Analysis of individual- and time-specific covariate effects on survival of Serinus serinus in north-eastern Spain

We developed models for the analysis of recapture data for 2678 serins ( Serinus serinus ) ringed in north-eastern Spain since 1985. We investigated several time- and individual-specific factors as potential predictors of overall mortality and dispersal patterns, and of gender and age differences in these patterns. Time-specific covariates included minimum daily temperature, days below freezing, and abundance of a strong competitor, siskins ( Carduelis spinus ) during winter, and maximum temperature and rainfall during summer. Individual covariates included body mass (i.e. body condition), and wing length (i.e. flying ability), and interactions between body mass and environmental factors. We found little support of a predictive relationship between environmental factors and survival, but good evidence of relationships between body mass and survival, especially for juveniles. Juvenile survival appears to vary in a curvilinear manner with increasing mass, suggesting that there may exist an optimal mass beyond which increases are detrimental. The mass-survival relationship does seem to be influenced by at least one environmental factor, namely the abundance of wintering siskins. When siskins are abundant, increases in body mass appear to relate strongly to increasing survival. When siskin numbers are average or low the relationship is largely reversed, suggesting that the presence of strong competition mitigates the otherwise largely negative aspects of greater body mass. Wing length in juveniles also appears to be related positively to survival, perhaps largely due to the influence of a few unusually large juveniles with adult-like survival. Further work is needed to test these relationships, ideally under experimentation.     

Asymmetric exchange between populations differing in habitat quality: A metapopulation study on the citril finch

The citril finch ( Serinus citrinella ) is a Cardueline finch restricted to the high mountains of western Europe. Since 1991 we have captured-recaptured about 6000 birds in two contrasting subpopulations located on the same mountain but separated by 5 km in distance. Citril finches, at the north-facing locality (La Vansa), rely more on Pine trees ( Pinus uncinata ) as their main food source, than birds at the south-facing locality (La Bofia), which rely more on herb seeds, which are of lower energetic content. Birds at La Vansa had higher body mass and fat score than those at La Bofia, suggesting that La Vansa was a site of higher-quality than La Bofia. By the use of a metapopulation approach and multistate models, we found that citril finches at the high-quality locality (La Vansa) showed higher survival rates than those at the low-quality one (La Bofia) (Vansa adults: φ = 0.42 - 0.04, juveniles: φ = 0.34 - 0.05; Bofia adults: φ = 0.35 - 0.04, juveniles: φ = 0.28 - 0.05). Dispersal was also asymmetric and higher for juvenile birds, with movement rates for juvenile citril finches from the low-quality to the higher-quality locality (Bofia to Vansa: é = 0.38 - 0.10) higher than the reverse (Vansa to Bofia: é = 0.09 - 0.03). We also investigated time-specific factors (e.g. meteorological data and fructification rate of Pinus ) as potential predictors of overall mortality and dispersal patterns. The results do not allow strong conclusions regarding the impact of these factors on survival and movement rates. Patterns of movement found in the Citril Finch between localities document a new model for the dispersal of species from low to high quality habitats, which we label of 'sources and pools'. This contrasts with currently accepted models of 'sources and sinks', in which movement is from high to low quality habitats, and 'Ideal Free Distributions', in which there is a balanced dispersal between habitats of different quality.     

Variable selection for spatial Poisson point processes via a regularization method

It is often of interest to use regression analysis to study the relationship between occurrence of events in space and spatially-indexed covariates. One model for such regression analysis is the Poisson point process. Here, we develop a method to perform the selection of covariates and the estimation of model parameters simultaneously for this model via a regularization method. We assess the finite-sample properties of our method with a simulation study. In addition, we propose a variant of our method that allows the selection of covariates at multiple pixel resolutions. For illustration, we consider the locations of a tree species, Beilschmiedia pendula, in a study plot at Barro Colorado Island in central Panama. We find that Beilschmiedia pendula occurs in greater abundance at locations with higher elevation and steeper slope. Also, we identify three species to which Beilschmiedia pendula tends to be attracted, two species by which it appears to be repelled, and a species with no apparent relationship.     

An Extended Mixture Distribution Survival Tree for Patient Pathway Prognostication

Mixture distribution survival trees are constructed by approximating different nodes in the tree by distinct types of mixture distributions to improve within node homogeneity. Previously, we proposed a mixture distribution survival tree-based method for determining clinically meaningful patient groups from a given dataset of patients’ length of stay. This article extends this approach to examine the interrelationship between length of stay in hospital, outcome measures, and other covariates. We describe an application of this approach to patient pathway and examine the relationship between length of stay in hospital and/or treatment outcome using five-years’ retrospective data of stroke patients.     

Urn Sampling and the Proportional Hazard Model

This paper investigates the urn sampling analogue for the score statistic relating survival to covariates assuming a proportional hazard model. The exact permutation distribution can be calculated as well as the exact low order moments for arbitrary censoring patterns. The asymptotic distribution of the score statistic is an easy consequence. The method is naturally extended to deal with the multivariate case, time varying covariates and interval censoring. Finally the relationship between the censoring process, the survival times and covariates are studied considering different reference sets for the distribution of the score statistic. Some assumptions about the censoring process are investigated and as a consequence the effect of censoring is clarified.     

Nonparametric Covariate-Adjusted Association Tests Based on the Generalized Kendall's Tau()

Identifying the risk factors for comorbidity is important in psychiatric research. Empirically, studies have shown that testing multiple, correlated traits simultaneously is more powerful than testing a single trait at a time in association analysis. Furthermore, for complex diseases, especially mental illnesses and behavioral disorders, the traits are often recorded in different scales such as dichotomous, ordinal and quantitative. In the absence of covariates, nonparametric association tests have been developed for multiple complex traits to study comorbidity. However, genetic studies generally contain measurements of some covariates that may affect the relationship between the risk factors of major interest (such as genes) and the outcomes. While it is relatively easy to adjust these covariates in a parametric model for quantitative traits, it is challenging for multiple complex traits with possibly different scales. In this article, we propose a nonparametric test for multiple complex traits that can adjust for covariate effects. The test aims to achieve an optimal scheme of adjustment by using a maximum statistic calculated from multiple adjusted test statistics. We derive the asymptotic null distribution of the maximum test statistic, and also propose a resampling approach, both of which can be used to assess the significance of our test. Simulations are conducted to compare the type I error and power of the nonparametric adjusted test to the unadjusted test and other existing adjusted tests. The empirical results suggest that our proposed test increases the power through adjustment for covariates when there exist environmental effects, and is more robust to model misspecifications than some existing parametric adjusted tests. We further demonstrate the advantage of our test by analyzing a data set on genetics of alcoholism.     

Variable selection and importance in presence of high collinearity: an application to the prediction of lean body mass from multi-frequency bioelectrical impedance

In prediction problems both response and covariates may have high correlation with a second group of influential regressors, that can be considered as background variables. An important challenge is to perform variable selection and importance assessment among the covariates in the presence of these variables. A clinical example is the prediction of the lean body mass (response) from bioimpedance (covariates), where anthropometric measures play the role of background variables. We introduce a reduced dataset in which the variables are defined as the residuals with respect to the background, and perform variable selection and importance assessment both in linear and random forest models. Using a clinical dataset of multi-frequency bioimpedance, we show the effectiveness of this method to select the most relevant predictors of the lean body mass beyond anthropometry.     

Estimation of the Average Survival Function Using a Censored Data Regression Model

In the presence of covariates information, assuming the linear relationship between a transformation of survival time and covariates, we propose a new estimator of survival function and show its consistency. In addition, a comparison of the proposed estimator with the product-limit estimator introduced by Kaplan and Meier (1958) is performed through Monte Carlo simulation studies. We illustrate the proposed estimator with the updated Stanford heart transplant data.     

Re-analysis of a banding study to test the effects of an experimental increase in bag limits of mourning doves

In 1966-1971, eastern US states with hunting seasons on mourning doves ( Zenaida macroura ) participated in a study designed to estimate the effects of bag limit increases on population survival rates. More than 400 000 adult and juvenile birds were banded and released during this period, and subsequent harvest and return of bands, together with total harvest estimates from mail and telephone surveys of hunters, provided the database for analysis. The original analysis used an ANOVA framework, and resulted in inferences of no effect of bag limit increase on population parameters (Hayne 1975). We used a logistic regression analysis to infer that the bag limit increase did not cause a biologically significant increase in harvest rate and thus the experiment could not provide any insight into the relationship between harvest and annual survival rates. Harvest rate estimates of breeding populations from geographical subregions were used as covariates in a Program MARK analysis and revealed an association between annual survival and harvest rates, although this relationship is potentially confounded by a latitudinal gradient in survival rates of dove populations. We discuss methodological problems encountered in the analysis of these data, and provide recommendations for future studies of the relationship between harvest and annual survival rates of mourning dove populations.     

Measuring density dependence in survival from mark-recapture data

We discuss the analysis of mark-recapture data when the aim is to quantify density dependence between survival rate and abundance. We describe an analysis for a random effects model that includes a linear relationship between abundance and survival using an errors-in-variables regression estimator with analytical adjustment for approximate bias. The analysis is illustrated using data from short-tailed shearwaters banded for 48 consecutive years at Fisher Island, Tasmania, and Hutton's shearwater banded at Kaikoura, New Zealand for nine consecutive years. The Fisher Island data provided no evidence of a density dependence relationship between abundance and survival, and confidence interval widths rule out anything but small density dependent effects. The Hutton's shearwater data were equivocal with the analysis unable to rule out anything but a very strong density dependent relationship between survival and abundance.     

Statistical Monitoring of Nominal Logistic Profiles in Phase II

Statistical analysis of profile monitoring, a relatively new sub-area of statistical process control due to its applications in different industries, have urged researchers and practitioners to contribute to the developments of new monitoring methods. A statistical profile is a relationship between a quality characteristic (a response) and one or more independent variables to characterize quality of a process or a product. In this article, statistical profiles based on nominal responses are studied, where logistic regression is used to model the responses. Three approaches including likelihood ratio test (LRT), multivariate exponentially weighted moving average (MEWMA), and support vector machines (SVM) approaches are proposed to monitor quality of a process or product in Phase II. Performances of the proposed approaches are evaluated and compared using a case study. Moreover, the effect of two important factors on average run length (ARL) performance, number of levels and number of covariates, has been considered. Results indicate that performance of all approaches depends on the number of covariates and levels. As the number of these factors increases, SVM performance improves while performance of the other approaches deteriorates.     

Joint modeling of degradation and failure time data

This paper surveys some approaches to model the relationship between failure time data and covariate data like internal degradation and external environmental processes. These models which reflect the dependency between system state and system reliability include threshold models and hazard-based models. In particular, we consider the class of degradation–threshold–shock models (DTS models) in which failure is due to the competing causes of degradation and trauma. For this class of reliability models we express the failure time in terms of degradation and covariates. We compute the survival function of the resulting failure time and derive the likelihood function for the joint observation of failure times and degradation data at discrete times. We consider a special class of DTS models where degradation is modeled by a process with stationary independent increments and related to external covariates through a random time scale and extend this model class to repairable items by a marked point process approach. The proposed model class provides a rich conceptual framework for the study of degradation–failure issues.     

Measuring density dependence in survival from mark-recapture data

We discuss the analysis of mark-recapture data when the aim is to quantify density dependence between survival rate and abundance. We describe an analysis for a random effects model that includes a linear relationship between abundance and survival using an errors-in-variables regression estimator with analytical adjustment for approximate bias. The analysis is illustrated using data from short-tailed shearwaters banded for 48 consecutive years at Fisher Island, Tasmania, and Hutton's shearwater banded at Kaikoura, New Zealand for nine consecutive years. The Fisher Island data provided no evidence of a density dependence relationship between abundance and survival, and confidence interval widths rule out anything but small density dependent effects. The Hutton's shearwater data were equivocal with the analysis unable to rule out anything but a very strong density dependent relationship between survival and abundance.     

Confidence intervals for the difference between two median survival times for clustered survival data

Clustered survival data arise often in clinical trial design, where the correlated subunits from the same cluster are randomized to different treatment groups. Under such design, we consider the problem of constructing confidence interval for the difference of two median survival time given the covariates. We use Cox gamma frailty model to account for the within-cluster correlation. Based on the conditional confidence intervals, we can identify the possible range of covariates over which the two groups would provide different median survival times. The associated coverage probability and the expected length of the proposed interval are investigated via a simulation study. The implementation of the confidence intervals is illustrated using a real data set.     

Risk factors of coronary heart disease: a Bayesian model averaging approach

To analyse the risk factors of coronary heart disease (CHD), we apply the Bayesian model averaging approach that formalizes the model selection process and deals with model uncertainty in a discrete-time survival model to the data from the Framingham Heart Study. We also use the Alternating Conditional Expectation algorithm to transform the risk factors, such that their relationships with CHD are best described, overcoming the problem of coding such variables subjectively. For the Framingham Study, the Bayesian model averaging approach, which makes inferences about the effects of covariates on CHD based on an average of the posterior distributions of the set of identified models, outperforms the stepwise method in predictive performance. We also show that age, cholesterol, and smoking are nonlinearly associated with the occurrence of CHD and that P-values from models selected from stepwise methods tend to overestimate the evidence for the predictive value of a risk factor and ignore model uncertainty.     

Computationally efficient familywise error rate control in genome-wide association studies using score tests for generalized linear models

In genetic association studies, detecting phenotype–genotype association is a primary goal. We assume that the relationship between the data—phenotype, genetic markers and environmental covariates—can be modeled by a generalized linear model. The number of markers is allowed to be far greater than the number of individuals of the study. A multivariate score statistic is used to test each marker for association with a phenotype. We assume that the test statistics asymptotically follow a multivariate normal distribution under the complete null hypothesis of no phenotype–genotype association. We present the familywise error rate order k approximation method to find a local significance level (alternatively, an adjusted p-value) for each test such that the familywise error rate is controlled. The special case k=1 gives the Šidák method. As a by-product, an effective number of independent tests can be defined. Furthermore, if environmental covariates and genetic markers are uncorrelated, or no environmental covariates are present, we show that covariances between score statistics depend on genetic markers alone. This not only leads to more efficient calculations but also to a local significance level that is determined only by the collection of markers used, independent of the phenotypes and environmental covariates of the experiment at hand.     

The use of auxiliary variables in capture-recapture modelling: An overview

I review the use of auxiliary variables in capture-recapture models for estimation of demographic parameters (e.g. capture probability, population size, survival probability, and recruitment, emigration and immigration numbers). I focus on what has been done in current research and what still needs to be done. Typically in the literature, covariate modelling has made capture and survival probabilities functions of covariates, but there are good reasons also to make other parameters functions of covariates as well. The types of covariates considered include environmental covariates that may vary by occasion but are constant over animals, and individual animal covariates that are usually assumed constant over time. I also discuss the difficulties of using time-dependent individual animal covariates and some possible solutions. Covariates are usually assumed to be measured without error, and that may not be realistic. For closed populations, one approach to modelling heterogeneity in capture probabilities uses observable individual covariates and is thus related to the primary purpose of this paper. The now standard Huggins-Alho approach conditions on the captured animals and then uses a generalized Horvitz-Thompson estimator to estimate population size. This approach has the advantage of simplicity in that one does not have to specify a distribution for the covariates, and the disadvantage is that it does not use the full likelihood to estimate population size. Alternately one could specify a distribution for the covariates and implement a full likelihood approach to inference to estimate the capture function, the covariate probability distribution, and the population size. The general Jolly-Seber open model enables one to estimate capture probability, population sizes, survival rates, and birth numbers. Much of the focus on modelling covariates in program MARK has been for survival and capture probability in the Cormack-Jolly-Seber model and its generalizations (including tag-return models). These models condition on the number of animals marked and released. A related, but distinct, topic is radio telemetry survival modelling that typically uses a modified Kaplan-Meier method and Cox proportional hazards model for auxiliary variables. Recently there has been an emphasis on integration of recruitment in the likelihood, and research on how to implement covariate modelling for recruitment and perhaps population size is needed. The combined open and closed 'robust' design model can also benefit from covariate modelling and some important options have already been implemented into MARK. Many models are usually fitted to one data set. This has necessitated development of model selection criteria based on the AIC (Akaike Information Criteria) and the alternative of averaging over reasonable models. The special problems of estimating over-dispersion when covariates are included in the model and then adjusting for over-dispersion in model selection could benefit from further research.     

Cure rate survival models with missing covariates: a simulation study

In this paper we study the cure rate survival model involving a competitive risk structure with missing categorical covariates. A parametric distribution that can be written as a sequence of one-dimensional conditional distributions is specified for the missing covariates. We consider the missing data at random situation so that the missing covariates may depend only on the observed ones. Parameter estimates are obtained by using the EM algorithm via the method of weights. Extensive simulation studies are conducted and reported to compare estimates efficiency with and without missing data. As expected, the estimation approach taking into consideration the missing covariates presents much better efficiency in terms of mean square errors than the complete case situation. Effects of increasing cured fraction and censored observations are also reported. We demonstrate the proposed methodology with two real data sets. One involved the length of time to obtain a BS degree in Statistics, and another about the time to breast cancer recurrence.     

Fledging size and survival in snow geese: Timing is everything (or is it?)

In many birds, body size at fledging is assumed to predict accurately the probability of subsequent survival, and size at fledging is often used as a proxy variable in analyses attempting to assess the pattern of natural selection on body size. However, in some species, size at fledging can vary significantly as a function of variation in the environmental component of growth. Such developmental plasticity has been demonstrated in several species of Arctic-breeding geese. In many cases, slower growth and reduced size at fledging has been suggested as the most parsimonious explanation for reduced post-fledging survival in goslings reared under poor environmental conditions. However, simply quantifying a relationship between mean size at fledging and mean survival rate (Francis et al ., 1992) may obscure the pattern of selection on the interaction of the genetic and environmental components of growth. The hypothesis that selection operates on the environmental component of body size at fledging, rather than the genetic component of size per se, was tested using data from the long-term study of Lesser Snow Geese ( Anser c. caerulescens ) breeding at La Pérouse Bay, Manitoba, Canada. Using data from female goslings measured at fledging, post-fledging survival rates were estimated using combined live encounter and dead recovery data (Burnham, 1993). To control for the covariation between growth and environmental factors, survival rates were constrained to be functions of individual covariation of size at fledging, and various measures of the timing of hatch; in all Arctic-breeding geese studied to date, late hatching goslings grow significantly more slowly than do early hatching goslings. The slower growth of late-hatching goslings has been demonstrated to reflect systematic changes in the environmental component of growth, and thus controlling for hatch date controls for a significant proportion of variation in the environmental component of growth. The relationship between size at fledging, hatch date and survival was found to be significantly non-linear; among early hatching goslings, there was little indication of significant differences in survival rate among large and small goslings. However, with increasingly later hatch dates, there was progressively greater mortality selection against smaller, slower growing goslings in most years. This would appear to suggest that body size matters, but not absolutely; small size leads to reduced survival for late-hatching goslings only at La Pe´rouse Bay. Since at least some of the variation in size among goslings for a given hatch date reflects genetic differences, this suggests selection may favour larger size at fledging, albeit only among late-hatching goslings.     

Curve prediction and clustering with mixtures of Gaussian process functional regression models

Shi, Wang, Murray-Smith and Titterington (Biometrics 63:714–723, 2007) proposed a Gaussian process functional regression (GPFR) model to model functional response curves with a set of functional covariates. Two main problems are addressed by their method: modelling nonlinear and nonparametric regression relationship and modelling covariance structure and mean structure simultaneously. The method gives very good results for curve fitting and prediction but side-steps the problem of heterogeneity. In this paper we present a new method for modelling functional data with ‘spatially’ indexed data, i.e., the heterogeneity is dependent on factors such as region and individual patient’s information. For data collected from different sources, we assume that the data corresponding to each curve (or batch) follows a Gaussian process functional regression model as a lower-level model, and introduce an allocation model for the latent indicator variables as a higher-level model. This higher-level model is dependent on the information related to each batch. This method takes advantage of both GPFR and mixture models and therefore improves the accuracy of predictions. The mixture model has also been used for curve clustering, but focusing on the problem of clustering functional relationships between response curve and covariates, i.e. the clustering is based on the surface shape of the functional response against the set of functional covariates. The model is examined on simulated data and real data.