototype algorithms using a new algorithm for fitting general PH distributions. The third part illustrates application of the results from the first and second parts. We first study the application of stochastic fault models for IP packet loss in fault-injection and investigate the interaction between fault models and traffic arrival streams and its impact on evaluation results. We then describe a library for random-variate generation from phase-type distributions and show its use in two case-studies.

The Nelson-Aalen estimator provides the basis for the ubiquitous Kaplan-Meier estimator, and therefore is an essential tool for nonparametric survival analysis. This article reviews martingale theory and its role in demonstrating that the Nelson-Aalen estimator is uniformly consistent for estimating the cumulative hazard function for right-censored continuous time-to-failure data.

As a result of social awareness of air emission due to the use of fossil fuels, the utilization of the natural wind power resources becomes an important option to avoid the dependence on fossil resources in industrial activities. For example, the maritime industry, which is responsible for more than 90% of the world trade transport, has already started to look for solutions to use wind power as auxiliary propulsion for ships. The practical installation of the wind facilities often requires large amount of investment, while uncertainties for the corresponding energy gains are large. Therefore a reliable model to describe the variability of wind speeds is needed to estimate the expected available wind power, coefficient of the variation of the power and other statistics of interest, e.g. expected length of the wind conditions favorable for the wind-energy harvesting. In this paper, wind speeds are modeled by means of a spatio-temporal transformed Gaussian field. Its dependence structure is localized by introduction of time and space dependent parameters in the field. The model has the advantage of having a relatively small number of parameters. These parameters have natural physical interpretation and are statistically fitted to represent variability of observed wind speeds in ERA Interim reanalysis data set.