Statistical power calculation and sample size determination for environmental studies with data below detection limits

Power calculation and sample size determination are critical in designing environmental monitoring programs. The traditional approach based on comparing the mean values may become statistically inappropriate and even invalid when substantial proportions of the response values are below the detection limits or censored because strong distributional assumptions have to be made on the censored observations when implementing the traditional procedures. In this paper, we propose a quantile methodology that is robust to outliers and can also handle data with a substantial proportion of below-detection-limit observations without the need of imputing the censored values. As a demonstration, we applied the methods to a nutrient monitoring project, which is a part of the Perth Long-Term Ocean Outlet Monitoring Program. In this example, the sample size required by our quantile methodology is, in fact, smaller than that by the traditional t-test, illustrating the merit of our method.

Evaluating multivariate volatility forecasts : how effective are statistical and economic loss functions?

Multivariate volatility forecasts are an important input in many financial applications, in particular portfolio optimisation problems. Given the number of models available and the range of loss functions to discriminate between them, it is obvious that selecting the optimal forecasting model is challenging. The aim of this thesis is to thoroughly investigate how effective many commonly used statistical (MSE and QLIKE) and economic (portfolio variance and portfolio utility) loss functions are at discriminating between competing multivariate volatility forecasts. An analytical investigation of the loss functions is performed to determine whether they identify the correct forecast as the best forecast. This is followed by an extensive simulation study examines the ability of the loss functions to consistently rank forecasts, and their statistical power within tests of predictive ability. For the tests of predictive ability, the model confidence set (MCS) approach of Hansen, Lunde and Nason (2003, 2011) is employed. As well, an empirical study investigates whether simulation findings hold in a realistic setting. In light of these earlier studies, a major empirical study seeks to identify the set of superior multivariate volatility forecasting models from 43 models that use either daily squared returns or realised volatility to generate forecasts. This study also assesses how the choice of volatility proxy affects the ability of the statistical loss functions to discriminate between forecasts. Analysis of the loss functions shows that QLIKE, MSE and portfolio variance can discriminate between multivariate volatility forecasts, while portfolio utility cannot. An examination of the effective loss functions shows that they all can identify the correct forecast at a point in time, however, their ability to discriminate between competing forecasts does vary. That is, QLIKE is identified as the most effective loss function, followed by portfolio variance which is then followed by MSE. The major empirical analysis reports that the optimal set of multivariate volatility forecasting models includes forecasts generated from daily squared returns and realised volatility. Furthermore, it finds that the volatility proxy affects the statistical loss functions’ ability to discriminate between forecasts in tests of predictive ability. These findings deepen our understanding of how to choose between competing multivariate volatility forecasts.

Improving the statistical preparation for measuring soil N2O flux by closed chamber

Nitrous oxide emissions from soil are known to be spatially and temporally volatile. Reliable estimation of emissions over a given time and space depends on measuring with sufficient intensity but deciding on the number of measuring stations and the frequency of observation can be vexing. The question of low frequency manual observations providing comparable results to high frequency automated sampling also arises. Data collected from a replicated field experiment was intensively studied with the intention to give some statistically robust guidance on these issues. The experiment had nitrous oxide soil to air flux monitored within 10 m by 2.5 m plots by automated closed chambers under a 3 h average sampling interval and by manual static chambers under a three day average sampling interval over sixty days. Observed trends in flux over time by the static chambers were mostly within the auto chamber bounds of experimental error. Cumulated nitrous oxide emissions as measured by each system were also within error bounds. Under the temporal response pattern in this experiment, no significant loss of information was observed after culling the data to simulate results under various low frequency scenarios. Within the confines of this experiment observations from the manual chambers were not spatially correlated above distances of 1 m. Statistical power was therefore found to improve due to increased replicates per treatment or chambers per replicate. Careful after action review of experimental data can deliver savings for future work.

Genome-wide association studies of quantitative traits with related individuals: Little (power) lost but much to be gained

For complex disease genetics research in human populations, remarkable progress has been made in recent times with the publication of a number of genome-wide association scans (GWAS) and subsequent statistical replications. These studies have identified new genes and pathways implicated in disease, many of which were not known before. Given these early successes, more GWAS are being conducted and planned, both for disease and quantitative phenotypes. Many researchers and clinicians have DNA samples available on collections of families, including both cases and controls. Twin registries around the world have facilitated the collection of large numbers of families, with DNA and multiple quantitative phenotypes collected on twin pairs and their relatives. In the design of a new GWAS with a fixed budget for the number of chips, the question arises whether to include or exclude related individuals. It is commonly believed to be preferable to use unrelated individuals in the first stage of a GWAS because relatives are 'over-matched' for genotypes. In this study, we quantify that for GWAS of a quantitative phenotype, relative to a sample of unrelated individuals surprisingly little power is lost when using relatives. The advantages of using relatives are manifold, including the ability to perform more quality control, the choice to perform within-family tests of association that are robust to population stratification, and the ability to perform joint linkage and association analysis. Therefore, the advantages of using relatives in GWAS for quantitative traits may well outweigh the small disadvantage in terms of statistical power.

Prostate cancer biomarkers and the emerging proteomic techniques used in biomarker research

Prostate cancer (CaP) is the second leading cause of cancer-related deaths in North American males and the most common newly diagnosed cancer in men world wide. Biomarkers are widely used for both early detection and prognostic tests for cancer. The current, commonly used biomarker for CaP is serum prostate specific antigen (PSA). However, the specificity of this biomarker is low as its serum level is not only increased in CaP but also in various other diseases, with age and even body mass index. Human body fluids provide an excellent resource for the discovery of biomarkers, with the advantage over tissue/biopsy samples of their ease of access, due to the less invasive nature of collection. However, their analysis presents challenges in terms of variability and validation. Blood and urine are two human body fluids commonly used for CaP research, but their proteomic analyses are limited both by the large dynamic range of protein abundance making detection of low abundance proteins difficult and in the case of urine, by the high salt concentration. To overcome these challenges, different techniques for removal of high abundance proteins and enrichment of low abundance proteins are used. Their applications and limitations are discussed in this review. A number of innovative proteomic techniques have improved detection of biomarkers. They include two dimensional differential gel electrophoresis (2D-DIGE), quantitative mass spectrometry (MS) and functional proteomic studies, i.e., investigating the association of post translational modifications (PTMs) such as phosphorylation, glycosylation and protein degradation. The recent development of quantitative MS techniques such as stable isotope labeling with amino acids in cell culture (SILAC), isobaric tags for relative and absolute quantitation (iTRAQ) and multiple reaction monitoring (MRM) have allowed proteomic researchers to quantitatively compare data from different samples. 2D-DIGE has greatly improved the statistical power of classical 2D gel analysis by introducing an internal control. This chapter aims to review novel CaP biomarkers as well as to discuss current trends in biomarker research from two angles: the source of biomarkers (particularly human body fluids such as blood and urine), and emerging proteomic approaches for biomarker research.

Recruiting and engaging new mothers in nutrition research studies : lessons from the Australian NOURISH randomised controlled trial

Background: Despite important implications for the budgets, statistical power and generalisability of research findings, detailed reports of recruitment and retention in randomised controlled trials (RCTs) are rare. The NOURISH RCT evaluated a community-based intervention for first-time mothers that promoted protective infant feeding practices as a primary prevention strategy for childhood obesity. The aim of this paper is to provide a detailed description and evaluation of the recruitment and retention strategies used. Methods: A two stage recruitment process designed to provide a consecutive sampling framework was used. First time mothers delivering healthy term infants were initially approached in postnatal wards of the major maternity services in two Australian cities for consent to later contact (Stage 1). When infants were about four months old mothers were re-contacted by mail for enrolment (Stage 2), baseline measurements (Time 1) and subsequent random allocation to the intervention or control condition. Outcomes were assessed at infant ages 14 months (Time 2) and 24 months (Time 3). Results: At Stage 1, 86% of eligible mothers were approached and of these women, 76% consented to later contact. At Stage 2, 3% had become ineligible and 76% could be recontacted. Of the latter, 44% consented to full enrolment and were allocated. This represented 21% of mothers screened as eligible at Stage 1. Retention at Time 3 was 78%. Mothers who did not consent or discontinued the study were younger and less likely to have a university education. Conclusions: The consent and retention rates of our sample of first time mothers are comparable with or better than other similar studies. The recruitment strategy used allowed for detailed information from non-consenters to be collected; thus selection bias could be estimated. Recommendations for future studies include being able to contact participants via mobile phone (particular text messaging), offering home visits to reduce participant burden and considering the use of financial incentives to support participant retention.

A web application to perform linkage disequilibrium and linkage analyses on a computational grid

Motivation: Unravelling the genetic architecture of complex traits requires large amounts of data, sophisticated models and large computational resources. The lack of user-friendly software incorporating all these requisites is delaying progress in the analysis of complex traits. Methods: Linkage disequilibrium and linkage analysis (LDLA) is a high-resolution gene mapping approach based on sophisticated mixed linear models, applicable to any population structure. LDLA can use population history information in addition to pedigree and molecular markers to decompose traits into genetic components. Analyses are distributed in parallel over a large public grid of computers in the UK. Results: We have proven the performance of LDLA with analyses of simulated data. There are real gains in statistical power to detect quantitative trait loci when using historical information compared with traditional linkage analysis. Moreover, the use of a grid of computers significantly increases computational speed, hence allowing analyses that would have been prohibitive on a single computer. © The Author 2009. Published by Oxford University Press. All rights reserved.

Inferring kangaroo phylogeny from incongruent nuclear and mitochondrial genes

The marsupial genus Macropus includes three subgenera, the familiar large grazing kangaroos and wallaroos of M. (Macropus) and M. (Osphranter), as well as the smaller mixed grazing/browsing wallabies of M. (Notamacropus). A recent study of five concatenated nuclear genes recommended subsuming the predominantly browsing Wallabia bicolor (swamp wallaby) into Macropus. To further examine this proposal we sequenced partial mitochondrial genomes for kangaroos and wallabies. These sequences strongly favour the morphological placement of W. bicolor as sister to Macropus, although place M. irma (black-gloved wallaby) within M. (Osphranter) rather than as expected, with M. (Notamacropus). Species tree estimation from separately analysed mitochondrial and nuclear genes favours retaining Macropus and Wallabia as separate genera. A simulation study finds that incomplete lineage sorting among nuclear genes is a plausible explanation for incongruence with the mitochondrial placement of W. bicolor, while mitochondrial introgression from a wallaroo into M. irma is the deepest such event identified in marsupials. Similar such coalescent simulations for interpreting gene tree conflicts will increase in both relevance and statistical power as species-level phylogenetics enters the genomic age. Ecological considerations in turn, hint at a role for selection in accelerating the fixation of introgressed or incompletely sorted loci. More generally the inclusion of the mitochondrial sequences substantially enhanced phylogenetic resolution. However, we caution that the evolutionary dynamics that enhance mitochondria as speciation indicators in the presence of incomplete lineage sorting may also render them especially susceptible to introgression.

Phenotypical characterisation of the isolated Norfolk Island population focusing on epidemiological indicators of cardiovascular disease

Objectives Only 193 people from Pitcairn Island, all descended from 9 ‘Bounty’ mutineers and 12 Tahitian women, moved to the uninhabited Norfolk Island in 1856. Our objective was to assess the population of Norfolk Island, several thousand km off the eastern coast of Australia, as a genetic isolate of potential use for cardiovascular disease (CVD) gene mapping. Methods A total of 602 participants, approximately two thirds of the island’s present adult population, were characterized for a panel of CVD risk factors. Statistical power and heritability were calculated. Results Norfolk Islander’s possess an increased prevalence of hypertension, obesity and multiple CVD risk factors when compared to outbred Caucasian populations. 64% of the study participants were descendents of the island’s original founder population. Triglycerides, cholesterol, and blood pressures all had heritabilities above 0.2. Conclusions The Norfolk land population is a potentially useful genetic isolate for gene mapping studies aimed at identifying CVD risk factor quantitative trait loci (QTL).

Estimating local stream fish assemblage attributes: Sampling effort and efficiency at two spatial scales

As part of a wider study to develop an ecosystem-health monitoring program for wadeable streams of south-eastern Queensland, Australia, comparisons were made regarding the accuracy, precision and relative efficiency of single-pass backpack electrofishing and multiple-pass electrofishing plus supplementary seine netting to quantify fish assemblage attributes at two spatial scales (within discrete mesohabitat units and within stream reaches consisting of multiple mesohabitat units). The results demonstrate that multiple-pass electrofishing plus seine netting provide more accurate and precise estimates of fish species richness, assemblage composition and species relative abundances in comparison to single-pass electrofishing alone, and that intensive sampling of three mesohabitat units (equivalent to a riffle-run-pool sequence) is a more efficient sampling strategy to estimate reach-scale assemblage attributes than less intensive sampling over larger spatial scales. This intensive sampling protocol was sufficiently sensitive that relatively small differences in assemblage attributes (<20%) could be detected with a high statistical power (1-β > 0.95) and that relatively few stream reaches (<4) need be sampled to accurately estimate assemblage attributes close to the true population means. The merits and potential drawbacks of the intensive sampling strategy are discussed, and it is deemed to be suitable for a range of monitoring and bioassessment objectives.

Progress towards understanding the genetics of posttraumatic stress disorder

Posttraumatic stress disorder (PTSD) is a complex syndrome that occurs following exposure to a potentially life threatening traumatic event. This review summarises the literature on the genetics of PTSD including gene–environment interactions (GxE), epigenetics and genetics of treatment response. Numerous genes have been shown to be associated with PTSD using candidate gene approaches. Genome-wide association studies have been limited due to the large sample size required to reach statistical power. Studies have shown that GxE interactions are important for PTSD susceptibility. Epigenetics plays an important role in PTSD susceptibility and some of the most promising studies show stress and child abuse trigger epigenetic changes. Much of the molecular genetics of PTSD remains to be elucidated. However, it is clear that identifying genetic markers and environmental triggers has the potential to advance early PTSD diagnosis and therapeutic interventions and ultimately ease the personal and financial burden of this debilitating disorder.

Quantifying the heritability of task-related brain activation and performance during the N-back working memory task: A twin fMRI study

Working memory-related brain activation has been widely studied, and impaired activation patterns have been reported for several psychiatric disorders. We investigated whether variation in N-back working memory brain activation is genetically influenced in 60 pairs of twins, (29 monozygotic (MZ), 31 dizygotic (DZ); mean age 24.4 ± 1.7S.D.). Task-related brain response (BOLD percent signal difference of 2 minus 0-back) was measured in three regions of interest. Although statistical power was low due to the small sample size, for middle frontal gyrus, angular gyrus, and supramarginal gyrus, the MZ correlations were, in general, approximately twice those of the DZ pairs, with non-significant heritability estimates (14-30%) in the low-moderate range. Task performance was strongly influenced by genes (57-73%) and highly correlated with cognitive ability (0.44-0.55). This study, which will be expanded over the next 3 years, provides the first support that individual variation in working memory-related brain activation is to some extent influenced by genes.

Heritability of working memory brain activation

Although key to understanding individual variation in task-related brain activation, the genetic contribution to these individual differences remains largely unknown. Here we report voxel-by-voxel genetic model fitting in a large sample of 319 healthy, young adult, human identical and fraternal twins (mean ± SD age, 23.6 ±1.8 years) who performed an n-back working memory task during functional magnetic resonance imaging (fMRI) at a high magnetic field (4 tesla). Patterns of task-related brain response (BOLD signal difference of 2-back minus 0-back) were significantly heritable, with the highest estimates (40 - 65%) in the inferior, middle, and superior frontal gyri, left supplementary motor area, precentral and postcentral gyri, middle cingulate cortex, superior medial gyrus, angular gyrus, superior parietal lobule, including precuneus, and superior occipital gyri. Furthermore, high test-retest reliability for a subsample of 40 twins indicates that nongenetic variance in the fMRI brain response is largely due to unique environmental influences rather than measurement error. Individual variations in activation of the working memory network are therefore significantly influenced by genetic factors. By establishing the heritability of cognitive brain function in a large sample that affords good statistical power, and using voxel-by-voxel analyses, this study provides the necessary evidence for task-related brain activation to be considered as an endophenotype for psychiatric or neurological disorders, and represents a substantial new contribution to the field of neuroimaging genetics. These genetic brain maps should facilitate discovery of gene variants influencing cognitive brain function through genome-wide association studies, potentially opening up new avenues in the treatment of brain disorders.

Multi-site study of additive genetic effects on fractional anisotropy of cerebral white matter: Comparing meta and megaanalytical approaches for data pooling

Combining datasets across independent studies can boost statistical power by increasing the numbers of observations and can achieve more accurate estimates of effect sizes. This is especially important for genetic studies where a large number of observations are required to obtain sufficient power to detect and replicate genetic effects. There is a need to develop and evaluate methods for joint-analytical analyses of rich datasets collected in imaging genetics studies. The ENIGMA-DTI consortium is developing and evaluating approaches for obtaining pooled estimates of heritability through meta-and mega-genetic analytical approaches, to estimate the general additive genetic contributions to the intersubject variance in fractional anisotropy (FA) measured from diffusion tensor imaging (DTI). We used the ENIGMA-DTI data harmonization protocol for uniform processing of DTI data from multiple sites. We evaluated this protocol in five family-based cohorts providing data from a total of 2248 children and adults (ages: 9-85) collected with various imaging protocols. We used the imaging genetics analysis tool, SOLAR-Eclipse, to combine twin and family data from Dutch, Australian and Mexican-American cohorts into one large "mega-family". We showed that heritability estimates may vary from one cohort to another. We used two meta-analytical (the sample-size and standard-error weighted) approaches and a mega-genetic analysis to calculate heritability estimates across-population. We performed leave-one-out analysis of the joint estimates of heritability, removing a different cohort each time to understand the estimate variability. Overall, meta- and mega-genetic analyses of heritability produced robust estimates of heritability.

Subcortical brain alterations in major depressive disorder: findings from the ENIGMA Major Depressive Disorder working group

The pattern of structural brain alterations associated with major depressive disorder (MDD) remains unresolved. This is in part due to small sample sizes of neuroimaging studies resulting in limited statistical power, disease heterogeneity and the complex interactions between clinical characteristics and brain morphology. To address this, we meta-analyzed three-dimensional brain magnetic resonance imaging data from 1728 MDD patients and 7199 controls from 15 research samples worldwide, to identify subcortical brain volumes that robustly discriminate MDD patients from healthy controls. Relative to controls, patients had significantly lower hippocampal volumes (Cohen’s d=−0.14, % difference=−1.24). This effect was driven by patients with recurrent MDD (Cohen’s d=−0.17, % difference=−1.44), and we detected no differences between first episode patients and controls. Age of onset ⩽21 was associated with a smaller hippocampus (Cohen’s d=−0.20, % difference=−1.85) and a trend toward smaller amygdala (Cohen’s d=−0.11, % difference=−1.23) and larger lateral ventricles (Cohen’s d=0.12, % difference=5.11). Symptom severity at study inclusion was not associated with any regional brain volumes. Sample characteristics such as mean age, proportion of antidepressant users and proportion of remitted patients, and methodological characteristics did not significantly moderate alterations in brain volumes in MDD. Samples with a higher proportion of antipsychotic medication users showed larger caudate volumes in MDD patients compared with controls. This currently largest worldwide effort to identify subcortical brain alterations showed robust smaller hippocampal volumes in MDD patients, moderated by age of onset and first episode versus recurrent episode status.