Motorway crash duration and its determinants: Do durations vary across motorways?

Traffic congestion has been a growing issue in many metropolitan areas during recent years, which necessitates the identification of its key contributors and development of sustainable strategies to help decrease its adverse impacts on traffic networks. Road incidents generally and crashes specifically have been acknowledged as the cause of a large proportion of travel delays in urban areas and account for 25% to 60% of traffic congestion on motorways. Identifying the critical determinants of travel delays has been of significant importance to the incident management systems which constantly collect and store the incident duration data. This study investigates the individual and simultaneous differential effects of the relevant determinants on motorway crash duration probabilities. In particular, it applies parametric Accelerated Failure Time (AFT) hazard-based models to develop in-depth insights into how the crash-specific characteristic and the associated temporal and infrastructural determinants impact the duration. AFT models with both fixed and random parameters have been calibrated on one year of traffic crash records from two major Australian motorways in South East Queensland and the differential effects of determinants on crash survival functions have been studied on these two motorways individually. A comprehensive spectrum of commonly used parametric fixed parameter AFT models, including generalized gamma and generalized F families, have been compared to random parameter AFT structures in terms of goodness of fit to the duration data and as a result, the random parameter Weibull AFT model has been selected as the most appropriate model. Significant determinants of motorway crash duration included traffic diversion requirement, crash injury type, number and type of vehicles involved in a crash, day of week and time of day, towing support requirement and damage to the infrastructure. A major finding of this research is that the motorways under study are significantly different in terms of crash durations; such that motorway exhibits durations that are on average 19% shorter compared to the durations on motorway. The differential effects of explanatory variables on crash durations are also different on the two motorways. The detailed presented analysis confirms that, looking at the motorway network as a whole, neglecting the individual differences between roads, can lead to erroneous interpretations of duration and inefficient strategies for mitigating travel delays along a particular motorway.

Markers Models in Survival Analysis and Applications to Issues Associated with AIDS

Jewell and Kalbfleisch (1992) consider the use of marker processes for applications related to estimation of the survival distribution of time to failure. Marker processes were assumed to be stochastic processes that, at a given point in time, provide information about the current hazard and consequently on the remaining time to failure. Particular attention was paid to calculations based on a simple additive model for the relationship between the hazard function at time t and the history of the marker process up until time t. Specific applications to the analysis of AIDS data included the use of markers as surrogate responses for onset of AIDS with censored data and as predictors of the time elapsed since infection in prevalent individuals. Here we review recent work on the use of marker data to tackle these kinds of problems with AIDS data. The Poisson marker process with an additive model, introduced in Jewell and Kalbfleisch (1992) may be a useful "test" example for comparison of various procedures.

Bayesian survival analysis using gene expression

This thesis developed and applied Bayesian models for the analysis of survival data. The gene expression was considered as explanatory variables within the Bayesian survival model which can be considered the new contribution in the analysis of such data. The censoring factor that is inherent of survival data has also been addressed in terms of its impact on the fitting of a finite mixture of Weibull distribution with and without covariates. To investigate this, simulation study were carried out under several censoring percentages. Censoring percentage as high as 80% is acceptable here as the work involved high dimensional data. Lastly the Bayesian model averaging approach was developed to incorporate model uncertainty in the prediction of survival.

Survival analysis of time-to-event data in respiratory health research studies

This article provides a review of techniques for the analysis of survival data arising from respiratory health studies. Popular techniques such as the Kaplan–Meier survival plot and the Cox proportional hazards model are presented and illustrated using data from a lung cancer study. Advanced issues are also discussed, including parametric proportional hazards models, accelerated failure time models, time-varying explanatory variables, simultaneous analysis of multiple types of outcome events and the restricted mean survival time, a novel measure of the effect of treatment.

Survival analysis of time-to-event data in respiratory health research studies

This article provides a review of techniques for the analysis of survival data arising from respiratory health studies. Popular techniques such as the Kaplan–Meier survival plot and the Cox proportional hazards model are presented and illustrated using data from a lung cancer study. Advanced issues are also discussed, including parametric proportional hazards models, accelerated failure time models, time-varying explanatory variables, simultaneous analysis of multiple types of outcome events and the restricted mean survival time, a novel measure of the effect of treatment.

Survival Analysis of Patients with Heart Failure: Implications of Time-Varying Regression Effects in Modeling Mortality

Background: Several models have been designed to predict survival of patients with heart failure. These, while available and widely used for both stratifying and deciding upon different treatment options on the individual level, have several limitations. Specifically, some clinical variables that may influence prognosis may have an influence that change over time. Statistical models that include such characteristic may help in evaluating prognosis. The aim of the present study was to analyze and quantify the impact of modeling heart failure survival allowing for covariates with time-varying effects known to be independent predictors of overall mortality in this clinical setting. Methodology: Survival data from an inception cohort of five hundred patients diagnosed with heart failure functional class III and IV between 2002 and 2004 and followed-up to 2006 were analyzed by using the proportional hazards Cox model and variations of the Cox's model and also of the Aalen's additive model. Principal Findings: One-hundred and eighty eight (188) patients died during follow-up. For patients under study, age, serum sodium, hemoglobin, serum creatinine, and left ventricular ejection fraction were significantly associated with mortality. Evidence of time-varying effect was suggested for the last three. Both high hemoglobin and high LV ejection fraction were associated with a reduced risk of dying with a stronger initial effect. High creatinine, associated with an increased risk of dying, also presented an initial stronger effect. The impact of age and sodium were constant over time. Conclusions: The current study points to the importance of evaluating covariates with time-varying effects in heart failure models. The analysis performed suggests that variations of Cox and Aalen models constitute a valuable tool for identifying these variables. The implementation of covariates with time-varying effects into heart failure prognostication models may reduce bias and increase the specificity of such models.

Survival Analysis with Large Dimensional Covariates: An Application in Microarray Studies

Use of microarray technology often leads to high-dimensional and low- sample size data settings. Over the past several years, a variety of novel approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptation of the elastic net approach is presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time (AFT) model. Assessment of the two methods is conducted through simulation studies and through analysis of microarray data obtained from a set of patients with diffuse large B-cell lymphoma where time to survival is of interest. The approaches are shown to match or exceed the predictive performance of a Cox-based and an AFT-based variable selection method. The methods are moreover shown to be much more computationally efficient than their respective Cox- and AFT- based counterparts.

Semiparametric Normal Transformation Models for Spatially Correlated Survival Data

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiological studies. In this paper, we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivariate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields. We study the relationship of the spatial correlation structure of the transformed normal variables and the dependence measures of the original survival times. Direct nonparametric maximum likelihood estimation in such models is practically prohibited due to the high dimensional intractable integration of the likelihood function and the infinite dimensional nuisance baseline hazard parameter. We hence develop a class of spatial semiparametric estimating equations, which conveniently estimate the population-level regression coefficients and the dependence parameters simultaneously. We study the asymptotic properties of the proposed estimators, and show that they are consistent and asymptotically normal. The proposed method is illustrated with an analysis of data from the East Boston Ashma Study and its performance is evaluated using simulations.

Survival analysis of longevity in siblings

Do siblings of centenarians tend to have longer life spans? To answer this question, life spans of 184 siblings for 42 centenarians have been evaluated. Two important questions have been addressed in analyzing the sibling data. First, a standard needs to be established, to which the life spans of 184 siblings are compared. In this report, an external reference population is constructed from the U.S. life tables. Its estimated mortality rates are treated as baseline hazards from which the relative mortality of the siblings are estimated. Second, the standard survival models which assume independent observations are invalid when correlation within family exists, underestimating the true variance. Methods that allow correlations are illustrated by three different methods. First, the cumulative relative excess mortality between siblings and their comparison group is calculated and used as an effective graphic tool, along with the Product Limit estimator of the survival function. The variance estimator of the cumulative relative excess mortality is adjusted for the potential within family correlation using Taylor linearization approach. Second, approaches that adjust for the inflated variance are examined. They are adjusted one-sample log-rank test using design effect originally proposed by Rao and Scott in the correlated binomial or Poisson distribution setting and the robust variance estimator derived from the log-likelihood function of a multiplicative model. Nether of these two approaches provide correlation estimate within families, but the comparison with the comparison with the standard remains valid under dependence. Last, using the frailty model concept, the multiplicative model, where the baseline hazards are known, is extended by adding a random frailty term that is based on the positive stable or the gamma distribution. Comparisons between the two frailty distributions are performed by simulation. Based on the results from various approaches, it is concluded that the siblings of centenarians had significant lower mortality rates as compared to their cohorts. The frailty models also indicate significant correlations between the life spans of the siblings. ^

Survival analysis of circulating tumor cells in triple-negative breast cancer

Background. Breast cancer is the most frequently diagnosed cancer and the leading cause of cancer death among females, accounting for 23% (1.38 million) of the total new cancer cases and 14% (458,400) of the total cancer deaths in 2008. [1] Triple-negative breast cancer (TNBC) is an aggressive phenotype comprising 10–20% of all breast cancers (BCs). [2-4] TNBCs show absence of estrogen, progesterone and HER2/neu receptors on the tumor cells. Because of the absence of these receptors, TNBCs are not candidates for targeted therapies. Circulating tumor cells (CTCs) are observed in blood of breast cancer patients even at early stages (Stage I & II) of the disease. Immunological and molecular analysis can be used to detect the presence of tumor cells in the blood (Circulating tumor cells; CTCs) of many breast cancer patients. These cells may explain relapses in early stage breast cancer patients even after adequate local control. CTC detection may be useful in identifying patients at risk for disease progression, and therapies targeting CTCs may improve outcome in patients harboring them. Methods . In this study we evaluated 80 patients with TNBC who are enrolled in a larger prospective study conducted at M D Anderson Cancer Center in order to determine whether the presence of circulating tumor cells is a significant prognostic factor in relapse free and overall survival . Patients with metastatic disease at the time of presentation were excluded from the study. CTCs were assessed using CellSearch System™ (Veridex, Raritan, NJ). CTCs were defined as nucleated cells lacking the presence of CD45 but expressing cytokeratins 8, 18 or 19. The distribution of patient and tumor characteristics was analyzed using chi square test and Fisher's exact test. Log rank test and Cox regression analysis was applied to establish the association of circulating tumor cells with relapse free and overall survival. Results. The median age of the study participants was 53years. The median duration of follow-up was 40 months. Eighty-eight percent (88%) of patients were newly diagnosed (without a previous history of breast cancer), and (60%) of patients were chemo naïve (had not received chemotherapy at the time of their blood draw for CTC analysis). Tumor characteristics such as stage (P=0.40), tumor size (P=69), sentinel nodal involvement (P=0.87), axillary lymph node involvement (P=0.13), adjuvant therapy (P=0.83), and high histological grade of tumor (P=0.26) did not predict the presence of CTCs. However, CTCs predicted worse relapse free survival (1 or more CTCs log rank P value = 0.04, at 2 or more CTCs P = 0.02 and at 3 or more CTCs P < 0.0001) and overall survival (at 1 or more CTCs log rank P value = 0.08, at 2 or more CTCs P = 0.01 and at 3 or more CTCs P = 0.0001. Conclusions. The number of circulating tumor cells predicted worse relapse free survival and overall survival in TNBC patients.^

Modelling seed germination in forest tree species through survival analysis. The Pinus pinea L. case study

The direct application of existing models for seed germination may often be inadequate in the context of ecology and forestry germination experiments. This is because basic model assumptions are violated and variables available to forest managers are rarely used. In this paper, we present a method which addresses the aforementioned shortcomings. The approach is illustrated through a case study of Pinus pinea L. Our findings will also shed light on the role of germination in the general failure of natural regeneration in managed forests of this species. The presented technique consists of a mixed regression model based on survival analysis. Climate and stand covariates were tested. Data for fitting the model were gathered from a 5-year germination experiment in a mature, managed P. pinea stand in the Northern Plateau of Spain in which two different stand densities can be found. The model predictions proved to be unbiased and highly accurate when compared with the training data. Germination in P. pinea was controlled through thermal variables at stand level. At microsite level, low densities negatively affected the probability of germination. A time-lag in the response was also detected. Overall, the proposed technique provides a reliable alternative to germination modelling in ecology/forestry studies by using accessible/ suitable variables. The P. pinea case study highlights the importance of producing unbiased predictions. In this species, the occurrence and timing of germination suggest a very different regeneration strategy from that understood by forest managers until now, which may explain the high failure rate of natural regeneration in managed stands. In addition, these findings provide valuable information for the management of P. pinea under climate-change conditions.

Repeated occurrence of basal cell carcinoma of the skin and multifailure survival analysis: Follow-up data from the nambour skin cancer prevention trial

The aim of this study was to apply multifailure survival methods to analyze time to multiple occurrences of basal cell carcinoma (BCC). Data from 4.5 years of follow-up in a randomized controlled trial, the Nambour Skin Cancer Prevention Trial (1992-1996), to evaluate skin cancer prevention were used to assess the influence of sunscreen application on the time to first BCC and the time to subsequent BCCs. Three different approaches of time to ordered multiple events were applied and compared: the Andersen-Gill, Wei-Lin-Weissfeld, and Prentice-Williams-Peterson models. Robust variance estimation approaches were used for all multifailure survival models. Sunscreen treatment was not associated with time to first occurrence of a BCC (hazard ratio = 1.04, 95% confidence interval: 0.79, 1.45). Time to subsequent BCC tumors using the Andersen-Gill model resulted in a lower estimated hazard among the daily sunscreen application group, although statistical significance was not reached (hazard ratio = 0.82, 95% confidence interval: 0.59, 1.15). Similarly, both the Wei-Lin-Weissfeld marginal-hazards and the Prentice-Williams-Peterson gap-time models revealed trends toward a lower risk of subsequent BCC tumors among the sunscreen intervention group. These results demonstrate the importance of conducting multiple-event analysis for recurring events, as risk factors for a single event may differ from those where repeated events are considered.