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.

Analysis of the Stayability in Milk Buffaloes using Survival Models

In this study the trait Stayability (SA) was evaluated according to the year of cull after first calvin, i.e., SA 1 to 6 for 1 to 6 years from first calving in lactating females from bubaline milk herds spread in nine farms located in São Paulo state. Informations were used regarding 1027 lactating Murrah breed buffaloes. The statistical analyses were made using LIFEREG (SAS, 1999) procedure. The SA was evaluated using the fixed effects: farm production, birth year, calving season (Season 1- April to September and Season 2 October - March) and class of milk yield at 270 days. The age at first calving (AFC) was considered as a random effect. The mean observed for total milk yield was 1458.75Kg. Calving Season 2 encloses 65.6% of births. The means of cull age, in months, and the percentage of SA were, respectively: 10.69 e 69% (SA1), 19.30 e 63% (SA2), 26.4 e 54% (SA3), 33.15 e 42% (SA4), 38.53 e 36% (SA5) e 42.65 e 26% (SA6). It is verified that most of culls happens after the first lactation, among the sixth and eleventh month after first calving. It was observed that the factors: farm production, birth year and class of milk yield at 270 days affected significantly all SAs. Factors like calving season and the age at first calving (AFC) were only significant for SAL Being significant the factor AFC in level of 1% and factor time in 10%. For other SAs these factors were not statistically significant.

Analysis of culling probability in dairy buffalo using survival models

In order to contribute to the genetic breeding programs of buffaloes, this study aimed to determine the influence of environmental effects on the stayability (ST) of dairy female Murrah buffalo in the herd. Data from 1016 buffaloes were used. ST was defined as the ability of the female to remain in the herd for 1, 2, 3, 4, 5 or 6 years after the first calving. Environmental effects were studied by survival analysis, adjusted to the fixed effects of farm, year and season of birth, class of first-lactation milk yield and age at first calving. The data were analyzed using the LIFEREG procedure of the SAS program that fits parametric models to failure time data (culling or ST = 0), and estimates parameters by maximum likelihood estimation. Breeding farm, year of birth and first-lactation milk yield significantly influenced (P < 0.0001) the ST to the specific ages (1 to 6 years after the first calving). Buffaloes that were older at first calving presented higher probabilities of being culled 1 year after the first calving, without any effect on culling at older ages. Buffaloes with a higher milk yield at first calving presented a lower culling probability and remained for a longer period of time in the herd. The effects of breeding farm, year of birth and first-lactation milk yield should be included in models used for the analysis of ST in buffaloes. Copyright © The Animal Consortium 2010.

Mixture Cure Survival Models with Dependent Censoring

A number of authors have studies the mixture survival model to analyze survival data with nonnegligible cure fractions. A key assumption made by these authors is the independence between the survival time and the censoring time. To our knowledge, no one has studies the mixture cure model in the presence of dependent censoring. To account for such dependence, we propose a more general cure model which allows for dependent censoring. In particular, we derive the cure models from the perspective of competing risks and model the dependence between the censoring time and the survival time using a class of Archimedean copula models. Within this framework, we consider the parameter estimation, the cure detection, and the two-sample comparison of latency distribution in the presence of dependent censoring when a proportion of patients is deemed cured. Large sample results using the martingale theory are obtained. We applied the proposed methodologies to the SEER prostate cancer data.

Validation and refinement of survival models for liver retransplantation

Orthotopic liver retransplantation (re-OLT) is highly controversial. The objectives of this study were to determine the validity of a recently developed United Network for Organ Sharing (UNOS) multivariate model using an independent cohort of patients undergoing re-OLT outside the United States, to determine whether incorporation of other variables that were incomplete in the UNOS registry would provide additional prognostic information, to develop new models combining data sets from both cohorts, and to evaluate the validity of the model for end-stage liver disease (MELD) in patients undergoing re-OLT. Two hundred eighty-one adult patients undergoing re-OLT (between 1986 and 1999) at 6 foreign transplant centers comprised the validation cohort. We found good agreement between actual survival and predicted survival in the validation cohort; 1-year patient survival rates in the low-, intermediate-, and high-risk groups (as assigned by the original UNOS model) were 72%, 68%, and 36%, respectively (P < .0001). In the patients for whom the international normalized ratio (INR) of prothrombin time was available, MELD correlated with outcome following re-OLT; the median MELD scores for patients surviving at least 90 days compared with those dying within 90 days were 20.75 versus 25.9, respectively (P = .004). Utilizing both patient cohorts (n = 979), a new model, based on recipient age, total serum bilirubin, creatinine, and interval to re-OLT, was constructed (whole model χ(2) = 105, P < .0001). Using the c-statistic with 30-day, 90-day, 1-year, and 3-year mortality as the end points, the area under the receiver operating characteristic (ROC) curves for 4 different models were compared. In conclusion, prospective validation and use of these models as adjuncts to clinical decision making in the management of patients being considered for re-OLT are warranted.

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.

Application of Mixture Models to Survival Data

Survival models are being widely applied to the engineering field to model time-to-event data once censored data is here a common issue. Using parametric models or not, for the case of heterogeneous data, they may not always represent a good fit. The present study relays on critical pumps survival data where traditional parametric regression might be improved in order to obtain better approaches. Considering censored data and using an empiric method to split the data into two subgroups to give the possibility to fit separated models to our censored data, we’ve mixture two distinct distributions according a mixture-models approach. We have concluded that it is a good method to fit data that does not fit to a usual parametric distribution and achieve reliable parameters. A constant cumulative hazard rate policy was used as well to check optimum inspection times using the obtained model from the mixture-model, which could be a plus when comparing with the actual maintenance policies to check whether changes should be introduced or not.

Survival Extrapolation In The Presence Of Cause Specific Hazards.

Health economic evaluations require estimates of expected survival from patients receiving different interventions, often over a lifetime. However, data on the patients of interest are typically only available for a much shorter follow-up time, from randomised trials or cohorts. Previous work showed how to use general population mortality to improve extrapolations of the short-term data, assuming a constant additive or multiplicative effect on the hazards for all-cause mortality for study patients relative to the general population. A more plausible assumption may be a constant effect on the hazard for the specific cause of death targeted by the treatments. To address this problem, we use independent parametric survival models for cause-specific mortality among the general population. Because causes of death are unobserved for the patients of interest, a polyhazard model is used to express their all-cause mortality as a sum of latent cause-specific hazards. Assuming proportional cause-specific hazards between the general and study populations then allows us to extrapolate mortality of the patients of interest to the long term. A Bayesian framework is used to jointly model all sources of data. By simulation, we show that ignoring cause-specific hazards leads to biased estimates of mean survival when the proportion of deaths due to the cause of interest changes through time. The methods are applied to an evaluation of implantable cardioverter defibrillators for the prevention of sudden cardiac death among patients with cardiac arrhythmia. After accounting for cause-specific mortality, substantial differences are seen in estimates of life years gained from implantable cardioverter defibrillators.

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.

SURVIVAL PREDICTION FOR BRAIN TUMOR PATIENTS USING GENE EXPRESSION DATA

Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. In order to evaluate this hypothesis, the general goal of this research is to build models for survival prediction of glioma patients using DNA molecular profiles (U133 Affymetrix gene expression microarrays) along with clinical information. First, a predictive Random Forest model is built for binary outcomes (i.e. short vs. long-term survival) and a small subset of genes whose expression values can be used to predict survival time is selected. Following, a new statistical methodology is developed for predicting time-to-death outcomes using Bayesian ensemble trees. Due to a large heterogeneity observed within prognostic classes obtained by the Random Forest model, prediction can be improved by relating time-to-death with gene expression profile directly. We propose a Bayesian ensemble model for survival prediction which is appropriate for high-dimensional data such as gene expression data. Our approach is based on the ensemble "sum-of-trees" model which is flexible to incorporate additive and interaction effects between genes. We specify a fully Bayesian hierarchical approach and illustrate our methodology for the CPH, Weibull, and AFT survival models. We overcome the lack of conjugacy using a latent variable formulation to model the covariate effects which decreases computation time for model fitting. Also, our proposed models provides a model-free way to select important predictive prognostic markers based on controlling false discovery rates. We compare the performance of our methods with baseline reference survival methods and apply our methodology to an unpublished data set of brain tumor survival times and gene expression data, selecting genes potentially related to the development of the disease under study. A closing discussion compares results obtained by Random Forest and Bayesian ensemble methods under the biological/clinical perspectives and highlights the statistical advantages and disadvantages of the new methodology in the context of DNA microarray data analysis.