Robust estimating functions and bias correction for longitudinal data analysis

Robust methods are useful in making reliable statistical inferences when there are small deviations from the model assumptions. The widely used method of the generalized estimating equations can be "robustified" by replacing the standardized residuals with the M-residuals. If the Pearson residuals are assumed to be unbiased from zero, parameter estimators from the robust approach are asymptotically biased when error distributions are not symmetric. We propose a distribution-free method for correcting this bias. Our extensive numerical studies show that the proposed method can reduce the bias substantially. Examples are given for illustration.

Effects of variance-function misspecification in analysis of longitudinal data

The approach of generalized estimating equations (GEE) is based on the framework of generalized linear models but allows for specification of a working matrix for modeling within-subject correlations. The variance is often assumed to be a known function of the mean. This article investigates the impacts of misspecifying the variance function on estimators of the mean parameters for quantitative responses. Our numerical studies indicate that (1) correct specification of the variance function can improve the estimation efficiency even if the correlation structure is misspecified; (2) misspecification of the variance function impacts much more on estimators for within-cluster covariates than for cluster-level covariates; and (3) if the variance function is misspecified, correct choice of the correlation structure may not necessarily improve estimation efficiency. We illustrate impacts of different variance functions using a real data set from cow growth.

Estimation of growth parameters from multiple-recapture data

This article develops a method for analysis of growth data with multiple recaptures when the initial ages for all individuals are unknown. The existing approaches either impute the initial ages or model them as random effects. Assumptions about the initial age are not verifiable because all the initial ages are unknown. We present an alternative approach that treats all the lengths including the length at first capture as correlated repeated measures for each individual. Optimal estimating equations are developed using the generalized estimating equations approach that only requires the first two moment assumptions. Explicit expressions for estimation of both mean growth parameters and variance components are given to minimize the computational complexity. Simulation studies indicate that the proposed method works well. Two real data sets are analyzed for illustration, one from whelks (Dicathais aegaota) and the other from southern rock lobster (Jasus edwardsii) in South Australia.

A maximum-likelihood method for estimating natural mortality and catchability coefficient from catch-and-effort data

A simple stochastic model of a fish population subject to natural and fishing mortalities is described. The fishing effort is assumed to vary over different periods but to be constant within each period. A maximum-likelihood approach is developed for estimating natural mortality (M) and the catchability coefficient (q) simultaneously from catch-and-effort data. If there is not enough contrast in the data to provide reliable estimates of both M and q, as is often the case in practice, the method can be used to obtain the best possible values of q for a range of possible values of M. These techniques are illustrated with tiger prawn (Penaeus semisulcatus) data from the Northern Prawn Fishery of Australia.

Estimating equations with nonignorably missing response data

Troxel, Lipsitz, and Brennan (1997, Biometrics 53, 857-869) considered parameter estimation from survey data with nonignorable nonresponse and proposed weighted estimating equations to remove the biases in the complete-case analysis that ignores missing observations. This paper suggests two alternative modifications for unbiased estimation of regression parameters when a binary outcome is potentially observed at successive time points. The weighting approach of Robins, Rotnitzky, and Zhao (1995, Journal of the American Statistical Association 90, 106-121) is also modified to obtain unbiased estimating functions. The suggested estimating functions are unbiased only when the missingness probability is correctly specified, and misspecification of the missingness model will result in biases in the estimates. Simulation studies are carried out to assess the performance of different methods when the covariate is binary or normal. For the simulation models used, the relative efficiency of the two new methods to the weighting methods is about 3.0 for the slope parameter and about 2.0 for the intercept parameter when the covariate is continuous and the missingness probability is correctly specified. All methods produce substantial biases in the estimates when the missingness model is misspecified or underspecified. Analysis of data from a medical survey illustrates the use and possible differences of these estimating functions.

Estimating equations for parameters in stochastic growth models from tag-recapture data

James (1991, Biometrics 47, 1519-1530) constructed unbiased estimating functions for estimating the two parameters in the von Bertalanffy growth curve from tag-recapture data. This paper provides unbiased estimating functions for a class of growth models that incorporate stochastic components and explanatory variables. a simulation study using seasonal growth models indicates that the proposed method works well while the least-squares methods that are commonly used in the literature may produce substantially biased estimates. The proposed model and method are also applied to real data from tagged rack lobsters to assess the possible seasonal effect on growth.

Estimating equations for removal data analysis

We consider the problem of estimating a population size from successive catches taken during a removal experiment and propose two estimating functions approaches, the traditional quasi-likelihood (TQL) approach for dependent observations and the conditional quasi-likelihood (CQL) approach using the conditional mean and conditional variance of the catch given previous catches. Asymptotic covariance of the estimates and the relationship between the two methods are derived. Simulation results and application to the catch data from smallmouth bass show that the proposed estimating functions perform better than other existing methods, especially in the presence of overdispersion.

A quasi-likelihood approach for ordered categorical data with overdispersion

Quasi-likelihood (QL) methods are often used to account for overdispersion in categorical data. This paper proposes a new way of constructing a QL function that stems from the conditional mean-variance relationship. Unlike traditional QL approaches to categorical data, this QL function is, in general, not a scaled version of the ordinary log-likelihood function. A simulation study is carried out to examine the performance of the proposed QL method. Fish mortality data from quantal response experiments are used for illustration.

Integrating voice and data on SALAN: an experimental local area network

This paper is concerned with the integration of voice and data on an experimental local area network used by the School of Automation, of the Indian Institute of Science. SALAN (School of Automation Local Area Network) consists of a number of microprocessor-based communication nodes linked to a shared coaxial cable transmission medium. The communication nodes handle the various low-level functions associated with computer communication, and interface user data equipment to the network. SALAN at present provides a file transfer facility between an Intel Series III microcomputer development system and a Texas Instruments Model 990/4 microcomputer system. Further, a packet voice communication system has also been implemented on SALAN. The various aspects of the design and implementation of the above two utilities are discussed.

Concordant molecular and phenotypic data delineate new taxonomy and conservation priorities for the endangered mountain yellow-legged frog

The mountain yellow-legged frog Rana muscosa sensu lato, once abundant in the Sierra Nevada of California and Nevada, and the disjunct Transverse Ranges of southern California, has declined precipitously throughout its range, even though most of its habitat is protected. The species is now extinct in Nevada and reduced to tiny remnants in southern California, where as a distinct population segment, it is classified as Endangered. Introduced predators (trout), air pollution and an infectious disease (chytridiomycosis) threaten remaining populations. A Bayesian analysis of 1901 base pairs of mitochondrial DNA confirms the presence of two deeply divergent clades that come into near contact in the Sierra Nevada. Morphological studies of museum specimens and analysis of acoustic data show that the two major mtDNA clades are readily differentiated phenotypically. Accordingly, we recognize two species, Rana sierrae, in the northern and central Sierra Nevada, and R. muscosa, in the southern Sierra Nevada and southern California. Existing data indicate no range overlap. These results have important implications for the conservation of these two species as they illuminate a profound mismatch between the current delineation of the distinct population segments (southern California vs. Sierra Nevada) and actual species boundaries. For example, our study finds that remnant populations of R. muscosa exist in both the southern Sierra Nevada and the mountains of southern California, which may broaden options for management. In addition, despite the fact that only the southern California populations are listed as Endangered, surveys conducted since 1995 at 225 historic (1899-1994) localities from museum collections show that 93.3% (n=146) of R. sierrae populations and 95.2% (n=79) of R. muscosa populations are extinct. Evidence presented here underscores the need for revision of protected population status to include both species throughout their ranges.

Harnessing information from injury narrative in the 'big data' era: Understanding and applying machine learning for injury surveillance

Objective Vast amounts of injury narratives are collected daily and are available electronically in real time and have great potential for use in injury surveillance and evaluation. Machine learning algorithms have been developed to assist in identifying cases and classifying mechanisms leading to injury in a much timelier manner than is possible when relying on manual coding of narratives. The aim of this paper is to describe the background, growth, value, challenges and future directions of machine learning as applied to injury surveillance. Methods This paper reviews key aspects of machine learning using injury narratives, providing a case study to demonstrate an application to an established human-machine learning approach. Results The range of applications and utility of narrative text has increased greatly with advancements in computing techniques over time. Practical and feasible methods exist for semi-automatic classification of injury narratives which are accurate, efficient and meaningful. The human-machine learning approach described in the case study achieved high sensitivity and positive predictive value and reduced the need for human coding to less than one-third of cases in one large occupational injury database. Conclusion The last 20 years have seen a dramatic change in the potential for technological advancements in injury surveillance. Machine learning of ‘big injury narrative data’ opens up many possibilities for expanded sources of data which can provide more comprehensive, ongoing and timely surveillance to inform future injury prevention policy and practice.

Modelling the distribution and relative abundance of feral camels in the Northern Territory using count data

The objectives of this study were to predict the potential distribution, relative abundance and probability of habitat use by feral camels in southern Northern Territory. Aerial survey data were used to model habitat association. The characteristics of ‘used’ (where camels were observed) v. ‘unused’ (pseudo-absence) sites were compared. Habitat association and abundance were modelled using generalised additive model (GAM) methods. The models predicted habitat suitability and the relative abundance of camels in southern Northern Territory. The habitat suitability maps derived in the present study indicate that camels have suitable habitat in most areas of southern Northern Territory. The index of abundance model identified areas of relatively high camel abundance. Identifying preferred habitats and areas of high abundance can help focus control efforts.

The genetic association between personality and major depression or bipolar disorder. A polygenic score analysis using genome-wide association data

The relationship between major depressive disorder (MDD) and bipolar disorder (BD) remains controversial. Previous research has reported differences and similarities in risk factors for MDD and BD, such as predisposing personality traits. For example, high neuroticism is related to both disorders, whereas openness to experience is specific for BD. This study examined the genetic association between personality and MDD and BD by applying polygenic scores for neuroticism, extraversion, openness to experience, agreeableness and conscientiousness to both disorders. Polygenic scores reflect the weighted sum of multiple single-nucleotide polymorphism alleles associated with the trait for an individual and were based on a meta-analysis of genome-wide association studies for personality traits including 13,835 subjects. Polygenic scores were tested for MDD in the combined Genetic Association Information Network (GAIN-MDD) and MDD2000+ samples (N=8921) and for BD in the combined Systematic Treatment Enhancement Program for Bipolar Disorder and Wellcome Trust Case-Control Consortium samples (N=6329) using logistic regression analyses. At the phenotypic level, personality dimensions were associated with MDD and BD. Polygenic neuroticism scores were significantly positively associated with MDD, whereas polygenic extraversion scores were significantly positively associated with BD. The explained variance of MDD and BD, approximately 0.1%, was highly comparable to the variance explained by the polygenic personality scores in the corresponding personality traits themselves (between 0.1 and 0.4%). This indicates that the proportions of variance explained in mood disorders are at the upper limit of what could have been expected. This study suggests shared genetic risk factors for neuroticism and MDD on the one hand and for extraversion and BD on the other.

A hidden Markov model approach for determining vessel activity from vessel monitoring system data.

Many fisheries worldwide have adopted vessel monitoring systems (VMS) for compliance purposes. An added benefit of these systems is that they collect a large amount of data on vessel locations at very fine spatial and temporal scales. This data can provide a wealth of information for stock assessment, research, and management. However, since most VMS implementations record vessel location at set time intervals with no regard to vessel activity, some methodology is required to determine which data records correspond to fishing activity. This paper describes a probabilistic approach, based on hidden Markov models (HMMs), to determine vessel activity. A HMM provides a natural framework for the problem and, by definition, models the intrinsic temporal correlation of the data. The paper describes the general approach that was developed and presents an example of this approach applied to the Queensland trawl fishery off the coast of eastern Australia. Finally, a simulation experiment is presented that compares the misallocation rates of the HMM approach with other approaches.

Short- and long-term movement patterns in the freshwater whipray (Himantura dalyensis) determined by the signal processing of passive acoustic telemetry data.

Patterns of movement in aquatic animals reflect ecologically important behaviours. Cyclical changes in the abiotic environment influence these movements, but when multiple processes occur simultaneously, identifying which is responsible for the observed movement can be complex. Here we used acoustic telemetry and signal processing to define the abiotic processes responsible for movement patterns in freshwater whiprays (Himantura dalyensis). Acoustic transmitters were implanted into the whiprays and their movements detected over 12 months by an array of passive acoustic receivers, deployed throughout 64 km of the Wenlock River, Qld, Australia. The time of an individual's arrival and departure from each receiver detection field was used to estimate whipray location continuously throughout the study. This created a linear-movement-waveform for each whipray and signal processing revealed periodic components within the waveform. Correlation of movement periodograms with those from abiotic processes categorically illustrated that the diel cycle dominated the pattern of whipray movement during the wet season, whereas tidal and lunar cycles dominated during the dry season. The study methodology represents a valuable tool for objectively defining the relationship between abiotic processes and the movement patterns of free-ranging aquatic animals and is particularly expedient when periods of no detection exist within the animal location data.