A bivariate joint frailty model with mixture framework for survival analysis of recurrent events with dependent censoring and cure fraction

In the study of multiple failure time data with recurrent clinical endpoints, the classical independent censoring assumption in survival analysis can be violated when the evolution of the recurrent events is correlated with a censoring mechanism such as death. Moreover, in some situations, a cure fraction appears in the data because a tangible proportion of the study population benefits from treatment and becomes recurrence free and insusceptible to death related to the disease. A bivariate joint frailty mixture cure model is proposed to allow for dependent censoring and cure fraction in recurrent event data. The latency part of the model consists of two intensity functions for the hazard rates of recurrent events and death, wherein a bivariate frailty is introduced by means of the generalized linear mixed model methodology to adjust for dependent censoring. The model allows covariates and frailties in both the incidence and the latency parts, and it further accounts for the possibility of cure after each recurrence. It includes the joint frailty model and other related models as special cases. An expectation-maximization (EM)-type algorithm is developed to provide residual maximum likelihood estimation of model parameters. Through simulation studies, the performance of the model is investigated under different magnitudes of dependent censoring and cure rate. The model is applied to data sets from two colorectal cancer studies to illustrate its practical value.     

On the validity of time‐dependent AUC estimation in the presence of cure fraction

During the last decades, several approaches have been proposed to estimate the time‐dependent area under the receiver operating characteristic curve (AUC) of risk tools derived from survival data. The validity of these estimators relies on some regularity assumptions among which a survival function being proper. In practice, this assumption is not always satisfied because a fraction of the population may not be susceptible to experience the event of interest even for long follow‐up. Studying the sensitivity of the proposed estimators to the violation of this assumption is of substantial interest. In this paper, we investigate the performance of a nonparametric simple estimator, developed for classical survival data, in the case when the population exhibits a cure fraction. Motivated from the current practice of deriving risk tools in oncology and cardiovascular disease prevention, we also assess the loss, in terms of predictive performance, when deriving risk tools from survival models that do not acknowledge the presence of cure. The simulation results show that the investigated method is valid even under the presence of cure. They also show that risk tools derived from survival models that ignore the presence of cure have smaller AUC compared to those derived from survival models that acknowledge the presence of cure. This was also attested with a real data analysis from a breast cancer study.     

A General Class of Semiparametric Transformation Frailty Models for Nonproportional Hazards Survival Data

Summary We propose a semiparametrically efficient estimation of a broad class of transformation regression models for nonproportional hazards data. Classical transformation models are to be viewed from a frailty model paradigm, and the proposed method provides a unified approach that is valid for both continuous and discrete frailty models. The proposed models are shown to be flexible enough to model long‐term follow‐up survival data when the treatment effect diminishes over time, a case for which the PH or proportional odds assumption is violated, or a situation in which a substantial proportion of patients remains cured after treatment. Estimation of the link parameter in frailty distribution, considered to be unknown and possibly dependent on a time‐independent covariates, is automatically included in the proposed methods. The observed information matrix is computed to evaluate the variances of all the parameter estimates. Our likelihood‐based approach provides a natural way to construct simple statistics for testing the PH and proportional odds assumptions for usual survival data or testing the short‐ and long‐term effects for survival data with a cure fraction. Simulation studies demonstrate that the proposed inference procedures perform well in realistic settings. Applications to two medical studies are provided.     

Bayesian cure rate frailty models with application to a root canal therapy study

Due to natural or artificial clustering, multivariate survival data often arise in biomedical studies, for example, a dental study involving multiple teeth from each subject. A certain proportion of subjects in the population who are not expected to experience the event of interest are considered to be "cured" or insusceptible. To model correlated or clustered failure time data incorporating a surviving fraction, we propose two forms of cure rate frailty models. One model naturally introduces frailty based on biological considerations while the other is motivated from the Cox proportional hazards frailty model. We formulate the likelihood functions based on piecewise constant hazards and derive the full conditional distributions for Gibbs sampling in the Bayesian paradigm. As opposed to the Cox frailty model, the proposed methods demonstrate great potential in modeling multivariate survival data with a cure fraction. We illustrate the cure rate frailty models with a root canal therapy data set.     

Mean residual life cure models for right-censored data with and without length-biased sampling

We propose a semiparametric mean residual life mixture cure model for right-censored survival data with a cured fraction. The model employs the proportional mean residual life model to describe the effects of covariates on the mean residual time of uncured subjects and the logistic regression model to describe the effects of covariates on the cure rate. We develop estimating equations to estimate the proposed cure model for the right-censored data with and without length-biased sampling, the latter is often found in prevalent cohort studies. In particular, we propose two estimating equations to estimate the effects of covariates in the cure rate and a method to combine them to improve the estimation efficiency. The consistency and asymptotic normality of the proposed estimates are established. The finite sample performance of the estimates is confirmed with simulations. The proposed estimation methods are applied to a clinical trial study on melanoma and a prevalent cohort study on early-onset type 2 diabetes mellitus.     

Bayesian Semiparametric Models for Survival Data with a Cure Fraction

We propose methods for Bayesian inference for a new class of semiparametric survival models with a cure fraction. Specifically, we propose a semiparametric cure rate model with a smoothing parameter that controls the degree of parametricity in the right tail of the survival distribution. We show that such a parameter is crucial for these kinds of models and can have an impact on the posterior estimates. Several novel properties of the proposed model are derived. In addition, we propose a class of improper noninformative priors based on this model and examine the properties of the implied posterior. Also, a class of informative priors based on historical data is proposed and its theoretical properties are investigated. A case study involving a melanoma clinical trial is discussed in detail to demonstrate the proposed methodology.     

A bivariate frailty model with a cure fraction for modeling familial correlations in diseases

We suggest a cure-mixture model to analyze bivariate time-to-event data, as motivated by the article of Chatterjee and Shih (2001, Biometrics 57, 779-786), but with a simpler estimation procedure and the correlated gamma-frailty model instead of the shared gamma-frailty model. This approach allows us to deal with left-truncated and right-censored lifetime data, and accounts for heterogeneity, as well as for an insusceptible (cure) fraction in the study population. We perform a simulation study to evaluate the properties of the estimates in the proposed model and apply it to breast cancer incidence data for 5857 Swedish female monozygotic and dizygotic twin pairs from the so-called old cohort of the Swedish Twin Registry. This model is used to estimate the size of the susceptible fraction and the correlation between the frailties of the twin partners. Possible extensions, advantages, and limitations of the proposed method are discussed.     

GIS在生物质能源研究中的应用

生物质资源分布广阔而分散,且与环境、气候、土壤、土地利用等关系密切.地理信息系统(geographic information systems,GIS)具有空间数据分析功能以及易于与其他应用模型和算法相结合等特性,使其在生物质能源研究中具有优势.本文系统总结了国内外学者在生物质能源GIS应用方面的研究,着重讨论了GIS在生物质能开发可行性、生物质资源量及分布评估、生物质开发利用布局、生物质燃烧气体排放评估以及生物质能源信息系统等方面的应用,进而提出了GIS在生物质能源方面应用的3个趋势,即丰富数据源、提升数据处理和决策支持能力以及方案在线生成.     

Bayesian functional integral method for inferring continuous data from discrete measurements

Inference of the insulin secretion rate (ISR) from C-peptide measurements as a quantification of pancreatic β-cell function is clinically important in diseases related to reduced insulin sensitivity and insulin action. ISR derived from C-peptide concentration is an example of nonparametric Bayesian model selection where a proposed ISR time-course is considered to be a "model". An inferred value of inaccessible continuous variables from discrete observable data is often problematic in biology and medicine, because it is a priori unclear how robust the inference is to the deletion of data points, and a closely related question, how much smoothness or continuity the data actually support. Predictions weighted by the posterior distribution can be cast as functional integrals as used in statistical field theory. Functional integrals are generally difficult to evaluate, especially for nonanalytic constraints such as positivity of the estimated parameters. We propose a computationally tractable method that uses the exact solution of an associated likelihood function as a prior probability distribution for a Markov-chain Monte Carlo evaluation of the posterior for the full model. As a concrete application of our method, we calculate the ISR from actual clinical C-peptide measurements in human subjects with varying degrees of insulin sensitivity. Our method demonstrates the feasibility of functional integral Bayesian model selection as a practical method for such data-driven inference, allowing the data to determine the smoothing timescale and the width of the prior probability distribution on the space of models. In particular, our model comparison method determines the discrete time-step for interpolation of the unobservable continuous variable that is supported by the data. Attempts to go to finer discrete time-steps lead to less likely models.     

Convergence time to the Ewens sampling formula in the infinite alleles Moran model

In this paper, we establish an upper bound for time to convergence to stationarity for the discrete time infinite alleles Moran model. If M is the population size and μ is the mutation rate, this bound gives a cutoff time of log(M μ)/μ generations. The stationary distribution for this process in the case of sampling without replacement is the Ewens sampling formula. We show that the bound for the total variation distance from the generation t distribution to the Ewens sampling formula is well approximated by one of the extreme value distributions, namely, a standard Gumbel distribution. Beginning with the card shuffling examples of Aldous and Diaconis and extending the ideas of Donnelly and Rodrigues for the two allele model, this model adds to the list of Markov chains that show evidence for the cutoff phenomenon. Because of the broad use of infinite alleles models, this cutoff sets the time scale of applicability for statistical tests based on the Ewens sampling formula and other tests of neutrality in a number of population genetic studies.     

Defective regression models for cure rate modeling with interval‐censored data

Regression models in survival analysis are most commonly applied for right‐censored survival data. In some situations, the time to the event is not exactly observed, although it is known that the event occurred between two observed times. In practice, the moment of observation is frequently taken as the event occurrence time, and the interval‐censored mechanism is ignored. We present a cure rate defective model for interval‐censored event‐time data. The defective distribution is characterized by a density function whose integration assumes a value less than one when the parameter domain differs from the usual domain. We use the Gompertz and inverse Gaussian defective distributions to model data containing cured elements and estimate parameters using the maximum likelihood estimation procedure. We evaluate the performance of the proposed models using Monte Carlo simulation studies. Practical relevance of the models is illustrated by applying datasets on ovarian cancer recurrence and oral lesions in children after liver transplantation, both of which were derived from studies performed at A.C. Camargo Cancer Center in São Paulo, Brazil.     

Risk‐adjusted monitoring of time to event in the presence of long‐term survivors

The use of control charts for monitoring schemes in medical context should consider adjustments to incorporate the specific risk for each individual. Some authors propose the use of a risk‐adjusted survival time cumulative sum (RAST CUSUM) control chart to monitor a time‐to‐event outcome, possibly right censored, using conventional survival models, which do not contemplate the possibility of cure of a patient. We propose to extend this approach considering a risk‐adjusted CUSUM chart, based on a cure rate model. We consider a regression model in which the covariates affect the cure fraction. The CUSUM scores are obtained for Weibull and log‐logistic promotion time model to monitor a scale parameter for nonimmune individuals. A simulation study was conducted to evaluate and compare the performance of the proposed chart (RACUF CUSUM) with RAST CUSUM, based on optimal control limits and average run length in different situations. As a result, we note that the RAST CUSUM chart is inappropriate when applied to data with a cure rate, while the proposed RACUF CUSUM chart seems to have similar performance if applied to data without a cure rate. The proposed chart is illustrated with simulated data and with a real data set of patients with heart failure treated at the Heart Institute (InCor), at the University of São Paulo, Brazil.     

Birnbaum–Saunders frailty regression models: Diagnostics and application to medical data

In survival models, some covariates affecting the lifetime could not be observed or measured. These covariates may correspond to environmental or genetic factors and be considered as a random effect related to a frailty of the individuals explaining their survival times. We propose a methodology based on a Birnbaum–Saunders frailty regression model, which can be applied to censored or uncensored data. Maximum‐likelihood methods are used to estimate the model parameters and to derive local influence techniques. Diagnostic tools are important in regression to detect anomalies, as departures from error assumptions and presence of outliers and influential cases. Normal curvatures for local influence under different perturbations are computed and two types of residuals are introduced. Two examples with uncensored and censored real‐world data illustrate the proposed methodology. Comparison with classical frailty models is carried out in these examples, which shows the superiority of the proposed model.     

Resolvability of fluorescence lifetime distributions using phase fluorometry.

The analysis of the fluorescence decay using discrete exponential components assumes that a small number of species is present. In the absence of a definite kinetic model or when a large number of species is present, the exponential analysis underestimates the uncertainty of the recovered lifetime values. A different approach to determine the lifetime of a population of molecules is the use of probability density functions and lifetime distributions. Fluorescence decay data from continuous distributions of exponentially decaying components were generated. Different magnitudes of error were added to the data to simulate experimental conditions. The resolvability of the distributional model was studied by fitting the simulated data to one and two exponentials. The maximum width of symmetric distributions (uniform, gaussian, and lorentzian), which cannot be distinguished from single and double exponential fits for statistical errors of 1 and 0.1%, were determined. The width limits are determined by the statistical error of the data. It is also shown that, in the frequency domain, the discrete exponential analysis does not uniformly weights all the components of a distribution. This systematic error is less important when probability and distribution functions are used to recover the decay. Finally, it is shown that real lifetime distributions can be proved using multimodal probability density functions. In the companion paper that follows we propose a physical approach, which provides lifetime distribution functions for the tryptophan decay in proteins. In the third companion paper (Alcala, J.R., E. Gratton, and F.J. Prendergast, 1987, Biophys. J., in press) we use the distribution functions obtained to fit data from the fluorescence decay of single tryptophan proteins.     

A frailty mixture cure model with application to hospital admission data [corrected

Mixture cure models have been utilized to analyze survival data with possible cure. This paper considers the inclusion of frailty into the mixture cure model to model recurrent event data with a cure fraction. An attractive feature of the proposed model is the allowance for heterogeneity in risk among those individuals experiencing the event of interest in addition to the incorporation of a cured component. Maximum likelihood estimates can be obtained using the Expectation Maximization algorithm and standard errors are calculated from the Bootstrap method. The model is applied to hospital readmission data among colorectal cancer patients.     

Approximate Bayesian estimation of extinction rate in the Finnish Daphnia magna metapopulation

Approximate Bayesian computation (ABC) is useful for parameterizing complex models in population genetics. In this study, ABC was applied to simultaneously estimate parameter values for a model of metapopulation coalescence and test two alternatives to a strict metapopulation model in the well‐studied network of Daphnia magna populations in Finland. The models shared four free parameters: the subpopulation genetic diversity (θ_S), the rate of gene flow among patches (4Nm), the founding population size (N₀) and the metapopulation extinction rate (e) but differed in the distribution of extinction rates across habitat patches in the system. The three models had either a constant extinction rate in all populations (strict metapopulation), one population that was protected from local extinction (i.e. a persistent source), or habitat‐specific extinction rates drawn from a distribution with specified mean and variance. Our model selection analysis favoured the model including a persistent source population over the two alternative models. Of the closest 750 000 data sets in Euclidean space, 78% were simulated under the persistent source model (estimated posterior probability = 0.769). This fraction increased to more than 85% when only the closest 150 000 data sets were considered (estimated posterior probability = 0.774). Approximate Bayesian computation was then used to estimate parameter values that might produce the observed set of summary statistics. Our analysis provided posterior distributions for e that included the point estimate obtained from previous data from the Finnish D. magna metapopulation. Our results support the use of ABC and population genetic data for testing the strict metapopulation model and parameterizing complex models of demography.     

On a class of non-linear transformation cure rate models

In this paper, we propose a generalization of the mixture (binary) cure rate model, motivated by the existence of a zero-modified (inflation or deflation) distribution, on the initial number of causes, under a competing cause scenario. This non-linear transformation cure rate model is in the same form of models studied in the past; however, following our approach, we are able to give a realistic interpretation to a specific class of proper transformation functions, for the cure rate modeling. The estimation of the parameters is then carried out using the maximum likelihood method along with a profile approach. A simulation study examines the accuracy of the proposed estimation method and the model discrimination based on the likelihood ratio test. For illustrative purposes, analysis of two real life data-sets, one on recidivism and another on cutaneous melanoma, is also carried out.     

Conformational heterogeneity of creatine kinase determined from phase resolved fluorometry.

Fluorescence lifetimes of dimeric rabbit muscle creatine kinase specifically dansylated at both active sites and the homologous monomeric lobster muscle arginine kinase singly dansylated were determined using phase-modulation methods with global analysis of overdetermined data sets. For both proteins, the data is adequately described by three discrete exponential decays or a Lorentzian double distributed decay. Analogue phase resolved spectroscopy also reveals the presence of at least two distinct fluorophore domains for the dansyl moieties of creatine kinase. The model fluorophore, dansyllysine, exhibits a monoexponential decay with a value that is highly solvent dependent. Because the monomeric arginine kinase exhibits essentially the same decay law as doubly derivatized dimeric creatine kinase, it is proposed that the multiple lifetimes of creatine kinase reflect two or more isomeric dimeric states and not subunit asymmetry within a conformationally homogeneous dimeric population. Exposure of arginine kinase to 6 M guanidinium chloride results in a shift to shorter lifetimes and narrowing of the lifetime distributions. Creatine kinase displays a small narrowing of the distribution, but little change in fractional populations or lifetimes. These results suggest the presence of structural elements resistant to denaturation. The longest lifetime component in the triexponential discrete decay law of doubly dansylated creatine kinase is totally unquenched by acrylamide, whereas the two shorter lifetime components exhibit limited dynamic quenching. Steady-state quenching by acrylamide is significant and reveals a sharp distinction between accessible and nonaccessible dansyl groups. The major mechanism for interaction between the dansyl moieties and acrylamide is, atypically, static quenching.(ABSTRACT TRUNCATED AT 250 WORDS)     

Geostatistical modelling of regional bird species richness: exploring environmental proxies for conservation purpose

Identifying spatial patterns in species diversity represents an essential task to be accounted for when establishing conservation strategies or monitoring programs. Predicting patterns of species richness by a model-based approach has recently been recognised as a significant component of conservation planning. Finding those environmental predictors which are related to these patterns is crucial since they may represent surrogates of biodiversity, indicating in a fast and cheap way the spatial location of biodiversity hotspots and, consequently, where conservation efforts should be addressed. Predictive models based on classical multiple linear regression or generalised linear models crowded the recent ecological literature. However, very often, problems related with spatial autocorrelation in observed data were not adequately considered. Here, a spatially-explicit data-set on birds presence and distribution across the whole Tuscany region was analysed. Species richness was calculated within 1 × 1 km grid cells and 10 environmental predictors (e.g. altitude, habitat diversity and satellite-derived landscape heterogeneity indices) were included in the analysis. Integrating spatial components of variation with predictive ecological factors, i.e. using geostatistical models, a general model of bird species richness was developed and used to obtain predictive regional maps of bird diversity hotspots. A meaningful subset of environmental predictors, namely habitat productivity, habitat heterogeneity, combined with topographic and geographic information, were included in the final geostatistical model. Conservation strategies based on the predicted hotspots as well as directions for increasing sampling effort efficiency could be extrapolated by the proposed model.     

Challenges of predicting the potential distribution of a slow-spreading invader: a habitat suitability map for an invasive riparian tree

Understanding the potential spread of invasive species is essential for land managers to prevent their establishment and restore impacted habitat. Habitat suitability modeling provides a tool for researchers and managers to understand the potential extent of invasive species spread. Our goal was to use habitat suitability modeling to map potential habitat of the riparian plant invader, Russian olive (Elaeagnus angustifolia). Russian olive has invaded riparian habitat across North America and is continuing to expand its range. We compiled 11 disparate datasets for Russian olive presence locations (n = 1,051 points and 139 polygons) in the western US and used Maximum entropy (Maxent) modeling to develop two habitat suitability maps for Russian olive in the western United States: one with coarse-scale water data and one with fine-scale water data. Our models were able to accurately predict current suitable Russian olive habitat (Coarse model: training AUC = 0.938, test AUC = 0.907; Fine model: training AUC = 0.923, test AUC = 0.885). Distance to water was the most important predictor for Russian olive presence in our coarse-scale water model, but it was only the fifth most important variable in the fine-scale model, suggesting that when water bodies are considered on a fine scale, Russian olive does not necessarily rely on water. Our model predicted that Russian olive has suitable habitat further west from its current distribution, expanding into the west coast and central North America. Our methodology proves useful for identifying potential future areas of invasion. Model results may be influenced by locations of cultivated individuals and sampling bias. Further study is needed to examine the potential for Russian olive to invade beyond its current range. Habitat suitability modeling provides an essential tool for enhancing our understanding of invasive species spread.