Application of Mixture Models to Survival Data

Survival models are being widely applied to the engineering field to model time-to-event data once censored data is here a common issue. Using parametric models or not, for the case of heterogeneous data, they may not always represent a good fit. The present study relays on critical pumps survival data where traditional parametric regression might be improved in order to obtain better approaches. Considering censored data and using an empiric method to split the data into two subgroups to give the possibility to fit separated models to our censored data, we’ve mixture two distinct distributions according a mixture-models approach. We have concluded that it is a good method to fit data that does not fit to a usual parametric distribution and achieve reliable parameters. A constant cumulative hazard rate policy was used as well to check optimum inspection times using the obtained model from the mixture-model, which could be a plus when comparing with the actual maintenance policies to check whether changes should be introduced or not.

Hazard based models for freeway traffic incident duration

Assessing and prioritising cost-effective strategies to mitigate the impacts of traffic incidents and accidents on non-recurrent congestion on major roads represents a significant challenge for road network managers. This research examines the influence of numerous factors associated with incidents of various types on their duration. It presents a comprehensive traffic incident data mining and analysis by developing an incident duration model based on twelve months of incident data obtained from the Australian freeway network. Parametric accelerated failure time (AFT) survival models of incident duration were developed, including log-logistic, lognormal, and Weibul-considering both fixed and random parameters, as well as a Weibull model with gamma heterogeneity. The Weibull AFT models with random parameters were appropriate for modelling incident duration arising from crashes and hazards. A Weibull model with gamma heterogeneity was most suitable for modelling incident duration of stationary vehicles. Significant variables affecting incident duration include characteristics of the incidents (severity, type, towing requirements, etc.), and location, time of day, and traffic characteristics of the incident. Moreover, the findings reveal no significant effects of infrastructure and weather on incident duration. A significant and unique contribution of this paper is that the durations of each type of incident are uniquely different and respond to different factors. The results of this study are useful for traffic incident management agencies to implement strategies to reduce incident duration, leading to reduced congestion, secondary incidents, and the associated human and economic losses.

The impact of risk-reducing hysterectomy and bilateral salpingo-oophorectomy on survival in patients with a history of breast cancer – a population-based data linkage study

Prophylactic surgery including hysterectomy and bilateral salpingo-oophorectomy (BSO) is recommended in BRCA positive women, while in women from the general population, hysterectomy plus BSO may increase the risk of overall mortality. The effect of hysterectomy plus BSO on women previously diagnosed with breast cancer is unknown. We used data from a population-base data linkage study of all women diagnosed with primary breast cancer in Queensland, Australia between 1997 and 2008 (n=21,067). We fitted flexible parametric breast cancer specific and overall survival models with 95% confidence intervals (also known as Royston-Parmar models) to assess the impact of risk-reducing surgery (removal of uterus, one or both ovaries). We also stratified analyses by age 20-49 and 50-79 years, respectively. Overall, 1,426 women (7%) underwent risk-reducing surgery (13% of premenopausal women and 3% of postmenopausal women). No women who had risk-reducing surgery, compared to 171 who did not have risk-reducing surgery developed a gynaecological cancer. Overall, 3,165 (15%) women died, including 2,195 (10%) from breast cancer. Hysterectomy plus BSO was associated with significantly reduced risk of death overall (adjusted HR = 0.69, 95% CI 0.53-0.89; P =0.005). Risk reduction was greater among premenopausal women, whose risk of death halved (HR, 0.45; 95% CI, 0.25-0.79; P < 0.006). This was largely driven by reduction in breast cancer-specific mortality (HR, 0.43; 95% CI, 0.24-0.79; P < 0.006). This population-based study found that risk-reducing surgery halved the mortality risk for premenopausal breast cancer patients. Replication of our results in independent cohorts, and subsequently randomised trials are needed to confirm these findings.

Destructive weighted Poisson cure rate models

In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow a compound weighted Poisson distribution. This model is more flexible in terms of dispersion than the promotion time cure model. Moreover, it gives an interesting and realistic interpretation of the biological mechanism of the occurrence of event of interest as it includes a destructive process of the initial risk factors in a competitive scenario. In other words, what is recorded is only from the undamaged portion of the original number of risk factors.

A flexible model for survival data with a cure rate: a Bayesian approach

In this paper we deal with a Bayesian analysis for right-censored survival data suitable for populations with a cure rate. We consider a cure rate model based on the negative binomial distribution, encompassing as a special case the promotion time cure model. Bayesian analysis is based on Markov chain Monte Carlo (MCMC) methods. We also present some discussion on model selection and an illustration with a real dataset.

A Bayesian Long-term Survival Model Parametrized in the Cured Fraction

The main goal of this paper is to investigate a cure rate model that comprehends some well-known proposals found in the literature. In our work the number of competing causes of the event of interest follows the negative binomial distribution. The model is conveniently reparametrized through the cured fraction, which is then linked to covariates by means of the logistic link. We explore the use of Markov chain Monte Carlo methods to develop a Bayesian analysis in the proposed model. The procedure is illustrated with a numerical example.

Psychosocial factors and survival of young women with breast cancer: a population-based prospective cohort study

Purpose: Most women with early-stage breast cancer believe that psychosocial factors are an important influence over whether their cancer will recur. Studies of the issue have produced conflicting results.

Patients and Methods: A population-based sample of 708 Australian women diagnosed before age 60 years with nonmetastatic breast cancer was observed for a median of 8.2 years. Depression and anxiety, coping style, and social support were assessed at a median of 11 months after diagnosis. Hazard ratios for distant disease-free survival (DDFS) and overall survival (OS) associated with psychosocial factors were estimated separately using Cox proportional hazards survival models, with and without adjustment for known prognostic factors.

Results: Distant recurrence occurred in 209 (33%) of 638 assessable patients, and 170 (24%) of 708 patients died during the follow-up period. There were no statistically significant associations between any of the measured psychosocial factors and DDFS or OS from the adjusted analyses. From unadjusted analyses, associations between greater anxious preoccupation and poorer DDFS and OS were observed (P = .02). These associations were no longer evident after adjustment for established prognostic factors; greater anxious preoccupation was associated with younger age at diagnosis (P = .03), higher tumor grade (P = .02), and greater number of involved axillary nodes (P = .008).

Conclusion: The findings do not support the measured psychosocial factors being an important influence on breast cancer outcomes. Interventions for adverse psychosocial factors are warranted to improve quality of life but should not be expected to improve survival.

SAS macros for point and interval estimation of area under the receiver operating characteristic curve for non-proportional and proportional hazards Weibull models

Aims and objectives  For prediction of risk of cardiovascular end points using survival models the proportional hazards assumption is often not met. Thus, non-proportional hazards models are more appropriate for developing risk prediction equations in such situations. However, computer program for evaluating the prediction performance of such models has been rarely addressed. We therefore developed SAS macro programs for evaluating the discriminative ability of a non-proportional hazards Weibull model developed by Anderson (1991) and that of a proportional hazards Weibull model using the area under receiver operating characteristic (ROC) curve.

Method  Two SAS macro programs for non-proportional hazards Weibull model using Proc NLIN and Proc NLP respectively and model validation using area under ROC curve (with its confidence limits) were written with SAS IML language. A similar SAS macro for proportional hazards Weibull model was also written.

Results  The computer program was applied to data on coronary heart disease incidence for a Framingham population cohort. The five risk factors considered were current smoking, age, blood pressure, cholesterol and obesity. The predictive ability of the non-proportional hazard Weibull model was slightly higher than that of its proportional hazard counterpart. An advantage of SAS Proc NLP in terms of the example provided here is that it provides significance level for the parameter estimates whereas Proc NLIN does not.

Conclusion  The program is very useful for evaluating the predictive performance of non-proportional and proportional hazards Weibull models.

SURVIVAL PREDICTION FOR BRAIN TUMOR PATIENTS USING GENE EXPRESSION DATA

Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. In order to evaluate this hypothesis, the general goal of this research is to build models for survival prediction of glioma patients using DNA molecular profiles (U133 Affymetrix gene expression microarrays) along with clinical information. First, a predictive Random Forest model is built for binary outcomes (i.e. short vs. long-term survival) and a small subset of genes whose expression values can be used to predict survival time is selected. Following, a new statistical methodology is developed for predicting time-to-death outcomes using Bayesian ensemble trees. Due to a large heterogeneity observed within prognostic classes obtained by the Random Forest model, prediction can be improved by relating time-to-death with gene expression profile directly. We propose a Bayesian ensemble model for survival prediction which is appropriate for high-dimensional data such as gene expression data. Our approach is based on the ensemble "sum-of-trees" model which is flexible to incorporate additive and interaction effects between genes. We specify a fully Bayesian hierarchical approach and illustrate our methodology for the CPH, Weibull, and AFT survival models. We overcome the lack of conjugacy using a latent variable formulation to model the covariate effects which decreases computation time for model fitting. Also, our proposed models provides a model-free way to select important predictive prognostic markers based on controlling false discovery rates. We compare the performance of our methods with baseline reference survival methods and apply our methodology to an unpublished data set of brain tumor survival times and gene expression data, selecting genes potentially related to the development of the disease under study. A closing discussion compares results obtained by Random Forest and Bayesian ensemble methods under the biological/clinical perspectives and highlights the statistical advantages and disadvantages of the new methodology in the context of DNA microarray data analysis.

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. ^

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.

On the Advancement of Probabilistic Models of Decompression Sickness

The work presented in this dissertation is focused on applying engineering methods to develop and explore probabilistic survival models for the prediction of decompression sickness in US NAVY divers. Mathematical modeling, computational model development, and numerical optimization techniques were employed to formulate and evaluate the predictive quality of models fitted to empirical data. In Chapters 1 and 2 we present general background information relevant to the development of probabilistic models applied to predicting the incidence of decompression sickness. The remainder of the dissertation introduces techniques developed in an effort to improve the predictive quality of probabilistic decompression models and to reduce the difficulty of model parameter optimization.

The first project explored seventeen variations of the hazard function using a well-perfused parallel compartment model. Models were parametrically optimized using the maximum likelihood technique. Model performance was evaluated using both classical statistical methods and model selection techniques based on information theory. Optimized model parameters were overall similar to those of previously published Results indicated that a novel hazard function definition that included both ambient pressure scaling and individually fitted compartment exponent scaling terms.

We developed ten pharmacokinetic compartmental models that included explicit delay mechanics to determine if predictive quality could be improved through the inclusion of material transfer lags. A fitted discrete delay parameter augmented the inflow to the compartment systems from the environment. Based on the observation that symptoms are often reported after risk accumulation begins for many of our models, we hypothesized that the inclusion of delays might improve correlation between the model predictions and observed data. Model selection techniques identified two models as having the best overall performance, but comparison to the best performing model without delay and model selection using our best identified no delay pharmacokinetic model both indicated that the delay mechanism was not statistically justified and did not substantially improve model predictions.

Our final investigation explored parameter bounding techniques to identify parameter regions for which statistical model failure will not occur. When a model predicts a no probability of a diver experiencing decompression sickness for an exposure that is known to produce symptoms, statistical model failure occurs. Using a metric related to the instantaneous risk, we successfully identify regions where model failure will not occur and identify the boundaries of the region using a root bounding technique. Several models are used to demonstrate the techniques, which may be employed to reduce the difficulty of model optimization for future investigations.

The prognostic significance of quality of life following breast cancer [Conference Abstract]

Introduction: Evidence suggests a positive association between quality of life (QOL). and overall survival(OS). among metastatic breast cancer (BC). patients, although the relationship in early-stage BC is unclear. This work examines the association between QOL and OS following a diagnosis of early-stage BC. ----- Methods: A population-based sample of Queensland women (n=287). with early-stage, invasive, unilateral BC, were prospectively observed for a median of 6.6 years. QOL was assessed at six and 18 months post-diagnosis using the Functional Assessment of Cancer Therapy, Breast FACT-B+4. questionnaire. Raw scores for the FACT-B+4 scales were computed and individuals were categorised according to whether QOL declined, remained stable or improved over time. OS was measured from the date of diagnosis to the date of death or was censored at the date of last follow-up. Risk ratios (RR) and 95% confidence intervals (CI). for the association between QOL and OS were obtained using Cox proportional hazards survival models adjusted for confounding characteristics. ----- Results: A total of 27 (9.4%). women died during the follow-up period. Three baseline QOL scales (emotional, general and overall QOL) were significantly associated with OS, with RRs ranging between 0.89 95% CI: 0.81, 0.98; P=0.01. and 0.98 (95% CI: 0.96, 0.99; P=0.03),indicating a 2%-11% reduced risk of death for every one unit increase in QOL. When QOL was categorised according to changes between six and 18 months post-diagnosis, analyses showed that for those who experienced declines in functional and physical QOL, risk of death increased by two- (95% CI: 1.43, 12.52; P<0.01) and four-fold (95% CI: 1.15, 7.19; P=0.02), respectively. Conclusions: This work indicates that specific QOL scales at six months post-diagnosis, and changes in certain QOL scales over the subsequent 12-month period (as measured by the FACT-B+4), are associated with overall survival in women with early-stage breast cancer.

Prognostic significance of IGF and ECM induced signalling proteins in breast cancer patients

Breast cancer is a leading contributor to the burden of disease in Australia. Fortunately, the recent introduction of diverse therapeutic strategies have improved the survival outcome for many women. Despite this, the clinical management of breast cancer remains problematic as not all approaches are sufficiently sophisticated to take into account the heterogeneity of this disease and are unable to predict disease progression, in particular, metastasis. As such, women with good prognostic outcomes are exposed to the side effects of therapies without added benefit. Furthermore, women with aggressive disease for whom these advanced treatments would deliver benefit cannot be distinguished and opportunities for more intensive or novel treatment are lost. This study is designed to identify novel factors associated with disease progression, and the potential to inform disease prognosis. Frequently overlooked, yet common mediators of disease are the interactions that take place between the insulin-like growth factor (IGF) system and the extracellular matrix (ECM). Our laboratory has previously demonstrated that multiprotein insulin-like growth factor-I (IGF-I): insulin-like growth factor binding protein (IGFBP): vitronectin (VN) complexes stimulate migration of breast cancer cells in vitro, via the cooperative involvement of the insulin-like growth factor type I receptor (IGF-IR) and VN-binding integrins. However, the effects of IGF and ECM protein interactions on the dissemination and progression of breast cancer in vivo are unknown. It was hypothesised that interactions between proteins required for IGF induced signalling events and those within the ECM contribute to breast cancer metastasis and are prognostic and predictive indicators of patient outcome. To address this hypothesis, semiquantitative immunohistochemistry (IHC) analyses were performed to compare the extracellular and subcellular distribution of IGF and ECM induced signalling proteins between matched normal, primary cancer, and metastatic cancer among archival formalin-fixed paraffin-embedded (FFPE) breast tissue samples collected from women attending the Princess Alexandra Hospital, Brisbane. Multivariate Cox proportional hazards (PH) regression survival models in conjunction with a modified „purposeful selection of covariates. method were applied to determine the prognostic potential of these proteins. This study provides the first in-depth, compartmentalised analysis of the distribution of IGF and ECM induced signalling proteins. As protein function and protein localisation are closely correlated, these findings provide novel insights into IGF signalling and ECM protein function during breast cancer development and progression. Distinct IGF signalling and ECM protein immunoreactivity was observed in the stroma and/or in subcellular locations in normal breast, primary cancer and metastatic cancer tissues. Analysis of the presence and location of stratifin (SFN) suggested a causal relationship in ECM remodelling events during breast cancer development and progression. The results of this study have also suggested that fibronectin (FN) and ¥â1 integrin are important for the formation of invadopodia and epithelial-to-mesenchymal transition (EMT) events. Our data also highlighted the importance of the temporal and spatial distribution of IGF induced signalling proteins in breast cancer metastasis; in particular, SFN, enhancer-of-split and hairy-related protein 2 (SHARP-2), total-akt/protein kinase B 1 (Total-AKT1), phosphorylated-akt/protein kinase B (P-AKT), extracellular signal-related kinase-1 and extracellular signal-related kinase-2 (ERK1/2) and phosphorylated-extracellular signal-related kinase-1 and extracellular signal-related kinase-2 (P-ERK1/2). Multivariate survival models were created from the immunohistochemical data. These models were found to fit well with these data with very high statistical confidence. Numerous prognostic confounding effects and effect modifications were identified among elements of the ECM and IGF signalling cascade and corroborate the survival models. This finding provides further evidence for the prognostic potential of IGF and ECM induced signalling proteins. In addition, the adjusted measures of associations obtained in this study have strengthened the validity and utility of the resulting models. The findings from this study provide insights into the biological interactions that occur during the development of breast tissue and contribute to disease progression. Importantly, these multivariate survival models could provide important prognostic and predictive indicators that assist the clinical management of breast disease, namely in the early identification of cancers with a propensity to metastasise, and/or recur following adjuvant therapy. The outcomes of this study further inform the development of new therapeutics to aid patient recovery. The findings from this study have widespread clinical application in the diagnosis of disease and prognosis of disease progression, and inform the most appropriate clinical management of individuals with breast cancer.

Modelling total duration of traffic incidents including incident detection and recovery time

Traffic incidents are key contributors to non-recurrent congestion, potentially generating significant delay. Factors that influence the duration of incidents are important to understand so that effective mitigation strategies can be implemented. To identify and quantify the effects of influential factors, a methodology for studying total incident duration based on historical data from an ‘integrated database’ is proposed. Incident duration models are developed using a selected freeway segment in the Southeast Queensland, Australia network. The models include incident detection and recovery time as components of incident duration. A hazard-based duration modelling approach is applied to model incident duration as a function of a variety of factors that influence traffic incident duration. Parametric accelerated failure time survival models are developed to capture heterogeneity as a function of explanatory variables, with both fixed and random parameters specifications. The analysis reveals that factors affecting incident duration include incident characteristics (severity, type, injury, medical requirements, etc.), infrastructure characteristics (roadway shoulder availability), time of day, and traffic characteristics. The results indicate that event type durations are uniquely different, thus requiring different responses to effectively clear them. Furthermore, the results highlight the presence of unobserved incident duration heterogeneity as captured by the random parameter models, suggesting that additional factors need to be considered in future modelling efforts.