A new class of survival regression models with heavy-tailed errors: robustness and diagnostics

Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability analyses to relate the total time until failure with some type of cumulative damage. In many problems related to the medical field, such as chronic cardiac diseases and different types of cancer, a cumulative damage caused by several risk factors might cause some degradation that leads to a fatigue process. In these cases, BS models can be suitable for describing the propagation lifetime. However, since the cumulative damage is assumed to be normally distributed in the BS distribution, the parameter estimates from this model can be sensitive to outlying observations. In order to attenuate this influence, we present in this paper BS models, in which a Student-t distribution is assumed to explain the cumulative damage. In particular, we show that the maximum likelihood estimates of the Student-t log-BS models attribute smaller weights to outlying observations, which produce robust parameter estimates. Also, some inferential results are presented. In addition, based on local influence and deviance component and martingale-type residuals, a diagnostics analysis is derived. Finally, a motivating example from the medical field is analyzed using log-BS regression models. Since the parameter estimates appear to be very sensitive to outlying and influential observations, the Student-t log-BS regression model should attenuate such influences. The model checking methodologies developed in this paper are used to compare the fitted models.

Modelling grouped survival times in toxicological studies using generalized additive models

A method for combining a proportional-hazards survival time model with a bioassay model where the log-hazard function is modelled as a linear or smoothing spline function of log-concentration combined with a smoothing spline function of time is described. The combined model is fitted to mortality numbers, resulting from survival times that are grouped due to a common set of observation times, using Generalized Additive Models (GAMs). The GAM fits mortalities as conditional binomials using an approximation to the log of the integral of the hazard function and is implemented using freely-available, general software for fitting GAMs. Extensions of the GAM are described to allow random effects to be fitted and to allow for time-varying concentrations by replacing time with a calibrated cumulative exposure variable with calibration parameter estimated using profile likelihood. The models are demonstrated using data from a studies of a marine and a, previously published, freshwater taxa. The marine study involved two replicate bioassays of the effect of zinc exposure on survival of an Antarctic amphipod, Orchomenella pinguides. The other example modelled survival of the daphnid, Daphnia magna, exposed to potassium dichromate and was fitted by both the GAM and the process-based DEBtox model. The GAM fitted with a cubic regression spline in time gave a 61 % improvement in fit to the daphnid data compared to DEBtox due to a non-monotonic hazard function. A simulation study using each of these hazard functions as operating models demonstrated that the GAM is overall more accurate in recovering lethal concentration values across the range of forms of the underlying hazard function compared to DEBtox and standard multiple endpoint probit analyses.

Tests of proportional hazards and proportional odds models for grouped survival data

In this paper, we derive score test statistics to discriminate between proportional hazards and proportional odds models for grouped survival data. These models are embedded within a power family transformation in order to obtain the score tests. In simple cases, some small-sample results are obtained for the score statistics using Monte Carlo simulations. Score statistics have distributions well approximated by the chi-squared distribution. Real examples illustrate the proposed tests.

Likelihood approximations and discrete models for tied survival data

Ties among event times are often recorded in survival studies. For example, in a two week laboratory study where event times are measured in days, ties are very likely to occur. The proportional hazards model might be used in this setting using an approximated partial likelihood function. This approximation works well when the number of ties is small. on the other hand, discrete regression models are suggested when the data are heavily tied. However, in many situations it is not clear which approach should be used in practice. In this work, empirical guidelines based on Monte Carlo simulations are provided. These recommendations are based on a measure of the amount of tied data present and the mean square error. An example illustrates the proposed criterion.

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.

Robust Inferences For Covariate Effects On Survival Time With Censored Linear Regression Models

Various inference procedures for linear regression models with censored failure times have been studied extensively. Recent developments on efficient algorithms to implement these procedures enhance the practical usage of such models in survival analysis. In this article, we present robust inferences for certain covariate effects on the failure time in the presence of "nuisance" confounders under a semiparametric, partial linear regression setting. Specifically, the estimation procedures for the regression coefficients of interest are derived from a working linear model and are valid even when the function of the confounders in the model is not correctly specified. The new proposals are illustrated with two examples and their validity for cases with practical sample sizes is demonstrated via a simulation study.

Development and Application of Predictive Models for Survival, Growth, and Death of Enteric Pathogens in Leafy Greens Supply Chain

Leafy greens are essential part of a healthy diet. Because of their health benefits, production and consumption of leafy greens has increased considerably in the U.S. in the last few decades. However, leafy greens are also associated with a large number of foodborne disease outbreaks in the last few years. The overall goal of this dissertation was to use the current knowledge of predictive models and available data to understand the growth, survival, and death of enteric pathogens in leafy greens at pre- and post-harvest levels. Temperature plays a major role in the growth and death of bacteria in foods. A growth-death model was developed for Salmonella and Listeria monocytogenes in leafy greens for varying temperature conditions typically encountered during supply chain. The developed growth-death models were validated using experimental dynamic time-temperature profiles available in the literature. Furthermore, these growth-death models for Salmonella and Listeria monocytogenes and a similar model for E. coli O157:H7 were used to predict the growth of these pathogens in leafy greens during transportation without temperature control. Refrigeration of leafy greens meets the purposes of increasing their shelf-life and mitigating the bacterial growth, but at the same time, storage of foods at lower temperature increases the storage cost. Nonlinear programming was used to optimize the storage temperature of leafy greens during supply chain while minimizing the storage cost and maintaining the desired levels of sensory quality and microbial safety. Most of the outbreaks associated with consumption of leafy greens contaminated with E. coli O157:H7 have occurred during July-November in the U.S. A dynamic system model consisting of subsystems and inputs (soil, irrigation, cattle, wildlife, and rainfall) simulating a farm in a major leafy greens producing area in California was developed. The model was simulated incorporating the events of planting, irrigation, harvesting, ground preparation for the new crop, contamination of soil and plants, and survival of E. coli O157:H7. The predictions of this system model are in agreement with the seasonality of outbreaks. This dissertation utilized the growth, survival, and death models of enteric pathogens in leafy greens during production and supply chain.

Integrating acoustic telemetry into mark-recapture models to improve the precision of apparent survival and abundance estimates

Capture-mark-recapture models are useful tools for estimating demographic parameters but often result in low precision when recapture rates are low. Low recapture rates are typical in many study systems including fishing-based studies. Incorporating auxiliary data into the models can improve precision and in some cases enable parameter estimation. Here, we present a novel application of acoustic telemetry for the estimation of apparent survival and abundance within capture-mark-recapture analysis using open population models. Our case study is based on simultaneously collecting longline fishing and acoustic telemetry data for a large mobile apex predator, the broadnose sevengill shark (Notorhynchus cepedianus), at a coastal site in Tasmania, Australia. Cormack-Jolly-Seber models showed that longline data alone had very low recapture rates while acoustic telemetry data for the same time period resulted in at least tenfold higher recapture rates. The apparent survival estimates were similar for the two datasets but the acoustic telemetry data showed much greater precision and enabled apparent survival parameter estimation for one dataset, which was inestimable using fishing data alone. Combined acoustic telemetry and longline data were incorporated into Jolly-Seber models using a Monte Carlo simulation approach. Abundance estimates were comparable to those with longline data only; however, the inclusion of acoustic telemetry data increased precision in the estimates. We conclude that acoustic telemetry is a useful tool for incorporating in capture-mark-recapture studies in the marine environment. Future studies should consider the application of acoustic telemetry within this framework when setting up the study design and sampling program.

Entrepreneurship and family firms : a case study in growth and survival

Entrepreneurial marketing has gained popularity in both the entrepreneurship and marketing disciplines in recent times. The success of ventures that have pursued what are considered non-traditional marketing approaches has been attributed to entrepreneurial marketing practices. Despite the multitude of marketing concepts and models, there are prominent venture successes that do not conform to these and have thus been put in the ''entrepreneurial'' box. One only has to look to the ''Virgin'' model to put this in context. Branson has proven for example that not ''sticking to the knitting'' can work with the ways the Virgin portfolio has been diversified. Consequently, an entrepreneurial orientation is considered a desirable philosophy and has become prominent in such industries as airlines and information technology. Miles and Arnold (1991) found that entrepreneurial orientation is positively correlated to marketing orientation. They propose that entrepreneurial orientation is a strategic response by firms to turbulence in the environment. While many marketing successes are analysed in hindsight using traditional marketing concepts and strategies, there are those that challenge standard marketing textbook recommendations. Marketing strategy is often viewed as a process of targeting, segmenting and positioning (STP). Academics and consultants advocate this approach along with the marketing and business plans. The reality however is that a number of businesses do not practice these and pursue alternative approaches. Other schools of thought and business models have been developing to explain differences in orientation such as branding (Keller 2001), the service-dominant logic (Vargo and Lusch 2004) and effectuation logic (Sarasvathy 2001). This indicates that scholars are now looking to cognate fields to explain a given phenomenon beyond their own disciplines. Bucking this trend is a growing number of researchers working at the interface between entrepreneurship and marketing. There is now an emerging body of work dedicated to this interface, hence the development of entrepreneurial marketing as an alternative to the traditional approaches. Hills and Hultman (2008:3) define entrepreneurial marketing as ''a spirit, an orientation as well as a process of passionately pursuing opportunities and launching and growing ventures that create perceived customer value through relationships by employing innovativeness, creativity, selling, market immersion, networking and flexibility.'' Although it started as a special interest group, entrepreneurial marketing is now gaining recognition in mainstream entrepreneurship and marketing literature. For example new marketing textbooks now incorporate an entrepreneurial marketing focus (Grewal and Levy 2008). The purpose of this paper is to explore what entrepreneurial approaches are used by entrepreneurs and their impact on the success of marketing activities. Methodology/Key Propositions In order to investigate this, we employ two cases: 42Below, vodka producers from New Zealand and Penderyn Distillery, whisky distillers from Wales. The cases were chosen based on the following criteria. Firstly, both companies originate from small economies. Secondly, both make products (spirits) from locations that are not traditionally regarded as producers of their flagship products and thirdly, the two companies are different from each other in terms of their age. Penderyn is an old company established in 1882, whereas 42Below was founded only in 1999. Vodka has never been associated with New Zealand. By the same token, whisky has always been associated with Scotland and Ireland but never been with Wales. Both companies defied traditional stereotypes in marketing their flagship products and found international success. Using a comparative a case study approach, we use Covin and Slevin's (1989) set of items that purport to measure entrepreneurial orientation and apply a qualitative lens on the approaches of both companies. These are: 1. cultural emphases on innovation and R&D 2. high rate of new product introduction 3. bold, innovative product development 4. initiator proactive posture 5. first to introduce new technologies and products 6. competitive posture toward competitor 7. strong prolictivity for high risk, high return projects 8. environment requires boldness to achieve objectives 9. when faced with risk, adopts aggressive, bold posture. Results and Implications We find that both companies have employed entrepreneurial marketing approaches but with different intensities. While acknowledging that they are different from the norm, the specifics of their individual approaches are dissimilar. Both companies have positioned their products at the premium end of their product categories and have emphasised quality and awards in their communication strategies. 42Below has carved an image of irreverence and being non-conformist. They have unashamedly utilised viral marketing and entered international markets by training bartenders and hosting unconventional events. They use edgy language such as vodka university, vodka professors and vodka ambassadors. Penderyn Distillery has taken a more traditional approach to marketing its products and portraying romantic images of age-old tradition of distilling as key to their positioning. Both companies enjoy success as evidenced by industry awards and international acclaim.

A review on reliability models with covariates

Modern Engineering Asset Management (EAM) requires the accurate assessment of current and the prediction of future asset health condition. Suitable mathematical models that are capable of predicting Time-to-Failure (TTF) and the probability of failure in future time are essential. In traditional reliability models, the lifetime of assets is estimated using failure time data. However, in most real-life situations and industry applications, the lifetime of assets is influenced by different risk factors, which are called covariates. The fundamental notion in reliability theory is the failure time of a system and its covariates. These covariates change stochastically and may influence and/or indicate the failure time. Research shows that many statistical models have been developed to estimate the hazard of assets or individuals with covariates. An extensive amount of literature on hazard models with covariates (also termed covariate models), including theory and practical applications, has emerged. This paper is a state-of-the-art review of the existing literature on these covariate models in both the reliability and biomedical fields. One of the major purposes of this expository paper is to synthesise these models from both industrial reliability and biomedical fields and then contextually group them into non-parametric and semi-parametric models. Comments on their merits and limitations are also presented. Another main purpose of this paper is to comprehensively review and summarise the current research on the development of the covariate models so as to facilitate the application of more covariate modelling techniques into prognostics and asset health management.