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 and iniquities in older Brazilians: a six year follow up survey in São Paulo, Brazil

Maria Lucia Lebrão is the Coordinator of the SABE study. Jair LF Santos and Yeda AO Duarte receive support from National Council of Research (CNPq). The SABE study is supported by The São Paulo Research Foundation (FAPESP).

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 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.

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. ^

Demographic analysis of Certified Industrial Hygienists (CIH) with the use of survival analysis techniques

Objective. The goal of this study is to characterize the current workforce of CIHs, the lengths of professional practice careers of the past and current CIHs.^ Methods. This is a secondary data analysis of data compiled from all of the nearly 50 annual roster listings of the American Board of Industrial Hygiene (ABIH) for Certified Industrial Hygienists active in each year since 1960. Survival analysis was performed as a technique to measure the primary outcome of interest. The technique which was involved in this study was the Kaplan-Meier method for estimating the survival function.^ Study subjects: The population to be studied is all Certified Industrial Hygienists (CIHs). A CIH is defined by the ABIH as an individual who has achieved the minimum requirements for education, working experience and through examination, has demonstrated a minimum level of knowledge and competency in the prevention of occupational illnesses. ^ Results. A Cox-proportional hazards model analysis was performed by different start-time cohorts of CIHs. In this model we chose cohort 1 as the reference cohort. The estimated relative risk of the event (defined as retirement, or absent from 5 consecutive years of listing) occurred for CIHs for cohorts 2,3,4,5 relative to cohort 1 is 0.385, 0.214, 0.234, 0.299 relatively. The result show that cohort 2 (CIHs issued from 1970-1980) has the lowest hazard ratio which indicates the lowest retirement rate.^ Conclusion. The manpower of CIHs (still actively practicing up to the end of 2009) increased tremendously starting in 1980 and grew into a plateau in recent decades. This indicates that the supply and demand of the profession may have reached equilibrium. More demographic information and variables are needed to actually predict the future number of CIHs needed. ^

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.

Phylogenetic analysis of “Volvocacae” for comparative genetic studies

Sequence analysis based on multiple isolates representing essentially all genera and species of the classic family Volvocaeae has clarified their phylogenetic relationships. Cloned internal transcribed spacer sequences (ITS-1 and ITS-2, flanking the 5.8S gene of the nuclear ribosomal gene cistrons) were aligned, guided by ITS transcript secondary structural features, and subjected to parsimony and neighbor joining distance analysis. Results confirm the notion of a single common ancestor, and Chlamydomonas reinharditii alone among all sequenced green unicells is most similar. Interbreeding isolates were nearest neighbors on the evolutionary tree in all cases. Some taxa, at whatever level, prove to be clades by sequence comparisons, but others provide striking exceptions. The morphological species Pandorina morum, known to be widespread and diverse in mating pairs, was found to encompass all of the isolates of the four species of Volvulina. Platydorina appears to have originated early and not to fall within the genus Eudorina, with which it can sometimes be confused by morphology. The four species of Pleodorina appear variously associated with Eudorina examples. Although the species of Volvox are each clades, the genus Volvox is not. The conclusions confirm and extend prior, more limited, studies on nuclear SSU and LSU rDNA genes and plastid-encoded rbcL and atpB. The phylogenetic tree suggests which classical taxonomic characters are most misleading and provides a framework for molecular studies of the cell cycle-related and other alterations that have engendered diversity in both vegetative and sexual colony patterns in this classical family.

Reproduction of farm animals and their improvement through testing and selection,

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