A hands-on approach for fitting long-term survival models under the GAMLSS framework

In many data sets from clinical studies there are patients insusceptible to the occurrence of the event of interest. Survival models which ignore this fact are generally inadequate. The main goal of this paper is to describe an application of the generalized additive models for location, scale, and shape (GAMLSS) framework to the fitting of long-term survival models. in this work the number of competing causes of the event of interest follows the negative binomial distribution. In this way, some well known models found in the literature are characterized as particular cases of our proposal. The model is conveniently parameterized in terms of the cured fraction, which is then linked to covariates. We explore the use of the gamlss package in R as a powerful tool for inference in long-term survival models. The procedure is illustrated with a numerical example. (C) 2009 Elsevier Ireland Ltd. All rights reserved.

COM-Poisson cure rate survival models and an application to a cutaneous melanoma data

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 the Conway-Maxwell Poisson distribution. This model includes as special cases some of the well-known cure rate models discussed in the literature. Next, we discuss the maximum likelihood estimation of the parameters of this cure rate survival model. Finally, we illustrate the usefulness of this model by applying it to a real cutaneous melanoma data. (C) 2009 Elsevier B.V. All rights reserved.

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.

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.

Cross-National Analysis of the Associations between Traumatic Events and Suicidal Behavior: Findings from the WHO World Mental Health Surveys

Background: Community and clinical data have suggested there is an association between trauma exposure and suicidal behavior (i.e., suicide ideation, plans and attempts). However, few studies have assessed which traumas are uniquely predictive of: the first onset of suicidal behavior, the progression from suicide ideation to plans and attempts, or the persistence of each form of suicidal behavior over time. Moreover, few data are available on such associations in developing countries. The current study addresses each of these issues. Methodology/Principal Findings: Data on trauma exposure and subsequent first onset of suicidal behavior were collected via structured interviews conducted in the households of 102,245 (age 18+) respondents from 21 countries participating in the WHO World Mental Health Surveys. Bivariate and multivariate survival models tested the relationship between the type and number of traumatic events and subsequent suicidal behavior. A range of traumatic events are associated with suicidal behavior, with sexual and interpersonal violence consistently showing the strongest effects. There is a dose-response relationship between the number of traumatic events and suicide ideation/attempt; however, there is decay in the strength of the association with more events. Although a range of traumatic events are associated with the onset of suicide ideation, fewer events predict which people with suicide ideation progress to suicide plan and attempt, or the persistence of suicidal behavior over time. Associations generally are consistent across high-, middle-, and low-income countries. Conclusions/Significance: This study provides more detailed information than previously available on the relationship between traumatic events and suicidal behavior and indicates that this association is fairly consistent across developed and developing countries. These data reinforce the importance of psychological trauma as a major public health problem, and highlight the significance of screening for the presence and accumulation of traumatic exposures as a risk factor for suicide ideation and attempt.

A frailty modeling approach for parental effects in animal breeding

Survival models involving frailties are commonly applied in studies where correlated event time data arise due to natural or artificial clustering. In this paper we present an application of such models in the animal breeding field. Specifically, a mixed survival model with a multivariate correlated frailty term is proposed for the analysis of data from over 3611 Brazilian Nellore cattle. The primary aim is to evaluate parental genetic effects on the trait length in days that their progeny need to gain a commercially specified standard weight gain. This trait is not measured directly but can be estimated from growth data. Results point to the importance of genetic effects and suggest that these models constitute a valuable data analysis tool for beef cattle breeding.

Methods for Equivalence and Noninferiority Testing

Classical hypothesis testing focuses on testing whether treatments have differential effects on outcome. However, sometimes clinicians may be more interested in determining whether treatments are equivalent or whether one has noninferior outcomes. We review the hypotheses for these noninferiority and equivalence research questions, consider power and sample size issues, and discuss how to perform such a test for both binary and survival outcomes. The methods are illustrated on 2 recent studies in hematopoietic cell transplantation.

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.

Regression models for grouped survival data: Estimation and sensitivity analysis

In this study, regression models are evaluated for grouped survival data when the effect of censoring time is considered in the model and the regression structure is modeled through four link functions. The methodology for grouped survival data is based on life tables, and the times are grouped in k intervals so that ties are eliminated. Thus, the data modeling is performed by considering the discrete models of lifetime regression. The model parameters are estimated by using the maximum likelihood and jackknife methods. To detect influential observations in the proposed models, diagnostic measures based on case deletion, which are denominated global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to those measures, the local influence and the total influential estimate are also employed. Various simulation studies are performed and compared to the performance of the four link functions of the regression models for grouped survival data for different parameter settings, sample sizes and numbers of intervals. Finally, a data set is analyzed by using the proposed regression models. (C) 2010 Elsevier B.V. All rights reserved.

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.

Assessing influence in survival data with a cure fraction and covariates

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classical analysis and Bayesian analysis assuming no informative priors for the parameters of the model with a cure fraction. A Bayesian approach was considered by using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to obtain the posterior summaries of interest. Some influence methods, such as the local influence, total local influence of an individual, local influence on predictions and generalized leverage were derived, analyzed and discussed in survival data with a cure fraction and covariates. The relevance of the approach was illustrated with a real data set, where it is shown that, by removing the most influential observations, the decision about which model best fits the data is changed.

Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

Prolonged Survival of Allografts Induced by Mycobacterial Hsp70 Is Dependent on CD4+CD25+Regulatory T Cells

Background: Heat shock proteins (Hsps) are stress induced proteins with immunomodulatory properties. The Hsp70 of Mycobacterium tuberculosis (TBHsp70) has been shown to have an anti-inflammatory role on rodent autoimmune arthritis models, and the protective effects were demonstrated to be dependent on interleukin-10 (IL-10). We have previously observed that TBHsp70 inhibited maturation of dendritic cells (DCs) and induced IL-10 production by these cells, as well as in synovial fluid cells. Methodology/Principal Findings: We investigated if TBHsp70 could inhibit allograft rejection in two murine allograft systems, a transplanted allogeneic melanoma and a regular skin allograft. In both systems, treatment with TBHsp70 significantly inhibited rejection of the graft, and correlated with regulatory T cells (Tregs) recruitment. This effect was not tumor mediated because injection of TBHsp70 in tumor-free mice induced an increase of Tregs in the draining lymph nodes as well as inhibition of proliferation of lymph node T cells and an increase in IL-10 production. Finally, TBHsp70 inhibited skin allograft acute rejection, and depletion of Tregs using a monoclonal antibody completely abolished this effect. Conclusions/Significance: We present the first evidence for an immunosuppressive role for this protein in a graft rejection system, using an innovative approach - immersion of the graft tissue in TBHsp70 solution instead of protein injection. Also, this is the first study that demonstrates dependence on Treg cells for the immunosuppressive role of TBHsp70. This finding is relevant for the elucidation of the immunomodulatory mechanism of TBHsp70. We propose that this protein can be used not only for chronic inflammatory diseases, but is also useful for organ transplantation management.