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.

The effect of an in–shoe orthotic heel lift on loading of the Achilles tendon during shod walking

- Study Design Controlled laboratory study - Objective To investigate the effect of a 12–mm in–shoe orthotic heel lift on Achilles tendon loading during shod walking using transmission–mode ultrasonography. - Background Orthotic heel lifts are thought to lower tension in the Achilles tendon but evidence for this effect is equivocal. - Methods The propagation speed of ultrasound, which is governed by the elastic modulus and density of tendon and is proportional to the tensile load to which it is exposed, was measured in the right Achilles tendon of twelve recreationally–active males during shod treadmill walking at matched speeds (3.4±0.7 km/h), with and without addition of a heel lift. Vertical ground reaction force and spatiotemporal gait parameters were simultaneously recorded. Data were acquired at 100Hz during 10s of steady–state walking. Statistical comparisons were made using paired t–tests (α=.05). - Results Ultrasound transmission speed in the Achilles tendon was characterized by two maxima (P1, P2) and minima (M1, M2) during walking. Addition of a heel lift to footwear resulted in a 2% increase and 2% decrease in the first vertical ground reaction force peak and the local minimum, respectively (P<.05). Peak ultrasonic velocity in the Achilles tendon (P1, P2, M2) was significantly lower with addition of an orthotic heel lift (P<.05). - Conclusions Peak ultrasound transmission speed in the Achilles tendon was lower with the addition of a 12–mm orthotic heel lift, indicating the heel lift reduced tensile load in the Achilles tendon, thereby counteracting the effect of footwear. These findings support the addition of orthotic heel lifts to footwear in the rehabilitation of Achilles tendon disorders where management aims to lower tension within the tendon. - Level of Evidence Therapy, level 2a

Tendinopathy alters ultrasound transmission in the patellar tendon during squatting

Measurement of loading patterns of the patellar tendon during activity is important in understanding tendon injury. We used transmission-mode ultrasonography to investigate patellar tendon loading during squatting in adults with and without tendinopathy. It was hypothesized that axial ultrasonic velocity, a surrogate measure of the elastic modulus of tendon, would be lower in tendinopathy. Ultrasound velocity was measured in both patellar tendons of adults with unilateral patellar tendinopathy (n=9) and in healthy controls (n=16) during a bilateral squat manoeuvre. Sagittal knee movement was measured simultaneously with an electrogoniometer. Statistical comparisons between healthy and injured tendons were made using 2–way mixed–design ANOVAs. Axial ultrasound velocity in both symptomatic and asymptomatic patellar tendons in tendinopathy was approximately 15% higher than in healthy tendons at the commencement (F1,23=5.2, P<.05) and completion (F1,23=4.5, P<.05) of the squat. While peak velocity was ≈5% higher during both flexion (F1,23=5.4, P<.05) and extension (F1,23=5.3, P<.05) phases, there was no significant between–group difference at the mid–point of the movement. There were no significant differences in the rate and magnitude of knee movement between groups. Although further research is required, these findings suggest enhanced baseline muscle activity in patellar tendinopathy and highlight fresh avenues for its clinical management.

Domain Adaptation on the Statistical Manifold

In this paper, we tackle the problem of unsupervised domain adaptation for classification. In the unsupervised scenario where no labeled samples from the target domain are provided, a popular approach consists in transforming the data such that the source and target distributions be- come similar. To compare the two distributions, existing approaches make use of the Maximum Mean Discrepancy (MMD). However, this does not exploit the fact that prob- ability distributions lie on a Riemannian manifold. Here, we propose to make better use of the structure of this man- ifold and rely on the distance on the manifold to compare the source and target distributions. In this framework, we introduce a sample selection method and a subspace-based method for unsupervised domain adaptation, and show that both these manifold-based techniques outperform the cor- responding approaches based on the MMD. Furthermore, we show that our subspace-based approach yields state-of- the-art results on a standard object recognition benchmark.

On the order of the fractional Laplacian in determining the spatio-temporal evolution of a space-fractional model of cardiac electrophysiology

Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. We consider a simplified model of electrical pulse propagation through cardiac tissue, namely the monodomain formulation of the Beeler-Reuter cell model on insulated tissue fibres, and obtain a space-fractional modification of the model by using the spectral definition of the one-dimensional continuous fractional Laplacian. The spectral decomposition of the fractional operator allows us to develop an efficient numerical method for the space-fractional problem. Particular attention is paid to the role played by the fractional operator in determining the solution behaviour and to the identification of crucial differences between the non-fractional and the fractional cases. We find a positive linear dependence of the depolarization peak height and a power law decay of notch and dome peak amplitudes for decreasing orders of the fractional operator. Furthermore, we establish a quadratic relationship in conduction velocity, and quantify the increasingly wider action potential foot and more pronounced dispersion of action potential duration, as the fractional order is decreased. A discussion of the physiological interpretation of the presented findings is made.

Moments of flux in intermediary liability for copyright infringement

This chapter provides an overview of a recent shift in regulatory strategies to address copyright infringement toward enlisting the assistance of general purpose Internet Service Providers. In Australia, the High Court held in 2012 that iiNet, a general purpose ISP, had no legal duty to police what its subscribers did with their internet connections. We provide an overview of three recent developments in Australian copyright law since that decision that demonstrate an emerging shift in the way that obligations are imposed on ISPs to govern the actions of their users without relying on secondary liability. The first is a new privately negotiated industry code that introduces a 'graduated response' system that requires ISPs to pass on warnings to subscribers who receive allegations of infringement. The second involves a recent series of Federal Court cases where rightsholders made a partially successful application to require ISPs to hand over the identifying details of subscribers whose households are alleged to have infringed copyright. The third is a new legislative scheme that will require ISPs to block access to foreign websites that 'facilitate' infringement. We argue that these shifts represent a greater sophistication in approaches to enrolling general purpose intermediaries in the regulatory project. We also suggest that these shifts represent a potentially disturbing trend towards enforcement of copyright law in a way that does not provide strong safeguards for the legitimate constitutional due process interests of users. We conclude with a call for greater attention and research to better understand how intermediaries make decisions when governing the conduct of users, how those decisions may be influenced by both state and non-state actors, and how the rights of individuals to due process can be adequately protected.

Hip power analysis in individuals with transfemoral amputation: A different strategy different from stabilisation during gait stance

Introduction and Objectives Joint moments and joint powers during gait are widely used to determine the effects of rehabilitation programs as well as prosthetic fitting. Following the definition of power (dot product of joint moment and joint angular velocity) it has been previously proposed to analyse the 3D angle between both vectors, αMw. Basically, joint power is maximised when both vectors are parallel and cancelled when both vectors are orthogonal. In other words, αMw < 60° reveals a propulsion configuration (more than 50% of the moment contribute to positive power) while αMw > 120° reveals a resistance configuration (more than 50% of the moment contribute to negative power). A stabilisation configuration (less than 50% of the moment contribute to power) corresponds to 60° < αMw < 120°. Previous studies demonstrated that hip joints of able-bodied adults (AB) are mainly in a stabilisation configuration (αMw about 90°) during the stance phase of gait. [1, 2] Individuals with transfemoral amputation (TFA) need to maximise joint power at the hip while controlling the prosthetic knee during stance. Therefore, we tested the hypothesis that TFAs should adopt a strategy that is different from a continuous stabilisation. The objective of this study was to compute joint power and αMw for TFA and to compare them with AB. Methods Three trials of walking at self-selected speed were analysed for 8 TFAs (7 males and 1 female, 46±10 years old, 1.78±0.08 m 82±13 kg) and 8 ABs (males, 25±3 years old, 1.75±0.04, m 67±6 kg). The joint moments are computed from a motion analysis system (Qualisys, Goteborg, Sweden) and a multi-axial transducer (JR3, Woodland, USA) mounted above the prosthetic knee for TFAs and from a motion analysis system (Motion Analysis, Santa Rosa, USA) and force plates (Bertec, Columbus, USA) for ABs. The TFAs were fitted with an OPRA (Integrum, AB, Gothengurg, Sweden) osseointegrated implant system and their prosthetic designs include pneumatic, hydraulic and microprocessor knees. Previous studies showed that the inverse dynamics computed from the multi-axial transducer is the proper method considering the absorption at the foot and resistance at the knee. Results The peak of positive power at loading response (H1) was earlier and lower for TFA compared to AB. Although the joint power is lower, the 3D angle between joint moment and joint angular velocity, αMw, reveals an obvious propulsion configuration (mean αMw about 20°) for TFA compared to a stabilisation configuration (mean αMw about 70°) for AB. The peaks of negative power at midstance (H2) and of positive power at preswing / initial swing (H3) occurred later, lower and longer for TFA compared to AB. Again, the joint powers are lower for TFA but, in this case, αMw is almost comparable (with a time lag), demonstrating a stabilisation (almost a resistance for TFA, mean αMw about 120°) and a propulsion configuration, respectively. The swing phase is not analysed in the present study. Conclusion The analysis of hip joint power may indicate that TFAs demonstrated less propulsion and resistance than ABs during the stance phase of gait. This is true from a quantitative point of view. On the contrary, the 3D angle between joint moment and joint angular velocity, αMw, reveals that TFAs have a remarkable propulsion strategy at loading response and almost a resistance strategy at midstance while ABs adopted a stabilisation strategy. The propulsion configuration, with αMw close to 0°, seems to aim at maximising the positive joint power. The configuration close to resistance, with αMw far from 180°, might aim at unlocking the prosthetic knee before swing while minimising the negative power. This analysis of both joint power and 3D angle between the joint moment and the joint angular velocity provides complementary insights into the gait strategies of TFA that can be used to support evidence-based rehabilitation and fitting of prosthetic components.

High-density fine-mapping of a chromosome 10q26 linkage peak suggests association between endometriosis and variants close to CYP2C19

OBJECTIVE To refine a previously reported linkage peak for endometriosis on chromosome 10q26, and conduct follow-up analyses and a fine-mapping association study across the region to identify new candidate genes for endometriosis. DESIGN Case-control study. SETTING Academic research. PATIENT(S) Cases=3,223 women with surgically confirmed endometriosis; controls=1,190 women without endometriosis and 7,060 population samples. INTERVENTION(S) Analysis of 11,984 single nucleotide polymorphisms on chromosome 10. MAIN OUTCOME MEASURE(S) Allele frequency differences between cases and controls. RESULT(S) Linkage analyses on families grouped by endometriosis symptoms (primarily subfertility) provided increased evidence for linkage (logarithm of odds score=3.62) near a previously reported linkage peak. Three independent association signals were found at 96.59 Mb (rs11592737), 105.63 Mb (rs1253130), and 124.25 Mb (rs2250804). Analyses including only samples from linkage families supported the association at all three regions. However, only rs11592737 in the cytochrome P450 subfamily C (CYP2C19) gene was replicated in an independent sample of 2,079 cases and 7,060 population controls. CONCLUSION(S) The role of the CYP2C19 gene in conferring risk for endometriosis warrants further investigation.

Susceptibility locus on chromosome 1q23-25 for a schizophrenia subtype resembling deficit schizophrenia identified by latent class analysis

Context: Identifying susceptibility genes for schizophrenia may be complicated by phenotypic heterogeneity, with some evidence suggesting that phenotypic heterogeneity reflects genetic heterogeneity. Objective: To evaluate the heritability and conduct genetic linkage analyses of empirically derived, clinically homogeneous schizophrenia subtypes. Design: Latent class and linkage analysis. Setting: Taiwanese field research centers. Participants: The latent class analysis included 1236 Han Chinese individuals with DSM-IV schizophrenia. These individuals were members of a large affected-sibling-pair sample of schizophrenia (606 ascertained families), original linkage analyses of which detected a maximum logarithm of odds (LOD) of 1.8 (z = 2.88) on chromosome 10q22.3. Main Outcome Measures: Multipoint exponential LOD scores by latent class assignment and parametric heterogeneity LOD scores. Results: Latent class analyses identified 4 classes, with 2 demonstrating familial aggregation. The first (LC2) described a group with severe negative symptoms, disorganization, and pronounced functional impairment, resembling “deficit schizophrenia.” The second (LC3) described a group with minimal functional impairment, mild or absent negative symptoms, and low disorganization. Using the negative/deficit subtype, we detected genome-wide significant linkage to 1q23-25 (LOD = 3.78, empiric genome-wide P = .01). This region was not detected using the DSM-IV schizophrenia diagnosis, but has been strongly implicated in schizophrenia pathogenesis by previous linkage and association studies.Variants in the 1q region may specifically increase risk for a negative/deficit schizophrenia subtype. Alternatively, these results may reflect increased familiality/heritability of the negative class, the presence of multiple 1q schizophrenia risk genes, or a pleiotropic 1q risk locus or loci, with stronger genotype-phenotype correlation with negative/deficit symptoms. Using the second familial latent class, we identified nominally significant linkage to the original 10q peak region. Conclusion: Genetic analyses of heritable, homogeneous phenotypes may improve the power of linkage and association studies of schizophrenia and thus have relevance to the design and analysis of genome-wide association studies.

GENEHUNTER: your 'one-stop shop' for statistical genetic analysis?

The past decade has brought a proliferation of statistical genetic (linkage) analysis techniques, incorporating new methodology and/or improvement of existing methodology in gene mapping, specifically targeted towards the localization of genes underlying complex disorders. Most of these techniques have been implemented in user-friendly programs and made freely available to the genetics community. Although certain packages may be more 'popular' than others, a common question asked by genetic researchers is 'which program is best for me?'. To help researchers answer this question, the following software review aims to summarize the main advantages and disadvantages of the popular GENEHUNTER package.

A genomewide screen for autism susceptibility loci

We report the analysis of 335 microsatellite markers genotyped in 110 multiplex families with autism. All families include at least two "affected" siblings, at least one of whom has autism; the remaining affected sibs carry diagnoses of either Asperger syndrome or pervasive developmental disorder. Affected sib-pair analysis yielded multipoint maximum LOD scores (MLS) that reach the accepted threshold for suggestive linkage on chromosomes 5, X, and 19. Nominal evidence for linkage (point-wise P<.05) was obtained on chromosomes 2, 3, 4, 8, 10, 11, 12, 15, 16, 18, and 20, and secondary loci were found on chromosomes 5 and 19. Analysis of families sharing alleles at the putative X chromosomal linked locus and one or more other putative linked loci produced an MLS of 3.56 for the DXS470-D19S174 marker combination. In an effort to increase power to detect linkage, scan statistics were used to evaluate the significance of peak LOD scores based on statistical evidence at adjacent marker loci. This analysis yielded impressive evidence for linkage to autism and autism-spectrum disorders with significant genomewide P values <.05 for markers on chromosomes 5 and 8 and with suggestive linkage evidence for a marker on chromosome 19.

Gravity-induced coronal plane joint moments in adolescent idiopathic scoliosis

Background Adolescent Idiopathic Scoliosis is the most common type of spinal deformity, and whilst the risk of progression appears to be biomechanically mediated (larger deformities are more likely to progress), the detailed biomechanical mechanisms driving progression are not well understood. Gravitational forces in the upright position are the primary sustained loads experienced by the spine. In scoliosis they are asymmetrical, generating moments about the spinal joints which may promote asymmetrical growth and deformity progression. Using 3D imaging modalities to estimate segmental torso masses allows the gravitational loading on the scoliotic spine to be determined. The resulting distribution of joint moments aids understanding of the mechanics of scoliosis progression. Methods Existing low-dose CT scans were used to estimate torso segment masses and joint moments for 20 female scoliosis patients. Intervertebral joint moments at each vertebral level were found by summing the moments of each of the torso segment masses above the required joint. Results The patients’ mean age was 15.3 years (SD 2.3; range 11.9 – 22.3 years); mean thoracic major Cobb angle 52° (SD 5.9°; range 42°-63°) and mean weight 57.5 kg (SD 11.5 kg; range 41 – 84.7 kg). Joint moments of up to 7 Nm were estimated at the apical level. No significant correlation was found between the patients’ major Cobb angles and apical joint moments. Conclusions Patients with larger Cobb angles do not necessarily have higher joint moments, and curve shape is an important determinant of joint moment distribution. These findings may help to explain the variations in progression between individual patients. This study suggests that substantial corrective forces are required of either internal instrumentation or orthoses to effectively counter the gravity-induced moments acting to deform the spinal joints of idiopathic scoliosis patients.

Insights into PBDE uptake, body burden, and elimination gained from Australian age–Concentration trends observed shortly after peak exposure

Background Population pharmacokinetic models combined with multiple sets of age– concentration biomonitoring data facilitate back-calculation of chemical uptake rates from biomonitoring data. Objectives We back-calculated uptake rates of PBDEs for the Australian population from multiple biomonitoring surveys (top-down) and compared them with uptake rates calculated from dietary intake estimates of PBDEs and PBDE concentrations in dust (bottom-up). Methods Using three sets of PBDE elimination half-lives, we applied a population pharmacokinetic model to the PBDE biomonitoring data measured between 2002–2003 and 2010–2011 to derive the top-down uptake rates of four key PBDE congeners and six age groups. For the bottom-up approach, we used PBDE concentrations measured around 2005. Results Top-down uptake rates of Σ4BDE (the sum of BDEs 47, 99, 100, and 153) varied from 7.9 to 19 ng/kg/day for toddlers and from 1.2 to 3.0 ng/kg/day for adults; in most cases, they were—for all age groups—higher than the bottom-up uptake rates. The discrepancy was largest for toddlers with factors up to 7–15 depending on the congener. Despite different elimination half-lives of the four congeners, the age–concentration trends showed no increase in concentration with age and were similar for all congeners. Conclusions In the bottom-up approach, PBDE uptake is underestimated; currently known pathways are not sufficient to explain measured PBDE concentrations, especially in young children. Although PBDE exposure of toddlers has declined in the past years, pre- and postnatal exposure to PBDEs has remained almost constant because the mothers’ PBDE body burden has not yet decreased substantially.

Statistical analysis of spectral data: A methodology for designing an intelligent monitoring system for the diabetic foot

Early detection of (pre-)signs of ulceration on a diabetic foot is valuable for clinical practice. Hyperspectral imaging is a promising technique for detection and classification of such (pre-)signs. However, the number of the spectral bands should be limited to avoid overfitting, which is critical for pixel classification with hyperspectral image data. The goal was to design a detector/classifier based on spectral imaging (SI) with a small number of optical bandpass filters. The performance and stability of the design were also investigated. The selection of the bandpass filters boils down to a feature selection problem. A dataset was built, containing reflectance spectra of 227 skin spots from 64 patients, measured with a spectrometer. Each skin spot was annotated manually by clinicians as "healthy" or a specific (pre-)sign of ulceration. Statistical analysis on the data set showed the number of required filters is between 3 and 7, depending on additional constraints on the filter set. The stability analysis revealed that shot noise was the most critical factor affecting the classification performance. It indicated that this impact could be avoided in future SI systems with a camera sensor whose saturation level is higher than 106, or by postimage processing.

Serum bilirubin concentration is modified by UGT1A1 Haplotypes and influences risk of type-2 diabetes in the Norfolk Island Genetic Isolate

Background Located in the Pacific Ocean between Australia and New Zealand, the unique population isolate of Norfolk Island has been shown to exhibit increased prevalence of metabolic disorders (type-2 diabetes, cardiovascular disease) compared to mainland Australia. We investigated this well-established genetic isolate, utilising its unique genomic structure to increase the ability to detect related genetic markers. A pedigree-based genome-wide association study of 16 routinely collected blood-based clinical traits in 382 Norfolk Island individuals was performed. Results A striking association peak was located at chromosome 2q37.1 for both total bilirubin and direct bilirubin, with 29 SNPs reaching statistical significance (P < 1.84 × 10−7). Strong linkage disequilibrium was observed across a 200 kb region spanning the UDP-glucuronosyltransferase family, including UGT1A1, an enzyme known to metabolise bilirubin. Given the epidemiological literature suggesting negative association between CVD-risk and serum bilirubin we further explored potential associations using stepwise multivariate regression, revealing significant association between direct bilirubin concentration and type-2 diabetes risk. In the Norfolk Island cohort increased direct bilirubin was associated with a 28 % reduction in type-2 diabetes risk (OR: 0.72, 95 % CI: 0.57-0.91, P = 0.005). When adjusted for genotypic effects the overall model was validated, with the adjusted model predicting a 30 % reduction in type-2 diabetes risk with increasing direct bilirubin concentrations (OR: 0.70, 95 % CI: 0.53-0.89, P = 0.0001). Conclusions In summary, a pedigree-based GWAS of blood-based clinical traits in the Norfolk Island population has identified variants within the UDPGT family directly associated with serum bilirubin levels, which is in turn implicated with reduced risk of developing type-2 diabetes within this population.