Cormack–Jolly–Seber model with environmental covariates: A P‐spline approach

In capture–recapture models, survival and capture probabilities can be modelled as functions of time‐varying covariates, such as temperature or rainfall. The Cormack–Jolly–Seber (CJS) model allows for flexible modelling of these covariates; however, the functional relationship may not be linear. We extend the CJS model by semi‐parametrically modelling capture and survival probabilities using a frequentist approach via P‐splines techniques. We investigate the performance of the estimators by conducting simulation studies. We also apply and compare these models with known semi‐parametric Bayesian approaches on simulated and real data sets.     

Design and Analysis of Multiple Events Case–Control Studies

Summary In case–control research where there are multiple case groups, standard analyses fail to make use of all available information. Multiple events case–control (MECC) studies provide a new approach to sampling from a cohort and are useful when it is desired to study multiple types of events in the cohort. In this design, subjects in the cohort who develop any event of interest are sampled, as well as a fraction of the remaining subjects. We show that a simple case–control analysis of data arising from MECC studies is biased and develop three general estimating‐equation‐based approaches to analyzing data from these studies. We conduct simulation studies to compare the efficiency of the various MECC analyses with each other and with the corresponding conventional analyses. It is shown that the gain in efficiency by using the new design is substantial in many situations. We demonstrate the application of our approach to a nested case–control study of the effect of oral sodium phosphate use on chronic kidney injury with multiple case definitions.     

A Bayesian Approach to Dose–Response Assessment and Synergy and Its Application to In Vitro Dose–Response Studies

Summary In this article, we propose a Bayesian approach to dose–response assessment and the assessment of synergy between two combined agents. We consider the case of an in vitro ovarian cancer research study aimed at investigating the antiproliferative activities of four agents, alone and paired, in two human ovarian cancer cell lines. In this article, independent dose–response experiments were repeated three times. Each experiment included replicates at investigated dose levels including control (no drug). We have developed a Bayesian hierarchical nonlinear regression model that accounts for variability between experiments, variability within experiments (i.e., replicates), and variability in the observed responses of the controls. We use Markov chain Monte Carlo to fit the model to the data and carry out posterior inference on quantities of interest (e.g., median inhibitory concentration IC ₅₀ ). In addition, we have developed a method, based on Loewe additivity, that allows one to assess the presence of synergy with honest accounting of uncertainty. Extensive simulation studies show that our proposed approach is more reliable in declaring synergy compared to current standard analyses such as the median‐effect principle/combination index method ( Chou and Talalay, 1984 , Advances in Enzyme Regulation 22, 27–55), which ignore important sources of variability and uncertainty.     

On Combining Family‐Based and Population‐Based Case–Control Data in Association Studies

Summary Combining data collected from different sources can potentially enhance statistical efficiency in estimating effects of environmental or genetic factors or gene–environment interactions. However, combining data across studies becomes complicated when data are collected under different study designs, such as family‐based and unrelated individual‐based case–control design. In this article, we describe likelihood‐based approaches that permit the joint estimation of covariate effects on disease risk under study designs that include cases, relatives of cases, and unrelated individuals. Our methods accommodate familial residual correlation and a variety of ascertainment schemes. Extensive simulation experiments demonstrate that the proposed methods for estimation and inference perform well in realistic settings. Efficiencies of different designs are contrasted in the simulation. We applied the methods to data from the Colorectal Cancer Family Registry.     

Missing Exposure Data in Stereotype Regression Model: Application to Matched Case–Control Study with Disease Subclassification

Summary With advances in modern medicine and clinical diagnosis, case–control data with characterization of finer subtypes of cases are often available. In matched case–control studies, missingness in exposure values often leads to deletion of entire stratum, and thus entails a significant loss in information. When subtypes of cases are treated as categorical outcomes, the data are further stratified and deletion of observations becomes even more expensive in terms of precision of the category‐specific odds‐ratio parameters, especially using the multinomial logit model. The stereotype regression model for categorical responses lies intermediate between the proportional odds and the multinomial or baseline category logit model. The use of this class of models has been limited as the structure of the model implies certain inferential challenges with nonidentifiability and nonlinearity in the parameters. We illustrate how to handle missing data in matched case–control studies with finer disease subclassification within the cases under a stereotype regression model. We present both Monte Carlo based full Bayesian approach and expectation/conditional maximization algorithm for the estimation of model parameters in the presence of a completely general missingness mechanism. We illustrate our methods by using data from an ongoing matched case–control study of colorectal cancer. Simulation results are presented under various missing data mechanisms and departures from modeling assumptions.     

Testing for Genetic Association in the Presence of Linkage and Gene–Covariate Interactions

In order to study family‐based association in the presence of linkage, we extend a generalized linear mixed model proposed for genetic linkage analysis (Lebrec and van Houwelingen (2007), Human Heredity 64 , 5–15) by adding a genotypic effect to the mean. The corresponding score test is a weighted family‐based association tests statistic, where the weight depends on the linkage effect and on other genetic and shared environmental effects. For testing of genetic association in the presence of gene–covariate interaction, we propose a linear regression method where the family‐specific score statistic is regressed on family‐specific covariates. Both statistics are straightforward to compute. Simulation results show that adjusting the weight for the within‐family variance structure may be a powerful approach in the presence of environmental effects. The test statistic for genetic association in the presence of gene–covariate interaction improved the power for detecting association. For illustration, we analyze the rheumatoid arthritis data from GAW15. Adjusting for smoking and anti‐cyclic citrullinated peptide increased the significance of the association with the DR locus.     

A new mixed‐effects regression model for the analysis of zero‐modified hierarchical count data

Count data sets are traditionally analyzed using the ordinary Poisson distribution. However, such a model has its applicability limited as it can be somewhat restrictive to handle specific data structures. In this case, it arises the need for obtaining alternative models that accommodate, for example, (a) zero‐modification (inflation or deflation at the frequency of zeros), (b) overdispersion, and (c) individual heterogeneity arising from clustering or repeated (correlated) measurements made on the same subject. Cases (a)–(b) and (b)–(c) are often treated together in the statistical literature with several practical applications, but models supporting all at once are less common. Hence, this paper's primary goal was to jointly address these issues by deriving a mixed‐effects regression model based on the hurdle version of the Poisson–Lindley distribution. In this framework, the zero‐modification is incorporated by assuming that a binary probability model determines which outcomes are zero‐valued, and a zero‐truncated process is responsible for generating positive observations. Approximate posterior inferences for the model parameters were obtained from a fully Bayesian approach based on the Adaptive Metropolis algorithm. Intensive Monte Carlo simulation studies were performed to assess the empirical properties of the Bayesian estimators. The proposed model was considered for the analysis of a real data set, and its competitiveness regarding some well‐established mixed‐effects models for count data was evaluated. A sensitivity analysis to detect observations that may impact parameter estimates was performed based on standard divergence measures. The Bayesian ‐value and the randomized quantile residuals were considered for model diagnostics.     

Prioritizing covariates in the planning of future studies in the meta‐analytic framework

Science can be seen as a sequential process where each new study augments evidence to the existing knowledge. To have the best prospects to make an impact in this process, a new study should be designed optimally taking into account the previous studies and other prior information. We propose a formal approach for the covariate prioritization, that is the decision about the covariates to be measured in a new study. The decision criteria can be based on conditional power, change of the p‐value, change in lower confidence limit, Kullback–Leibler divergence, Bayes factors, Bayesian false discovery rate or difference between prior and posterior expectation. The criteria can be also used for decisions on the sample size. As an illustration, we consider covariate prioritization based on genome‐wide association studies for C‐reactive protein levels and make suggestions on the genes to be studied further.     

Biologically meaningful scents: a framework for understanding predator–prey research across disciplines

Fear of predation is a universal motivator. Because predators hunt using stealth and surprise, there is a widespread ability among prey to assess risk from chemical information – scents – in their environment. Consequently, scents often act as particularly strong modulators of memory and emotions. Recent advances in ecological research and analytical technology are leading to novel ways to use this chemical information to create effective attractants, repellents and anti‐anxiolytic compounds for wildlife managers, conservation biologists and health practitioners. However, there is extensive variation in the design, results, and interpretation of studies of olfactory‐based risk discrimination. To understand the highly variable literature in this area, we adopt a multi‐disciplinary approach and synthesize the latest findings from neurobiology, chemical ecology, and ethology to propose a contemporary framework that accounts for such disparate factors as the time‐limited stability of chemicals, highly canalized mechanisms that influence prey responses, and the context within which these scents are detected (e.g. availability of alternative resources, perceived shelter, and ambient physical parameters). This framework helps to account for the wide range of reported responses by prey to predator scents, and explains, paradoxically, how the same individual predator scent can be interpreted as either safe or dangerous to a prey animal depending on how, when and where the cue was deposited. We provide a hypothetical example to illustrate the most common factors that influence how a predator scent (from dingoes, Canis dingo) may both attract and repel the same target organism (kangaroos, Macropus spp.). This framework identifies the catalysts that enable dynamic scents, odours or odorants to be used as attractants as well as deterrents. Because effective scent tools often relate to traumatic memories (fear and/or anxiety) that cause future avoidance, this information may also guide the development of appeasement, enrichment and anti‐anxiolytic compounds, and help explain the observed variation in post‐traumatic‐related behaviours (including post‐traumatic stress disorder, PTSD) among diverse terrestrial taxa, including humans.     

Using generalized autoregressive error models to understand fire–vegetation–soil feedbacks in a mulga–spinifex landscape mosaic

Aim To develop a new modelling approach for spatially autocorrelated non‐normal data, and apply it to a case study of the role that fire–vegetation–soil feedbacks play in maintaining boundaries between fire‐sensitive and fire‐promoted plant communities. Location A mulga (Acacia aneura) shrubland–spinifex (Triodia spp.) grassland mosaic, central Australia. Methods Autoregressive error models were extended to non‐normal data by incorporating neighbourhood values of the response and predictor variables into generalized nonlinear models. These models were used to examine the environmental correlates of three response variables: mulga cover; fire frequency in areas free of mulga; and the presence of mulga banding. Mulga cover and mulga banding were assessed visually by overlaying 4477 × 1 km² grid cells on both Landsat 7 ETM+ and very high resolution imagery. Fire frequency was estimated from an existing fire history for central Australia, based on remotely sensed fire scars. Results The autoregressive error models explained 27%, 47% and 57% of the null deviance of mulga cover, fire frequency and mulga banding, respectively, with 12%, 15% and 24% of the null deviance being explained by environmental variables alone. These models accounted for virtually all residual spatial autocorrelation. While there was a clear negative relationship between mulga cover and fire frequency, there was little evidence that mulga was being restricted to parts of the landscape with inherently low fire frequencies. Mulga was most abundant at very low slope angles and on red earths, both of which are likely to reflect high site productivity, while fire frequency was not clearly affected by slope angle and was also relatively high on red earths. Main conclusions The modelling approach we have developed provides a much needed way of analysing spatially autocorrelated non‐normal data and can be easily incorporated into an information‐theoretic modelling framework. Using this approach, we provide evidence that mulga and spinifex have a highly antagonistic relationship. In more productive parts of the landscape, mulga suppresses spinifex and fire, while in less productive parts of the landscape, fire and spinifex suppress mulga, leading to the remarkable abruptness of mulga–spinifex boundaries that are maintained via fire–vegetation–soil feedbacks.     

Combining capture–recapture data and pedigree information to assess heritability of demographic parameters in the wild

Quantitative genetic analyses have been increasingly used to estimate the genetic basis of life‐history traits in natural populations. Imperfect detection of individuals is inherent to studies that monitor populations in the wild, yet it is seldom accounted for by quantitative genetic studies, perhaps leading to flawed inference. To facilitate the inclusion of imperfect detection of individuals in such studies, we develop a method to estimate additive genetic variance and assess heritability for binary traits such as survival, using capture–recapture (CR) data. Our approach combines mixed‐effects CR models with a threshold model to incorporate discrete data in a standard ‘animal model’ approach. We employ Markov chain Monte Carlo sampling in a Bayesian framework to estimate model parameters. We illustrate our approach using data from a wild population of blue tits (Cyanistes caeruleus) and present the first estimate of heritability of adult survival in the wild. In agreement with the prediction that selection should deplete additive genetic variance in fitness, we found that survival had low heritability. Because the detection process is incorporated, capture–recapture animal models (CRAM) provide unbiased quantitative genetics analyses of longitudinal data collected in the wild.     

A biogeographic–ecological approach to disentangle reticulate evolution in the Triatoma phyllosoma species group (Heteroptera: Triatominae), vectors of Chagas disease

Introgression and incomplete lineage sorting (ILS) are two of the main sources of gene‐tree incongruence; both can confound the assessment of phylogenetic relationships among closely related species. The Triatoma phyllosoma species group is a clade of partially co‐distributed and cross‐fertile Chagas disease vectors. Despite previous efforts, the phylogeny of this group remains unresolved, largely because of substantial gene‐tree incongruence. Here, we sequentially address introgression and ILS to provide a robust phylogenetic hypothesis for the T. phyllosoma species group. To identify likely instances of introgression prior to molecular scrutiny, we assessed biogeographic data and information on fertility of inter‐specific crosses. We first derived a few explicit hybridization hypotheses by considering the degree of spatial overlap within each species pair. Then, we assessed the plausibility of these hypotheses in the light of each species pair's cross‐fertility. Using this contextual information, we evaluated mito‐nuclear (cyt b, ITS‐2) gene‐tree incongruence and found evidence suggesting introgression within two species pairs. Finally, we modeled ILS using a Bayesian multispecies coalescent approach and either (a) a “complete” dataset with all the specimens in our sample, or (b) a “filtered” dataset without putatively introgressed specimens. The “filtered tree” had higher posterior‐probability support, as well as more plausible topology and divergence times, than the “complete tree.” Detecting and filtering out introgression and modeling ILS allowed us to derive an improved phylogenetic hypothesis for the T. phyllosoma species group. Our results illustrate how biogeographic and ecological‐reproductive contextual information can help clarify the systematics and evolution of recently diverged taxa prone to introgression and ILS.     

Interplay between stress response genes associated with attention‐deficit hyperactivity disorder and brain volume

The glucocorticoid receptor plays a pivotal role in the brain's response to stress; a haplotype of functional polymorphisms in the NR3C1 gene encoding this receptor has been associated with attention‐deficit hyperactivity disorder (ADHD). The serotonin transporter (5‐HTT) gene polymorphism 5‐HTTLPR is known to influence the relation between stress exposure and ADHD severity, which may be partly because of its reported effects on glucocorticoid levels. We therefore investigated if NR3C1 moderates the relation of stress exposure with ADHD severity and brain structure, and the potential role of 5‐HTTLPR. Neuroimaging, genetic and stress exposure questionnaire data were available for 539 adolescents and young adults participating in the multicenter ADHD cohort study NeuroIMAGE (average age: 17.2 years). We estimated the effects of genetic variation in NR3C1 and 5‐HTT, stress exposure and their interactions on ADHD symptom count and gray matter volume. We found that individuals carrying the ADHD risk haplotype of NR3C1 showed significantly more positive relation between stress exposure and ADHD severity than non‐carriers. This gene–environment interaction was significantly stronger for 5‐HTTLPR L‐allele homozygotes than for S‐allele carriers. These two‐ and three‐way interactions were reflected in the gray matter volume of the cerebellum, parahippocampal gyrus, intracalcarine cortex and angular gyrus. Our findings illustrate how genetic variation in the stress response pathway may influence the effects of stress exposure on ADHD severity and brain structure. The reported interplay between NR3C1 and 5‐HTT may further explain some of the heterogeneity between studies regarding the role of these genes and hypothalamic–pituitary–adrenal axis activity in ADHD.     

Using aggregate data to estimate the standard error of a treatment–covariate interaction in an individual patient data meta‐analysis

Subgroup analyses are important to medical research because they shed light on the heterogeneity of treatment effectts. A treatment–covariate interaction in an individual patient data (IPD) meta‐analysis is the most reliable means to estimate how a subgroup factor modifies a treatment's effectiveness. However, owing to the challenges in collecting participant data, an approach based on aggregate data might be the only option. In these circumstances, it would be useful to assess the relative efficiency and power loss of a subgroup analysis without patient‐level data. We present methods that use aggregate data to estimate the standard error of an IPD meta‐analysis’ treatment–covariate interaction for regression models of a continuous or dichotomous patient outcome. Numerical studies indicate that the estimators have good accuracy. An application to a previously published meta‐regression illustrates the practical utility of the methodology.     

Statistical Inference for a Two‐Stage Outcome‐Dependent Sampling Design with a Continuous Outcome

Summary The two‐stage case–control design has been widely used in epidemiology studies for its cost‐effectiveness and improvement of the study efficiency ( White, 1982 , American Journal of Epidemiology 115, 119–128; Breslow and Cain, 1988 , Biometrika 75, 11–20). The evolution of modern biomedical studies has called for cost‐effective designs with a continuous outcome and exposure variables. In this article, we propose a new two‐stage outcome‐dependent sampling (ODS) scheme with a continuous outcome variable, where both the first‐stage data and the second‐stage data are from ODS schemes. We develop a semiparametric empirical likelihood estimation for inference about the regression parameters in the proposed design. Simulation studies were conducted to investigate the small‐sample behavior of the proposed estimator. We demonstrate that, for a given statistical power, the proposed design will require a substantially smaller sample size than the alternative designs. The proposed method is illustrated with an environmental health study conducted at National Institutes of Health.     

Continuous Covariates in Mark‐Recapture‐Recovery Analysis: A Comparison of Methods

Summary Time varying, individual covariates are problematic in experiments with marked animals because the covariate can typically only be observed when each animal is captured. We examine three methods to incorporate time varying, individual covariates of the survival probabilities into the analysis of data from mark‐recapture‐recovery experiments: deterministic imputation, a Bayesian imputation approach based on modeling the joint distribution of the covariate and the capture history, and a conditional approach considering only the events for which the associated covariate data are completely observed (the trinomial model). After describing the three methods, we compare results from their application to the analysis of the effect of body mass on the survival of Soay sheep (Ovis aries) on the Isle of Hirta, Scotland. Simulations based on these results are then used to make further comparisons. We conclude that both the trinomial model and Bayesian imputation method perform best in different situations. If the capture and recovery probabilities are all high, then the trinomial model produces precise, unbiased estimators that do not depend on any assumptions regarding the distribution of the covariate. In contrast, the Bayesian imputation method performs substantially better when capture and recovery probabilities are low, provided that the specified model of the covariate is a good approximation to the true data‐generating mechanism.