Nonparametric estimation of the survival function for ordered multivariate failure time data: a comparative study

In longitudinal studies of disease, patients may experience several events through a follow-up period. In these studies, the sequentially ordered events are often of interest and lead to problems that have received much attention recently. Issues of interest include the estimation of bivariate survival, marginal distributions and the conditional distribution of gap times. In this work we consider the estimation of the survival function conditional to a previous event. Different nonparametric approaches will be considered for estimating these quantities, all based on the Kaplan-Meier estimator of the survival function. We explore the finite sample behavior of the estimators through simulations. The different methods proposed in this article are applied to a data set from a German Breast Cancer Study. The methods are used to obtain predictors for the conditional survival probabilities as well as to study the influence of recurrence in overall survival.

A Note on the Asymptotic Variance of Survival Function in the Semi-Markov Model

In Malani and Neilsen (1992) we have proposed alternative estimates of survival function (for time to disease) using a simple marker that describes time to some intermediate stage in a disease process. In this paper we derive the asymptotic variance of one such proposed estimator using two different methods and compare terms of order 1/n when there is no censoring. In the absence of censoring the asymptotic variance obtained using the Greenwood type approach converges to exact variance up to terms involving 1/n. But the asymptotic variance obtained using the theory of the counting process and results from Voelkel and Crowley (1984) on semi-Markov processes has a different term of order 1/n. It is not clear to us at this point why the variance formulae using the latter approach give different results.

Survival function of ERK1/2 as IL-3-activated, staurosporine-resistant Bcl2 kinases

Bcl2 phosphorylation at Ser-70 may be required for the full and potent suppression of apoptosis in IL-3-dependent myeloid cells and can result from agonist activation of mitochondrial protein kinase C (PKC). Paradoxically, expression of exogenous Bcl2 can protect parental cells from apoptosis induced by the potent PKC inhibitor, staurosporine (stauro). High concentrations of stauro of up to 1 μM only partially inhibit IL-3-stimulated Bcl2 phosphorylation but completely block PKC-mediated Bcl2 phosphorylation in vitro. These data indicate a role for a stauro-resistant Bcl2 kinase (SRK). We show that aurintricarboxylic acid (ATA), a nonpeptide activator of cellular MEK/mitogen-activated protein kinase (MAPK) kinase, can induce Ser-70 phosphorylation of Bcl2 and support survival of cells expressing wild-type but not the phosphorylation-incompetent S70A mutant Bcl2. A role for a MEK/MAPK as a responsible SRK was implicated because the highly specific MEK/MAPK inhibitor, PD98059, also can only partially inhibit IL-3-induced Bcl2 phosphorylation, whereas the combination of PD98059 and stauro completely blocks phosphorylation and synergistically enhances apoptosis. p44MAPK/extracellular signal-regulated kinase 1 (ERK1) and p42 MAPK/ERK2 are activated by IL-3, colocalize with mitochondrial Bcl2, and can directly phosphorylate Bcl2 on Ser-70 in a stauro-resistant manner both in vitro and in vivo. These findings suggest a role for the ERK1/2 kinases as SRKs. Thus, the SRKs can serve to functionally link the IL-3-stimulated proliferative and survival signaling pathways and, in a novel capacity, may explain how Bcl2 can suppress stauro-induced apoptosis. In addition, although the mechanism of regulation of Bcl2 by phosphorylation is not yet clear, our results indicate that phosphorylation may functionally stabilize the Bcl2-Bax heterodimerization.

VanX, a bacterial d-alanyl-d-alanine dipeptidase: Resistance, immunity, or survival function?

The zinc-containing d-alanyl-d-alanine (d-Ala-d-Ala) dipeptidase VanX has been detected in both Gram-positive and Gram-negative bacteria, where it appears to have adapted to at least three distinct physiological roles. In pathogenic vancomycin-resistant enterococci, vanX is part of a five-gene cluster that is switched on to reprogram cell-wall biosynthesis to produce peptidoglycan chain precursors terminating in d-alanyl-d-lactate (d-Ala-d-lactate) rather than d-Ala-d-Ala. The modified peptidoglycan exhibits a 1,000-fold decrease in affinity for vancomycin, accounting for the observed phenotypic resistance. In the glycopeptide antibiotic producers Streptomyces toyocaensis and Amylocatopsis orientalis, a vanHAX operon may have coevolved with antibiotic biosynthesis genes to provide immunity by reprogramming cell-wall termini to d-Ala-d-lactate as antibiotic biosynthesis is initiated. In the Gram-negative bacterium Escherichia coli, which is never challenged by the glycopeptide antibiotics because they cannot penetrate the outer membrane permeability barrier, the vanX homologue (ddpX) is cotranscribed with a putative dipeptide transport system (ddpABCDF) in stationary phase by the transcription factor RpoS (σs). The combined action of DdpX and the permease would permit hydrolysis of d-Ala-d-Ala transported back into the cytoplasm from the periplasm as cell-wall crosslinks are refashioned. The d-Ala product could then be oxidized as an energy source for cell survival under starvation conditions.

BAFF and the regulation of B cell survival.

The TNF family member BAFF is a fundamental survival factor for B cells. BAFF binds to three receptors, only one of which, BAFF-R, does not cross-react with the BAFF-related ligand APRIL. The survival function of BAFF on B cells is mediated mainly by BAFF-R and is particularly effective in transitional B cells. BAFF depletion leads to a considerable decrease in mature B cells, without apparent effect on B cell genesis. Consistently, BAFF overexpression results in an expanded B cell compartment and autoimmunity in mice. Elevated amounts of BAFF can be found in the serum of patients suffering from autoimmune diseases. The BAFF system is a promising target for the treatment of autoimmune diseases.

Univariate Parametric Survival Analysis using GS-distributions

The GS-distribution is a family of distributions that provide an accurate representation of any unimodal univariate continuous distribution. In this contribution we explore the utility of this family as a general model in survival analysis. We show that the survival function based on the GS-distribution is able to provide a model for univariate survival data and that appropriate estimates can be obtained. We develop some hypotheses tests that can be used for checking the underlying survival model and for comparing the survival of different groups.

On the unification of long-term survival models

In this paper we extend the long-term survival model proposed by Chen et al. [Chen, M.-H., Ibrahim, J.G., Sinha, D., 1999. A new Bayesian model for survival data with a surviving fraction. journal of the American Statistical Association 94, 909-919] via the generating function of a real sequence introduced by Feller [Feller, W., 1968. An Introduction to Probability Theory and its Applications, third ed., vol. 1, Wiley, New York]. A direct consequence of this new formulation is the unification of the long-term survival models proposed by Berkson and Gage [Berkson, J., Gage, R.P., 1952. Survival cure for cancer patients following treatment. journal of the American Statistical Association 47, 501-515] and Chen et al. (see citation above). Also, we show that the long-term survival function formulated in this paper satisfies the proportional hazards property if, and only if, the number of competing causes related to the occurrence of an event of interest follows a Poisson distribution. Furthermore, a more flexible model than the one proposed by Yin and Ibrahim [Yin, G., Ibrahim, J.G., 2005. Cure rate models: A unified approach. The Canadian journal of Statistics 33, 559-570] is introduced and, motivated by Feller`s results, a very useful competing index is defined. (c) 2008 Elsevier B.V. All rights reserved.

Systematic review of the survival rate and incidence of biologic, technical, and esthetic complications of single implant abutments supporting fixed prostheses

Purpose: To assess the 5-year survival rate and number of technical, biologic, and esthetic complications involving implant abutments. Materials and Methods: Electronic (Medline) and hand searches were performed to assess studies on metal and ceramic implant abutments. Relevant data from a previous review were included. Two reviewers independently extracted the data. Failure and complication rates were analyzed, and estimates of 5-year survival proportions were calculated from the relationship between event rate and survival function. Multivariable robust Poisson regression was used to compare abutment characteristics. Results: The search yielded 1,558 titles and 274 abstracts. Twenty-four studies were selected for data analysis. The survival rate for ceramic abutments was 97.5% (95% confidence interval [CI]): 89.6% to 99.4%) and 97.6% (95% CI: 96.2% to 98.5%) for metal abutments. The overall 5-year rate for technical complications was 11.8% (95% CI: 8.5% to 16.3%), 8.9% (95% CI: 4.3% to 17.7%) for ceramic and 12.0% (95% CI: 8.5% to 16.8%) for metal abutments. Biologic complications occurred with an overall rate of 6.4% (95% CI: 3.3% to 12.0%), 10.4% (95% CI: 1.9% to 46.7%) for ceramic, and 6.1% (95% CI: 3.1% to 12.0%) for metal abutments. Conclusions: The present meta-analysis on single-implant prostheses presents high survival rates of single implants, abutments, and prostheses after 5 years of function. No differences were found for the survival and failure rates of ceramic and metal abutments. No significant differences were found for technical, biologic, and esthetic complications of internally and externally connected abutments.

p62/SQSTM1 upregulation constitutes a survival mechanism that occurs during granulocytic differentiation of acute myeloid leukemia cells.

The p62/SQSTM1 adapter protein has an important role in the regulation of several key signaling pathways and helps transport ubiquitinated proteins to the autophagosomes and proteasome for degradation. Here, we investigate the regulation and roles of p62/SQSTM1 during acute myeloid leukemia (AML) cell maturation into granulocytes. Levels of p62/SQSTM1 mRNA and protein were both significantly increased during all-trans retinoic acid (ATRA)-induced differentiation of AML cells through a mechanism that depends on NF-κB activation. We show that this response constitutes a survival mechanism that prolongs the life span of mature AML cells and mitigates the effects of accumulation of aggregated proteins that occurs during granulocytic differentiation. Interestingly, ATRA-induced p62/SQSTM1 upregulation was impaired in maturation-resistant AML cells but was reactivated when differentiation was restored in these cells. Primary blast cells of AML patients and CD34(+) progenitors exhibited significantly lower p62/SQSTM1 mRNA levels than did mature granulocytes from healthy donors. Our results demonstrate that p62/SQSTM1 expression is upregulated in mature compared with immature myeloid cells and reveal a pro-survival function of the NF-κB/SQSTM1 signaling axis during granulocytic differentiation of AML cells. These findings may help our understanding of neutrophil/granulocyte development and will guide the development of novel therapeutic strategies for refractory and relapsed AML patients with previous exposure to ATRA.

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. ^

Effects of informative censoring on the hazard function: Application to the proportional hazards regression model

The standard analyses of survival data involve the assumption that survival and censoring are independent. When censoring and survival are related, the phenomenon is known as informative censoring. This paper examines the effects of an informative censoring assumption on the hazard function and the estimated hazard ratio provided by the Cox model.^ The limiting factor in all analyses of informative censoring is the problem of non-identifiability. Non-identifiability implies that it is impossible to distinguish a situation in which censoring and death are independent from one in which there is dependence. However, it is possible that informative censoring occurs. Examination of the literature indicates how others have approached the problem and covers the relevant theoretical background.^ Three models are examined in detail. The first model uses conditionally independent marginal hazards to obtain the unconditional survival function and hazards. The second model is based on the Gumbel Type A method for combining independent marginal distributions into bivariate distributions using a dependency parameter. Finally, a formulation based on a compartmental model is presented and its results described. For the latter two approaches, the resulting hazard is used in the Cox model in a simulation study.^ The unconditional survival distribution formed from the first model involves dependency, but the crude hazard resulting from this unconditional distribution is identical to the marginal hazard, and inferences based on the hazard are valid. The hazard ratios formed from two distributions following the Gumbel Type A model are biased by a factor dependent on the amount of censoring in the two populations and the strength of the dependency of death and censoring in the two populations. The Cox model estimates this biased hazard ratio. In general, the hazard resulting from the compartmental model is not constant, even if the individual marginal hazards are constant, unless censoring is non-informative. The hazard ratio tends to a specific limit.^ Methods of evaluating situations in which informative censoring is present are described, and the relative utility of the three models examined is discussed. ^

Fuzzy risk index for power transformer failures due to external short-circuits

A novel methodology to assess the risk of power transformer failures caused by external faults, such as short-circuit, taking the paper insulation condition into account, is presented. The risk index is obtained by contrasting the insulation paper condition with the probability that the transformer withstands the short-circuit current flowing along the winding during an external fault. In order to assess the risk, this probability and the value of the degree of polymerization of the insulating paper are regarded as inputs of a type-2 fuzzy logic system (T2-FLS), which computes the fuzzy risk level. A Monte Carlo simulation has been used to find the survival function of the currents flowing through the transformer winding during a single-phase or a three-phase short-circuit. The Roy Billinton Test System and a real power system have been used to test the results. (C) 2008 Elsevier B.V. All rights reserved.

A Log-Linear Regression Model for the Beta-Weibull Distribution

We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes, and censoring percentages, several simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.