Handling of uncertain nest fates and variation in nest survival estimates

Researchers are moving their attention away from the Mayfield method of estimating nest success to advanced nest survival models that can be implemented within statistical software packages. In spite of this, little attention has been paid to developing formal rules for handling of ambiguous nesting data within these software-based methods. I compared the variation caused by differential handling of data between the hand-calculated Mayfield estimates and those obtained using the constant survival logistic-exposure method. Four variants of each of the two methods were applied to sets of nest records (n = 5,476) of nine open-nesting passerines. Of all nest fates, 57% (unweighted mean across species) were categorized as failed, 29% as successful and 14% as uncertain, according to either age criterion or combination of all fate evidence criteria. Different methods yielded survival estimates that differed as much as 6% over a 25-day nesting cycle. Variation in logistic-exposure survival estimates caused by the four variants of interval coding was higher (range = 4.4%) than variation in the Mayfield estimates (range = 2.7%) caused by the four variants of exposure termination. Researchers are urged to consider different handling of ambiguous nesting data as one of the many possible sources of bias when implementing any method of nest survival analysis.     

Age and clutch size variation in Dusky Flycatcher nest survival

Examination of spatial and temporal factors that influence nest survival can provide insight into habitat selection, reproductive decisions (e.g., clutch size), population dynamics, and conservation requirements for species. We used nest survival data for the Dusky Flycatcher Empidonax oberholseri to examine several factors that may influence nesting success. Our prediction was that the number of nest initiations would be positively associated with period nest survival. We used a model selection framework and found that nesting success was a function of clutch size and a cubic effect of age. Clutches with one, two, three, and four eggs had period survival rates of 0, 0.05, 0.33, and 0.49, respectively. Daily survival rates decreased from the onset of egg-laying and increased during the later stages of incubation before remaining relatively constant through the later portions of the nestling stage. Model-selection criterion provided support for a date effect on daily survival (i.e., daily nest survival declined across the nesting season) although the 95% confidence interval for the estimate included zero. We found that the majority of nest initiations occurred early in the nest season and declined across the season as period nest survival declined. Our prediction concerning nest survival was partially supported. In addition, we found substantial positive associations between clutch size and nest survival. While low daily survival rates for clutches with one or two eggs suggested that individuals may have reduced reproductive effort in response to nest predation risk, we did not find strong evidence that individuals reduced their clutch sizes in subsequent nest attempts. Alternative predictions, including the preferential settlement of higher quality individuals (e.g., those with the ability to lay full clutches to replace depredated nests) into high-quality habitat and differences in behavior patterns (e.g., number of visits to provision nestlings), may provide more consistent explanations for these patterns.     

Nest survival rate of Reeves's pheasant (Syrmaticus reevesii) based on artificial nest experiments

To explore the nest survival rate of Reeves's pheasant (Syrmaticus reevesii) and the nest-site factors that affect it,we conducted artificial nest experiments with reference to natural nests at Dongzhai National Nature Reserve (DNNR),Henan Province and Pingjingguan,Hubei Province from April to June 2014 simulating the situation in its early and later breeding season.We also determined distance characteristics of the nest sites by ArcGIS 10.0.Nest survival models were constructed in Program MARK for data analysis.Results indicated that in the early breeding season,the apparent survival rate (ASR) in DNNR (52.4％) was significantly greater than that in Pingjingguan (13.5％),and the ASR in the later breeding season in DNNR (26.7％) was not indistinctively correlated with Pingjingguan (3.2％).The daily survival rate (DSR) in the later breeding season was 93.8％ in DNNR and 92.0％ in Pingjingguan,respectively.The DSRs were both negatively correlated with nest distance to forest edges and settlements.The DSR in Pingjingguan was positively correlated with nest distance to paths and negatively correlated with nest distance to water sources.However,the DSR in DNNR was negatively correlated with nest distance to paths but positively correlated with nest distance to water sources.     

Modeling multivariate survival data by a semiparametric random effects proportional odds model

In this article, the focus is on the analysis of multivariate survival time data with various types of dependence structures. Examples of multivariate survival data include clustered data and repeated measurements from the same subject, such as the interrecurrence times of cancer tumors. A random effect semiparametric proportional odds model is proposed as an alternative to the proportional hazards model. The distribution of the random effects is assumed to be multivariate normal and the random effect is assumed to act additively to the baseline log-odds function. This class of models, which includes the usual shared random effects model, the additive variance components model, and the dynamic random effects model as special cases, is highly flexible and is capable of modeling a wide range of multivariate survival data. A unified estimation procedure is proposed to estimate the regression and dependence parameters simultaneously by means of a marginal-likelihood approach. Unlike the fully parametric case, the regression parameter estimate is not sensitive to the choice of correlation structure of the random effects. The marginal likelihood is approximated by the Monte Carlo method. Simulation studies are carried out to investigate the performance of the proposed method. The proposed method is applied to two well-known data sets, including clustered data and recurrent event times data.     

Effects of fire and grazing on grasshopper sparrow nest survival

Patch-burn grazing is a management framework designed to promote heterogeneity in grasslands, creating more diverse grassland structure to accommodate the habitat requirements of many grassland species, particularly grassland birds. Published studies on the effects of patch-burn grazing on passerines have been conducted on relatively large (430–980 ha pastures), contiguous grasslands, and only 1 of these studies has investigated the reproductive success of grassland birds. We assessed the effects of the patch-burn grazing and a more traditional treatment on the nesting ecology of grasshopper sparrows (Ammodramus savannarum) in small (<37 ha pastures) grasslands located in southern Iowa from May to August of 2008 and 2009. The study pastures were grazed from May to September and prescribed burns were conducted in the spring. We investigated the effects of treatments on clutch size and modeled grasshopper sparrow nest survival as a function of multiple biological and ecological factors. We found no difference in clutch size between treatments; however, we did find a reduction in clutch size for nests that were parasitized by brown-headed cowbirds (Molothrus ater). Constant daily survival rates were greater in patch-burn grazed pastures than in grazed-and-burned pastures (patch-burn grazed rate and grazed-and-burned rate ). Competitive survival models included year, stage of nest, nest age, and cool-season grass (csg) abundance within 5 m of the nest. Overall, csg abundance had the greatest effect on survival and had a negative influence. Although survival rates were highest in patch-burn grazed pastures, multiple factors influenced grasshopper sparrow survival. Nest survival rates for both treatments were relatively low, and variables other than treatment were more instrumental in predicting grasshopper sparrow survival. We recommend decreasing overall vegetation cover if increasing nesting habitat for grasshopper sparrows is a management goal. In addition, we recommend further investigation of heterogeneity management in fragmented landscapes to better understand how it affects biodiversity in relatively small management units that typify grassland habitats in the Midwest. © 2011 The Wildlife Society.     

Selecting factors predictive of heterogeneity in multivariate event time data

In multivariate survival analysis, investigators are often interested in testing for heterogeneity among clusters, both overall and within specific classes. We represent different hypotheses about the heterogeneity structure using a sequence of gamma frailty models, ranging from a null model with no random effects to a full model having random effects for each class. Following a Bayesian approach, we define prior distributions for the frailty variances consisting of mixtures of point masses at zero and inverse-gamma densities. Since frailties with zero variance effectively drop out of the model, this prior allocates probability to each model in the sequence, including the overall null hypothesis of homogeneity. Using a counting process formulation, the conditional posterior distributions of the frailties and proportional hazards regression coefficients have simple forms. Posterior computation proceeds via a data augmentation Gibbs sampling algorithm, a single run of which can be used to obtain model-averaged estimates of the population parameters and posterior model probabilities for testing hypotheses about the heterogeneity structure. The methods are illustrated using data from a lung cancer trial.     

Modeling heterogeneity for count data: A study of maternal mortality in health facilities in Mozambique

Count data are very common in health services research, and very commonly the basic Poisson regression model has to be extended in several ways to accommodate several sources of heterogeneity: (i) an excess number of zeros relative to a Poisson distribution, (ii) hierarchical structures, and correlated data, (iii) remaining “unexplained” sources of overdispersion. In this paper, we propose hierarchical zero‐inflated and overdispersed models with independent, correlated, and shared random effects for both components of the mixture model. We show that all different extensions of the Poisson model can be based on the concept of mixture models, and that they can be combined to account for all different sources of heterogeneity. Expressions for the first two moments are derived and discussed. The models are applied to data on maternal deaths and related risk factors within health facilities in Mozambique. The final model shows that the maternal mortality rate mainly depends on the geographical location of the health facility, the percentage of women admitted with HIV and the percentage of referrals from the health facility.     

Symmetric tests and confidence intervals for survival probabilities and quantiles of censored survival data

We describe existing tests and introduce two new tests concerning the value of a survival function. These tests may be used to construct a confidence interval for the survival probability at a given time or for a quantile of the survival distribution. Simulation studies show that error rates can differ substantially from their nominal values, particularly at survival probabilities close to zero or one. We recommend our new constrained bootstrap test for its good overall performance.     

Bias adjustment in Bayesian estimation of bird nest age-specific survival rates

The populations of many North American landbirds are showing signs of declining. Gathering information on breeding productivity allows early detection of unhealthy populations and helps develop good habitat-management practices. In this paper, we study the performance of the Bayesian model (He, 2003, Biometrics 59, 962-973) for age-specific nest survival rates with irregular visits. We find that the estimates are satisfactory except for the age-one survival rate. Usually the more days skipped between two visits, the more serious the underestimation of the age-one survival rate. We investigated the problem and developed three approaches to adjust for the underestimation bias. The simulation results show that the three approaches can significantly improve the estimation of the age-one survival rate.     

Additive mixed effect model for clustered failure time data

We propose an additive mixed effect model to analyze clustered failure time data. The proposed model assumes an additive structure and includes a random effect as an additional component. Our model imitates the commonly used mixed effect models in repeated measurement analysis but under the context of hazards regression; our model can also be considered as a parallel development of the gamma-frailty model in additive model structures. We develop estimating equations for parameter estimation and propose a way of assessing the distribution of the latent random effect in the presence of large clusters. We establish the asymptotic properties of the proposed estimator. The small sample performance of our method is demonstrated via a large number of simulation studies. Finally, we apply the proposed model to analyze data from a diabetic study and a treatment trial for congestive heart failure.     

Testing threshold and hormesis in a random effects dose-response model applied to developmental toxicity data

Here we describe a random effects threshold dose-response model for clustered binary-response data from developmental toxicity studies. For our model we assume that a hormetic effect occurs in addition to a threshold effect. Therefore, the dose-response curve is based on two components: relationships below the threshold (hormetic u-shaped model) and those above the threshold (logistic model). In the absence of hormesis and threshold effects, the estimation procedure is straightforward. We introduce score tests that are derived from a random effects hormetic-threshold dose-response model. The model and tests are applied to clustered binary data from developmental toxicity studies of animals to test for hormesis and threshold effects. We also compare the score test and likelihood ratio test to test for hormesis and threshold effects in a simulated study.     

Statistical inference in mixed models and analysis of twin and family data

Analysis of data from twin and family studies provides the foundation for studies of disease inheritance. The development of advanced theory and computational software for general linear models has generated considerable interest for using mixed-effect models to analyze twin and family data, as a computationally more convenient and theoretically more sound alternative to the classical structure equation modeling. Despite the long history of twin and family data analysis, some fundamental questions remain unanswered. We addressed two important issues. One is to determine the necessary and sufficient conditions for the identifiability in the mixed-effects models for twin and family data. The other is to derive the asymptotic distribution of the likelihood ratio test, which is novel due to the fact that the standard regularity conditions are not satisfied. We considered a series of specific yet important examples in which we demonstrated how to formulate mixed-effect models to appropriately reflect the data, and our key idea is the use of the Cholesky decomposition. Finally, we applied our method and theory to provide a more precise estimate of the heritability of two data sets than the previously reported estimate.     

Joint models for multivariate longitudinal and multivariate survival data

Joint modeling of longitudinal and survival data is becoming increasingly essential in most cancer and AIDS clinical trials. We propose a likelihood approach to extend both longitudinal and survival components to be multidimensional. A multivariate mixed effects model is presented to explicitly capture two different sources of dependence among longitudinal measures over time as well as dependence between different variables. For the survival component of the joint model, we introduce a shared frailty, which is assumed to have a positive stable distribution, to induce correlation between failure times. The proposed marginal univariate survival model, which accommodates both zero and nonzero cure fractions for the time to event, is then applied to each marginal survival function. The proposed multivariate survival model has a proportional hazards structure for the population hazard, conditionally as well as marginally, when the baseline covariates are specified through a specific mechanism. In addition, the model is capable of dealing with survival functions with different cure rate structures. The methodology is specifically applied to the International Breast Cancer Study Group (IBCSG) trial to investigate the relationship between quality of life, disease-free survival, and overall survival.     

On Computing a Likelihood Ratio Test Statistic in Physiological Response Slope Studies

We consider a structural model often used as the basis for analysis of response slopes in physiological studies, with particular emphasis on the problem of comparing the slopes for two samples. We simplify some of the calculations leading to a likelihood ratio test statistic for the hypothesis of equality of slopes. We show that these simplifications introduce additional computational stability, and illustrate our remarks in a numerical example.     

A semiparametric model for the analysis of recurrent-event panel data

In many longitudinal studies, interest focuses on the occurrence rate of some phenomenon for the subjects in the study. When the phenomenon is nonterminating and possibly recurring, the result is a recurrent-event data set. Examples include epileptic seizures and recurrent cancers. When the recurring event is detectable only by an expensive or invasive examination, only the number of events occurring between follow-up times may be available. This article presents a semiparametric model for such data, based on a multiplicative intensity model paired with a fully flexible nonparametric baseline intensity function. A random subject-specific effect is included in the intensity model to account for the overdispersion frequently displayed in count data. Estimators are determined from quasi-likelihood estimating functions. Because only first- and second-moment assumptions are required for quasi-likelihood, the method is more robust than those based on the specification of a full parametric likelihood. Consistency of the estimators depends only on the assumption of the proportional intensity model. The semiparametric estimators are shown to be highly efficient compared with the usual parametric estimators. As with semiparametric methods in survival analysis, the method provides useful diagnostics for specific parametric models, including a quasi-score statistic for testing specific baseline intensity functions. The techniques are used to analyze cancer recurrences and a pheromone-based mating disruption experiment in moths. A simulation study confirms that, for many practical situations, the estimators possess appropriate small-sample characteristics.     

Frailty modeling for spatially correlated survival data,with application to infant mortality in Minnesota

The use of survival models involving a random effect or 'frailty' term is becoming more common. Usually the random effects are assumed to represent different clusters, and clusters are assumed to be independent. In this paper, we consider random effects corresponding to clusters that are spatially arranged, such as clinical sites or geographical regions. That is, we might suspect that random effects corresponding to strata in closer proximity to each other might also be similar in magnitude. Such spatial arrangement of the strata can be modeled in several ways, but we group these ways into two general settings: geostatistical approaches, where we use the exact geographic locations (e.g. latitude and longitude) of the strata, and lattice approaches, where we use only the positions of the strata relative to each other (e.g. which counties neighbor which others). We compare our approaches in the context of a dataset on infant mortality in Minnesota counties between 1992 and 1996. Our main substantive goal here is to explain the pattern of infant mortality using important covariates (sex, race, birth weight, age of mother, etc.) while accounting for possible (spatially correlated) differences in hazard among the counties. We use the GIS ArcView to map resulting fitted hazard rates, to help search for possible lingering spatial correlation. The DIC criterion (Spiegelhalter et al., Journal of the Royal Statistical Society, Series B 2002, to appear) is used to choose among various competing models. We investigate the quality of fit of our chosen model, and compare its results when used to investigate neonatal versus post-neonatal mortality. We also compare use of our time-to-event outcome survival model with the simpler dichotomous outcome logistic model. Finally, we summarize our findings and suggest directions for future research.