A capture-recapture survival analysis model for radio-tagged animals

In recent years, survival analysis of radio-tagged animals has developed using methods based on the Kaplan-Meier method used in medical and engineering applications (Pollock et al. , 1989a,b). An important assumption of this approach is that all tagged animals with a functioning radio can be relocated at each sampling time with probability 1. This assumption may not always be reasonable in practice. In this paper, we show how a general capture-recapture model can be derived which allows for some probability (less than one) for animals to be relocated. This model is not simply a Jolly-Seber model because it is possible to relocate both dead and live animals, unlike when traditional tagging is used. The model can also be viewed as a generalization of the Kaplan-Meier procedure, thus linking the Jolly-Seber and Kaplan-Meier approaches to survival estimation. We present maximum likelihood estimators and discuss testing between submodels. We also discuss model assumptions and their validity in practice. An example is presented based on canvasback data collected by G. M. Haramis of Patuxent Wildlife Research Center, Laurel, Maryland, USA.     

Automatic model selection for high-dimensional survival analysis

Many different models for the analysis of high-dimensional survival data have been developed over the past years. While some of the models and implementations come with an internal parameter tuning automatism, others require the user to accurately adjust defaults, which often feels like a guessing game. Exhaustively trying out all model and parameter combinations will quickly become tedious or infeasible in computationally intensive settings, even if parallelization is employed. Therefore, we propose to use modern algorithm configuration techniques, e.g. iterated F-racing, to efficiently move through the model hypothesis space and to simultaneously configure algorithm classes and their respective hyperparameters. In our application we study four lung cancer microarray data sets. For these we configure a predictor based on five survival analysis algorithms in combination with eight feature selection filters. We parallelize the optimization and all comparison experiments with the BatchJobs and BatchExperiments R packages.     

A model selection criterion for clustered survival analysis with informative cluster size

We propose a model selection criterion for correlated survival data when the cluster size is informative to the outcome. This approach, called Resampling Cluster Survival Information Criterion (RCSIC), uses the Cox proportional hazards model that is weighted with the inverse of the cluster size. The RCSIC based on the within-cluster resampling idea takes into account the possible variability of the within-cluster subsampling and the possible informativeness of cluster sizes. The RCSIC allows for easy execution for the within-cluster resampling idea without a large number of resamples of the data. In contrast with the traditional model selection method in survival analysis, the RCSIC has an additional penalization for the within-cluster subsampling variability. Our simulations show the satisfactory results where the RCSIC provides a more robust power for variable selection in terms of clustered survival analysis, regardless of whether informative cluster size exists or not. Applying the RCSIC method to a periodontal disease studies, we identify the tooth loss in patients associated with the risk factors, Age, Filled Tooth, Molar, Crown, Decayed Tooth, and Smoking Status, respectively.     

The asymptotic distribution of a pivotal quantity for a capture-recapture model

A pivotal quantity for a capture-recapture model is introduced and used to construct an asymptotic confidence region for (ε,N), where ε is the capture efficiency and N is the population size. The true confidence levels of certain regions are obtained by simulation. Certain confidence regions for (ε,N) are drawn to show the size of the regions and to show how confidence limits for N depend on ε.     

A parametric empirical Bayes approach to the analysis of capture-recapture experiments

Empirical Bayes methods and a bootstrap bias adjustment procedure are used to estimate the size of a closed population when the individual capture probabilities are independently and identically distributed with a Beta distribution. The method is examined in simulations and applied to several well-known datasets. The simulations show the estimator performs as well as several other proposed parametric and non-parametric estimators.     

Bias in transition-specific survival and movement probabilities estimated using capture-recapture data

Transition probabilities can be estimated when capture-recapture data are available from each stratum on every capture occasion using a conditional likelihood approach with the Arnason-Schwarz model. To decompose the fundamental transition probabilities into derived parameters, all movement probabilities must sum to 1 and all individuals in stratum r at time i must have the same probability of survival regardless of which stratum the individual is in at time i + 1. If movement occurs among strata at the end of a sampling interval, survival rates of individuals from the same stratum are likely to be equal. However, if movement occurs between sampling periods and survival rates of individuals from the same stratum are not the same, estimates of stratum survival can be confounded with estimates of movement causing both estimates to be biased. Monte Carlo simulations were made of a three-sample model for a population with two strata using SURVIV. When differences were created in transition-specific survival rates for survival rates from the same stratum, relative bias was <2% in estimates of stratum survival and capture rates but relative bias in movement rates was much higher and varied. The magnitude of the relative bias in the movement estimate depended on the relative difference between the transition-specific survival rates and the corresponding stratum survival rate. The direction of the bias in movement rate estimates was opposite to the direction of this difference. Increases in relative bias due to increasing heterogeneity in probabilities of survival, movement and capture were small except when survival and capture probabilities were positively correlated within individuals.     

Time-dependent coefficients in a multi-event model for survival analysis

In an earlier work, a matrix-valued counting process model was proposed to deal with the occurrence of multiple events for each experimental unit, appealing to a Cox-type model to accommodate plausible concomitant variates. This model is generalized here to a more flexible one that incorporates time-dependent concomitant variates that might have time-dependent coefficients.     

A competing risks derivation of a mixture model for the analysis of survival data

Boag (1949) and Berkson and Gage (1952) proposed a mixture model for the analysis of survival time data when aproportion of treated patients are cured. This paper presents a derivation of the Boag/Berkson-Gage mixture model as well as a eneralization of the model based on the theory of competing risks. The assumptions underlying the model are stated and discussed and a general likelihood function is obtained. Use of the model is illustrated ith data from the Stanford Heart Transplant Program.     

A real survival analysis application via variable selection methods for Cox's proportional hazards model

Variable selection is fundamental to high-dimensional statistical modeling in diverse fields of sciences. In our health study, different statistical methods are applied to analyze trauma annual data, collected by 30 General Hospitals in Greece. The dataset consists of 6334 observations and 111 factors that include demographic, transport, and clinical data. The statistical methods employed in this work are the nonconcave penalized likelihood methods, Smoothly Clipped Absolute Deviation, Least Absolute Shrinkage and Selection Operator, and Hard, the maximum partial likelihood estimation method, and the best subset variable selection, adjusted to Cox's proportional hazards model and used to detect possible risk factors, which affect the length of stay in a hospital. A variety of different statistical models are considered, with respect to the combinations of factors while censored observations are present. A comparative survey reveals several differences between results and execution times of each method. Finally, we provide useful biological justification of our results.     

Separation of survival and movement rates in multi-state tag-return and capture-recapture models

There has been growing interest in the estimation of transition probabilities among stages (Hestbeck et al. , 1991; Brownie et al. , 1993; Schwarz et al. , 1993) in tag-return and capture-recapture models. This has been driven by the increasing interest in meta-population models in ecology and the need for parameter estimates to use in these models. These transition probabilities are composed of survival and movement rates, which can only be estimated separately when an additional assumption is made (Brownie et al. , 1993). Brownie et al. (1993) assumed that movement occurs at the end of the interval between time i and i + 1. We generalize this work to allow different movement patterns in the interval for multiple tag-recovery and capture-recapture experiments. The time of movement is a random variable with a known distribution. The model formulations can be viewed as matrix extensions to the model formulations of single open population capturerecapture and tag-recovery experiments (Jolly, 1965; Seber, 1965; Brownie et al. , 1985). We also present the results of a small simulation study for the tag-return model when movement time follows a beta distribution, and later another simulation study for the capture-recapture model when movement time follows a uniform distribution. The simulation studies use a modified program SURVIV (White, 1983). The Relative Standard Errors (RSEs) of estimates according to high and low movement rates are presented. We show there are strong correlations between movement and survival estimates in the case that the movement rate is high. We also show that estimators of movement rates to different areas and estimators of survival rates in different areas have substantial correlations.     

Bivariate frailty model for the analysis of multivariate survival time

Because of limitations of the univariate frailty model in analysis of multivariate survival data, a bivariate frailty model is introduced for the analysis of bivariate survival data. This provides tremendous flexibility especially in allowing negative associations between subjects within the same cluster. The approach involves incorporating into the model two possibly correlated frailties for each cluster. The bivariate lognormal distribution is used as the frailty distribution. The model is then generalized to multivariate survival data with two distinguished groups and also to alternating process data. A modified EM algorithm is developed with no requirement of specification of the baseline hazards. The estimators are generalized maximum likelihood estimators with subject-specific interpretation. The model is applied to a mental health study on evaluation of health policy effects for inpatient psychiatric care.     

Scnditignal inference and maximum likelihood in a capture-recapture model

A capture-recapture model is used to illustrate the use of sufficient statistics to factor the joint likelihood function into parts suitable for inferences, valid in samples of any size, on various subsets of the parameters. An assessment is made of the information ignored by confining attention to these parts of the likelihood function. The appropriate application of maximum likelihood estimation is illustrated as providing reasonably accurate approximations to these inferences. Although there are practical examples of this approach in the statistical literature, general awareness of the logical principles involved does not seem widespread. This paper illustrates and explains these logical principles in a more complex situation     

A flexible semiparametric transformation model for survival data

I suggest an extension of the semiparametric transformation model that specifies a time-varying regression structure for the transformation, and thus allows time-varying structure in the data. Special cases include a stratified version of the usual semiparametric transformation model. The model can be thought of as specifying a first order Taylor expansion of a completely flexible baseline. Large sample properties are derived and estimators of the asymptotic variances of the regression coefficients are given. The method is illustrated by a worked example and a small simulation study. A goodness of fit procedure for testing if the regression effects lead to a satisfactory fit is also suggested.     

A bivariate regression model for matched paired survival data: local influence and residual analysis

The use of bivariate distributions plays a fundamental role in survival and reliability studies. In this paper, we consider a location scale model for bivariate survival times based on the proposal of a copula to model the dependence of bivariate survival data. For the proposed model, we consider inferential procedures based on maximum likelihood. Gains in efficiency from bivariate models are also examined in the censored data setting. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the bivariate regression model for matched paired survival data. Sensitivity analysis methods such as local and total influence are presented and derived under three perturbation schemes. The martingale marginal and the deviance marginal residual measures are used to check the adequacy of the model. Furthermore, we propose a new measure which we call modified deviance component residual. The methodology in the paper is illustrated on a lifetime data set for kidney patients.     

A semiparametric multilevel survival model

Summary.  We propose a semiparametric multilevel survival model for clustered duration data in which the effect of a continuous covariate is represented by an unspecified, possibly non-linear, function. This model makes no distributional assumption about the cluster level random effects. The performance of the method is assessed via Monte Carlo simulations. The model is applied in an analysis of first-birth intervals in Bangladesh to examine period effects in the timing of first births, while allowing for clustering within communities; the analysis reveals a non-linear trend in the first-birth interval over time.     

Prior distributions for stratified capture-recapture models

We consider the Arnason-Schwarz model, usually used to estimate survival and movement probabilities from capture-recapture data. A missing data structure of this model is constructed which allows a clear separation of information relative to capture and relative to movement. Extensions of the Arnason-Schwarz model are considered. For example, we consider a model that takes into account both the individual migration history and the individual reproduction history. Biological assumptions of these extensions are summarized via a directed graph. Owing to missing data, the posterior distribution of parameters is numerically intractable. To overcome those computational difficulties we advocate a Gibbs sampling algorithm that takes advantage of the missing data structure inherent in capture-recapture models. Prior information on survival, capture and movement probabilities typically consists of a prior mean and of a prior 95% credible confidence interval. Dirichlet distributions are used to incorporate some prior information on capture, survival probabilities, and movement probabilities. Finally, the influence of the prior on the Bayesian estimates of movement probabilities is examined.     

Mixture models for capture-recapture count data

The contribution investigates the problem of estimating the size of a population, also known as the missing cases problem. Suppose a registration system is targeting to identify all cases having a certain characteristic such as a specific disease (cancer, heart disease, ...), disease related condition (HIV, heroin use, ...) or a specific behavior (driving a car without license). Every case in such a registration system has a certain notification history in that it might have been identified several times (at least once) which can be understood as a particular capture-recapture situation. Typically, cases are left out which have never been listed at any occasion, and it is this frequency one wants to estimate. In this paper modelling is concentrating on the counting distribution, e.g. the distribution of the variable that counts how often a given case has been identified by the registration system. Besides very simple models like the binomial or Poisson distribution, finite (nonparametric) mixtures of these are considered providing rather flexible modelling tools. Estimation is done using maximum likelihood by means of the EM algorithm. A case study on heroin users in Bangkok in the year 2001 is completing the contribution.     

Prior distributions for stratified capture-recapture models

We consider the Arnason-Schwarz model, usually used to estimate survival and movement probabilities from capture-recapture data. A missing data structure of this model is constructed which allows a clear separation of information relative to capture and relative to movement. Extensions of the Arnason-Schwarz model are considered. For example, we consider a model that takes into account both the individual migration history and the individual reproduction history. Biological assumptions of these extensions are summarized via a directed graph. Owing to missing data, the posterior distribution of parameters is numerically intractable. To overcome those computational difficulties we advocate a Gibbs sampling algorithm that takes advantage of the missing data structure inherent in capture-recapture models. Prior information on survival, capture and movement probabilities typically consists of a prior mean and of a prior 95% credible confidence interval. Dirichlet distributions are used to incorporate some prior information on capture, survival probabilities, and movement probabilities. Finally, the influence of the prior on the Bayesian estimates of movement probabilities is examined.     

A proportional-hazards model for survival analysis and long-term survivors modeling: application to amyotrophic lateral sclerosis data

The majority of survival data are affected by explanatory variables. We develop a new regression model for survival data analysis. As an alternative to standard mixture models, another model is proposed to describe the eventual presence of a surviving fraction. The proposed models are based on the Marshall–Olkin extended generalized Gompertz distribution. A maximum-likelihood inference is presented in the presence of covariates and a censorship phenomenon. Explanatory variables are incorporated into the model through proportional-hazards to evaluate the effect of risk factors on overall survival under different assumptions. Parametric, semi-parametric, and non-parametric methods are applied to survival analysis of patients treated for amyotrophic lateral sclerosis. Interesting results about riluzole use and other treatment effects on patients'' survival have been obtained.