Statistical modelling and power analysis for detecting trends in total suspended sediment loads

The export of sediments from coastal catchments can have detrimental impacts on estuaries and near shore reef ecosystems such as the Great Barrier Reef. Catchment management approaches aimed at reducing sediment loads require monitoring to evaluate their effectiveness in reducing loads over time. However, load estimation is not a trivial task due to the complex behaviour of constituents in natural streams, the variability of water flows and often a limited amount of data. Regression is commonly used for load estimation and provides a fundamental tool for trend estimation by standardising the other time specific covariates such as flow. This study investigates whether load estimates and resultant power to detect trends can be enhanced by (i) modelling the error structure so that temporal correlation can be better quantified, (ii) making use of predictive variables, and (iii) by identifying an efficient and feasible sampling strategy that may be used to reduce sampling error. To achieve this, we propose a new regression model that includes an innovative compounding errors model structure and uses two additional predictive variables (average discounted flow and turbidity). By combining this modelling approach with a new, regularly optimised, sampling strategy, which adds uniformity to the event sampling strategy, the predictive power was increased to 90%. Using the enhanced regression model proposed here, it was possible to detect a trend of 20% over 20 years. This result is in stark contrast to previous conclusions presented in the literature. (C) 2014 Elsevier B.V. All rights reserved.

Generalised growth models for aquatic species with an application to blacklip abalone (Haliotis rubra)

This paper presents a maximum likelihood method for estimating growth parameters for an aquatic species that incorporates growth covariates, and takes into consideration multiple tag-recapture data. Individual variability in asymptotic length, age-at-tagging, and measurement error are also considered in the model structure. Using distribution theory, the log-likelihood function is derived under a generalised framework for the von Bertalanffy and Gompertz growth models. Due to the generality of the derivation, covariate effects can be included for both models with seasonality and tagging effects investigated. Method robustness is established via comparison with the Fabens, improved Fabens, James and a non-linear mixed-effects growth models, with the maximum likelihood method performing the best. The method is illustrated further with an application to blacklip abalone (Haliotis rubra) for which a strong growth-retarding tagging effect that persisted for several months was detected

Modeling strategies in longitudinal data analysis: Covariate, variance function and correlation structure selection

A modeling paradigm is proposed for covariate, variance and working correlation structure selection for longitudinal data analysis. Appropriate selection of covariates is pertinent to correct variance modeling and selecting the appropriate covariates and variance function is vital to correlation structure selection. This leads to a stepwise model selection procedure that deploys a combination of different model selection criteria. Although these criteria find a common theoretical root based on approximating the Kullback-Leibler distance, they are designed to address different aspects of model selection and have different merits and limitations. For example, the extended quasi-likelihood information criterion (EQIC) with a covariance penalty performs well for covariate selection even when the working variance function is misspecified, but EQIC contains little information on correlation structures. The proposed model selection strategies are outlined and a Monte Carlo assessment of their finite sample properties is reported. Two longitudinal studies are used 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.

Criteria for working-correlation-structure selection in GEE: Assessment via simulation

Efficiency of analysis using generalized estimation equations is enhanced when intracluster correlation structure is accurately modeled. We compare two existing criteria (a quasi-likelihood information criterion, and the Rotnitzky-Jewell criterion) to identify the true correlation structure via simulations with Gaussian or binomial response, covariates varying at cluster or observation level, and exchangeable or AR(l) intracluster correlation structure. Rotnitzky and Jewell's approach performs better when the true intracluster correlation structure is exchangeable, while the quasi-likelihood criteria performs better for an AR(l) structure.

Analysing commercial catch and effort data from a penaeid trawl fishery: A comparison of linear models, mixed models, and generalised estimating equations approaches

Statistical methods are often used to analyse commercial catch and effort data to provide standardised fishing effort and/or a relative index of fish abundance for input into stock assessment models. Achieving reliable results has proved difficult in Australia's Northern Prawn Fishery (NPF), due to a combination of such factors as the biological characteristics of the animals, some aspects of the fleet dynamics, and the changes in fishing technology. For this set of data, we compared four modelling approaches (linear models, mixed models, generalised estimating equations, and generalised linear models) with respect to the outcomes of the standardised fishing effort or the relative index of abundance. We also varied the number and form of vessel covariates in the models. Within a subset of data from this fishery, modelling correlation structures did not alter the conclusions from simpler statistical models. The random-effects models also yielded similar results. This is because the estimators are all consistent even if the correlation structure is mis-specified, and the data set is very large. However, the standard errors from different models differed, suggesting that different methods have different statistical efficiency. We suggest that there is value in modelling the variance function and the correlation structure, to make valid and efficient statistical inferences and gain insight into the data. We found that fishing power was separable from the indices of prawn abundance only when we offset the impact of vessel characteristics at assumed values from external sources. This may be due to the large degree of confounding within the data, and the extreme temporal changes in certain aspects of individual vessels, the fleet and the fleet dynamics.

A generalized estimating equations approach for analysis of the impact of new technology on a trawl fishery

The article describes a generalized estimating equations approach that was used to investigate the impact of technology on vessel performance in a trawl fishery during 1988-96, while accounting for spatial and temporal correlations in the catch-effort data. Robust estimation of parameters in the presence of several levels of clustering depended more on the choice of cluster definition than on the choice of correlation structure within the cluster. Models with smaller cluster sizes produced stable results, while models with larger cluster sizes, that may have had complex within-cluster correlation structures and that had within-cluster covariates, produced estimates sensitive to the correlation structure. The preferred model arising from this dataset assumed that catches from a vessel were correlated in the same years and the same areas, but independent in different years and areas. The model that assumed catches from a vessel were correlated in all years and areas, equivalent to a random effects term for vessel, produced spurious results. This was an unexpected finding that highlighted the need to adopt a systematic strategy for modelling. The article proposes a modelling strategy of selecting the best cluster definition first, and the working correlation structure (within clusters) second. The article discusses the selection and interpretation of the model in the light of background knowledge of the data and utility of the model, and the potential for this modelling approach to apply in similar statistical situations.

Analysis of recreational fish catches – dealing with highly skewed distributions with many zeros

Data from surveys of recreational anglers fishing on three estuaries in eastern Australia reveal highly skewed distributions of catches with many zeros. Such data may be analysed using a two component approach involving a binary (zero/non-zero catch) response and the non-zero catches. A truncated regression model was effective in analysing the non-zero catches. Covariates were incorporated in the modelling, and their critical assessment has led to improved measures of fishing effort for this recreational fishery.

Disease mapping using Bayesian hierarchical models

description and analysis of geographically indexed health data with respect to demographic, environmental, behavioural, socioeconomic, genetic, and infectious risk factors (Elliott andWartenberg 2004). Disease maps can be useful for estimating relative risk; ecological analyses, incorporating area and/or individual-level covariates; or cluster analyses (Lawson 2009). As aggregated data are often more readily available, one common method of mapping disease is to aggregate the counts of disease at some geographical areal level, and present them as choropleth maps (Devesa et al. 1999; Population Health Division 2006). Therefore, this chapter will focus exclusively on methods appropriate for areal data...

Association of hearing impairment and subsequent driving mobility in older adults

- Purpose of the study Hearing impairment (HI) is associated with driving safety (e.g., increased crashes and poor on-road driving performance). However, little is known about HI and driving mobility. This study examined the longitudinal association of audiometric hearing with older adults’ driving mobility over three years. - Design and Methods Secondary data analyses were conducted of 500 individuals (63-90 years) from the Staying Keen in Later Life (SKILL) study. Hearing (pure tone average of 0.5, 1, and 2 kHz) was assessed in the better hearing ear and categorized into normal hearing <25 dB HL; mild HI 26-40 dB HL; or moderate and greater HI>41 dB HL. The Useful Field of View Test (UFOV) was used to estimate the risk for adverse driving events. MANCOVA compared driving mobility between HI levels across time, adjusting for age, sex, race, hypertension, and stroke. Adjusting for these same covariates, Cox regression analyses examined incidence of driving cessation by HI across three years. - Results Individuals with moderate or greater HI performed poorly on the UFOV, indicating increased risk for adverse driving events (p<.001). No significant differences were found among older adults with varying levels of HI for driving mobility (ps>.05), including driving cessation rates (p=.38), across time. - Implications Although prior research indicates older adults with HI may be at higher risk for crashes, they may not modify driving over time. Further exploration of this issue is required to optimize efforts to improve driving safety and mobility among older adults.

Mapping and characterisation of the inter-reefal benthic assemblages of the Torres Strait

A comprehensive survey of the benthic assemblages of the Torres Strait was conducted in order to provide critical baseline information for regional marine planning, assessing the environmental sustainability of fisheries and understanding the ecosystems of the region. Over 150 sites throughout the region were sampled with a modified prawn trawl, towed underwater video, pipe dredge and epibenthic sled. This manuscript provides a broad overview of the activities undertaken and data collected. Two thousand three hundred and seventy-two different nominal species were sampled by the trawl and sled, only 728 by both gears. The towed video was not able to provide the same level of taxonomic resolution of epibenthic taxa, but was particularly useful in areas where the seabed was too rough to be sampled. Data from the trawl, sled and video were combined to characterise the epibenthic assemblages of the region. Data from the towed video was also used to provide a characterisation of the inter-reefal benthic habitats, which was then analysed in combination with physical covariate data to examine relationships between the two. Levels of mud and gravel in the sediments, trawling effort and seabed current stress were the covariates most significantly correlated with the nature of the seabed habitats.

Impulsivity, health-related behaviour and disease : A prospective study

In clinical settings impulsivity refers to a symptom of psychiatric disorder, but nonclinically oriented research treats impulsivity as a personality and temperament dimension. This prospective study examined whether impulsivity predicts adverse health-related behaviour and increased risk of health problems in a large, nonclinical sample of 5433 subjects working in 12 Finnish hospitals. The data were collected using two questionnaire surveys at a 2-year interval. After controlling for alcohol use at baseline, higher impulsivity predicted increased alcohol consumption at follow-up in both genders (p < .01) and was associated with increased likelihood of becoming a heavy drinker or taking up smoking (p < .05). Impulsivity also predicted an increased number of cigarettes smoked per day in the follow-up among women (p < .001), but not among men, although adjustment for the number of cigarettes smoked at baseline attenuated these associations (p = .08 for women). In men, higher impulsivity was associated with shorter sleep duration and waking up several times per night independent of baseline characteristics (p < .01), whereas in women, higher impulsivity predicted difficulty in falling asleep and waking up feeling tired after the usual amount of sleep (p < .05). In women, these associations became nonsignificant after adjustment for pre-existing somatic and psychiatric diseases. Finally, higher impulsivity was associated with an increased 2-year incidence of physician-diagnosed peptic ulcer disease (adjusted odds ratio (OR) = 2.42, 95% confidence interval (CI) = 1.21 - 4.82) and onset of depression (OR = 1.95, 95% CI = 1.28 - 2.97) after adjustment for a variety of baseline covariates. In conclusion, this study shows that in a nonclinical population, impulsivity appears to be a risk factor for various unhealthy behaviour and health problems.

Inference of the genetic architecture underlying BMI and height with the use of 20,240 sibling pairs

Evidence that complex traits are highly polygenic has been presented by population-based genome-wide association studies (GWASs) through the identification of many significant variants, as well as by family-based de novo sequencing studies indicating that several traits have a large mutational target size. Here, using a third study design, we show results consistent with extreme polygenicity for body mass index (BMI) and height. On a sample of 20,240 siblings (from 9,570 nuclear families), we used a within-family method to obtain narrow-sense heritability estimates of 0.42 (SE = 0.17, p = 0.01) and 0.69 (SE = 0.14, p = 6 x 10(-)(7)) for BMI and height, respectively, after adjusting for covariates. The genomic inflation factors from locus-specific linkage analysis were 1.69 (SE = 0.21, p = 0.04) for BMI and 2.18 (SE = 0.21, p = 2 x 10(-10)) for height. This inflation is free of confounding and congruent with polygenicity, consistent with observations of ever-increasing genomic-inflation factors from GWASs with large sample sizes, implying that those signals are due to true genetic signals across the genome rather than population stratification. We also demonstrate that the distribution of the observed test statistics is consistent with both rare and common variants underlying a polygenic architecture and that previous reports of linkage signals in complex traits are probably a consequence of polygenic architecture rather than the segregation of variants with large effects. The convergent empirical evidence from GWASs, de novo studies, and within-family segregation implies that family-based sequencing studies for complex traits require very large sample sizes because the effects of causal variants are small on average.

Genetic influences on handedness: data from 25,732 Australian and Dutch twin families

Handedness refers to a consistent asymmetry in skill or preferential use between the hands and is related to lateralization within the brain of other functions such as language. Previous twin studies of handedness have yielded inconsistent results resulting from a general lack of statistical power to find significant effects. Here we present analyses from a large international collaborative study of handedness (assessed by writing/drawing or self report) in Australian and Dutch twins and their siblings (54,270 individuals from 25,732 families). Maximum likelihood analyses incorporating the effects of known covariates (sex, year of birth and birth weight) revealed no evidence of hormonal transfer, mirror imaging or twin specific effects. There were also no differences in prevalence between zygosity groups or between twins and their singleton siblings. Consistent with previous meta-analyses, additive genetic effects accounted for about a quarter (23.64%) of the variance (95%CI 20.17, 27.09%) with the remainder accounted for by non-shared environmental influences. The implications of these findings for handedness both as a primary phenotype and as a covariate in linkage and association analyses are discussed.

A Bayesian hurdle model for analysis of an insect resistance monitoring database

Motivated by the analysis of the Australian Grain Insect Resistance Database (AGIRD), we develop a Bayesian hurdle modelling approach to assess trends in strong resistance of stored grain insects to phosphine over time. The binary response variable from AGIRD indicating presence or absence of strong resistance is characterized by a majority of absence observations and the hurdle model is a two step approach that is useful when analyzing such a binary response dataset. The proposed hurdle model utilizes Bayesian classification trees to firstly identify covariates and covariate levels pertaining to possible presence or absence of strong resistance. Secondly, generalized additive models (GAMs) with spike and slab priors for variable selection are fitted to the subset of the dataset identified from the Bayesian classification tree indicating possibility of presence of strong resistance. From the GAM we assess trends, biosecurity issues and site specific variables influencing the presence of strong resistance using a variable selection approach. The proposed Bayesian hurdle model is compared to its frequentist counterpart, and also to a naive Bayesian approach which fits a GAM to the entire dataset. The Bayesian hurdle model has the benefit of providing a set of good trees for use in the first step and appears to provide enough flexibility to represent the influence of variables on strong resistance compared to the frequentist model, but also captures the subtle changes in the trend that are missed by the frequentist and naive Bayesian models. © 2014 Springer Science+Business Media New York.