Residuals for log-Burr XII regression models in survival analysis

In this paper, we compare three residuals to assess departures from the error assumptions as well as to detect outlying observations in log-Burr XII regression models with censored observations. These residuals can also be used for the log-logistic regression model, which is a special case of the log-Burr XII regression model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to the modified martingale-type residual in log-Burr XII regression models with censored data.

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.

Survival Analysis Employed in Predicting Corporate Failure: A Forecasting Model Proposal

In face of the current economic and financial environment, predicting corporate bankruptcy is arguably a phenomenon of increasing interest to investors, creditors, borrowing firms, and governments alike. Within the strand of literature focused on bankruptcy forecasting we can find diverse types of research employing a wide variety of techniques, but only a few researchers have used survival analysis for the examination of this issue. We propose a model for the prediction of corporate bankruptcy based on survival analysis, a technique which stands on its own merits. In this research, the hazard rate is the probability of ‘‘bankruptcy’’ as of time t, conditional upon having survived until time t. Many hazard models are applied in a context where the running of time naturally affects the hazard rate. The model employed in this paper uses the time of survival or the hazard risk as dependent variable, considering the unsuccessful companies as censured observations.

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.

Prognostic factors and survival analysis in a sample of oral squamous cell carcinoma patients

Objectives. The aims of this report were to describe the 5-year overall survival (OS) in a group of oral squamous cell carcinoma (OSCC) patients and to investigate the effects of age, gender, anatomic localization, tumor evolution time, smoking and alcohol intake, nodal status, tumoral recurrences, histologic classification, p53 and p63 immunoexpression, human papillomavirus DNA presence, and treatment on the prognostic outcome. Study design. Survival curves were generated using Kaplan-Meier method, and univariate and multivariate analyses were made using the log rank test and Cox regression, respectively. Results. The 5-year OS was 28.6%, and the univariate analysis showed significant results for p53 and p63 immunoexpression, age, and anatomic localization. The Cox regression demonstrated poor OS for tumors with p53 immunoexpression and for patients aged over 60 years. There were also significant differences in survival depending on the anatomic localizations. Conclusion. These results highlight the influence of p53 immunoexpression, age, and anatomic localization in OSCC evolution. (Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2008; 106: 685-95)

Occult Axillary Lymph Node Metastases in Breast Cancer Do Matter: Results of 10-Year Survival Analysis

Axillary lymph node status is one of the most powerful prognostic factors for patients with breast cancer and is often critical in stratifying patients into adjuvant treatment regimens. In 203 apparently node-negative cases of breast cancer, a combination of immunohistochemical staining and step-sectioning identified occult metastases in 25% of cases. Ten-year follow-up information is available for these patients. Histologic features of the primary tumor and immunohistochemical staining for estrogen receptor, progesterone receptor, Her-2, and p53 were also evaluated. With multivariate analysis, both occult metastases and higher histologic grade of the primary tumor were independent predictors of disease-free survival. Histologic grade was the only significant independent predictor of overall survival. Estrogen receptor, progesterone receptor, Her-2, and p53 status did not predict the presence of metastases or survival when all tumor types were considered together. Metastases >0.5 mm significantly predicted a poorer disease-free survival when invasive ductal carcinomas were considered alone. Histologic grade was significantly associated with disease-free survival in the premenopausal and perimenopausal patients but not in the postmenopausal patients. The presence of occult metastases approached significance for overall survival in the premenopausal and perimenopausal patients but not in the postmenopausal patients.

Survival analysis: a tool in the study of post-harvest diseases in peaches

Survival analysis is applied when the time until the occurrence of an event is of interest. Such data are routinely collected in plant diseases, although applications of the method are uncommon. The objective of this study was to use two studies on post-harvest diseases of peaches, considering two harvests together and the existence of random effect shared by fruits of a same tree, in order to describe the main techniques in survival analysis. The nonparametric Kaplan-Meier method, the log-rank test and the semi-parametric Cox's proportional hazards model were used to estimate the effect of cultivars and the number of days after full bloom on the survival to the brown rot symptom and the instantaneous risk of expressing it in two consecutive harvests. The joint analysis with baseline effect, varying between harvests, and the confirmation of the tree effect as a grouping factor with random effect were appropriate to interpret the phenomenon (disease) evaluated and can be important tools to replace or complement the conventional analysis, respecting the nature of the variable and the phenomenon.

Liver morphology with emphasis on bile ducts changes and survival analysis in mice submitted to multiple Schistosoma mansoni infections and chemotherapy

In an attempt to be as close as possible to the infected and treated patients of the endemic areas of schistosomiasis (S. mansoni) and in order to achieve a long period of follow-up, mice were repeatedly infected with a low number of cercariae. Survival data and histological variables such as schistosomal granuloma, portal changes, hepatocellular necrosis, hepatocellular regeneration, schistosomotic pigment, periductal fibrosis and chiefly bile ducts changes were analysed in the infected treated and non treated mice. Oxamniquine chemotherapy in repeatedly infected mice prolonged survival significantly when compared to non-treated animals (chi-square 9.24, p = 0.0024), thus confirming previous results with a similar experimental model but with a shorter term follow-up. Furthermore, mortality decreased rapidly after treatment suggesting an abrupt reduction in the severity of hepatic lesions. A morphological and immunohistochemical study of the liver was carried out. Portal fibrosis, with a pattern resembling human Symmers fibrosis was present at a late phase in the infected animals. Bile duct lesions were quite close to those described in human Mansonian schistosomiasis. Schistosomal antigen was observed in one isolated altered bile duct cell. The pathogenesis of the bile duct changes and its relation to the parasite infection and/or their antigens are discussed.