Bayesian parametric bootstrap for models with intractable likelihoods

In this paper it is demonstrated how the Bayesian parametric bootstrap can be adapted to models with intractable likelihoods. The approach is most appealing when the semi-automatic approximate Bayesian computation (ABC) summary statistics are selected. After a pilot run of ABC, the likelihood-free parametric bootstrap approach requires very few model simulations to produce an approximate posterior, which can be a useful approximation in its own right. An alternative is to use this approximation as a proposal distribution in ABC algorithms to make them more efficient. In this paper, the parametric bootstrap approximation is used to form the initial importance distribution for the sequential Monte Carlo and the ABC importance and rejection sampling algorithms. The new approach is illustrated through a simulation study of the univariate g-and- k quantile distribution, and is used to infer parameter values of a stochastic model describing expanding melanoma cell colonies.

A semiautomatic method to identify vertebral end plate lesions (Schmorl's nodes)

Background Context There are differences in definitions of end plate lesions (EPLs), often referred to as Schmorl’s nodes, that may, to some extent, account for the large range of reported prevalence (3.8 to 76%). Purpose To develop a technique to measure the size, prevalence and location of EPLs in a consistent manner. Study Design/Setting This study proposed a method using a detection algorithm which was applied to five adolescent females (average age 15.1 years, range 13.0 to 19.2 years) with idiopathic scoliosis (average major Cobb angle 60°, range 55 to 67°). Methods Existing low-dose, computed tomography scans were segmented semi-automatically to extract 3D morphology of each vertebral endplate. Any remaining attachments to the posterior elements of adjacent vertebrae or endplates were then manually sectioned. An automatic algorithm was used to determine the presence and position of EPLs. Results EPLs were identified in 15 of the 170 (8.8%) endplates analysed with an average depth of 3.1mm. 11/15 of the EPLs were seen in the lumbar spine. The algorithm was found to be most sensitive to changes in the minimum EPL gradient at the edges of the EPL. Conclusions This study describes an imaging analysis technique for consistent measurement of the prevalence, location and size of EPLs. The technique can be used to analyse large populations without observer errors in EPL definitions.

Traditional and geometric morphometrics detect morphological variation of lower pharyngeal jaw inCoris julis(Teleostei, Labridae)

In the present study, variation in the morphology of the lower pharyngeal element between two Sicilian populations of the rainbow wrasse Coris julis has been explored by the means of traditional morphometrics for size and geometric morphometrics for shape. Despite close geographical distance and probable high genetic flow between the populations, statistically significant differences have been found both for size and shape. In fact, one population shows a larger lower pharyngeal element that has a larger central tooth. Compared to the other population, this population also has medially enlarged lower pharyngeal jaws with a more pronounced convexity of the medial-posterior margin. The results are discussed in the light of a possible more pronounced durophagy of this population.

Bayesian refinement of association signals for 14 loci in 3 common diseases

To further investigate susceptibility loci identified by genome-wide association studies, we genotyped 5,500 SNPs across 14 associated regions in 8,000 samples from a control group and 3 diseases: type 2 diabetes (T2D), coronary artery disease (CAD) and Graves' disease. We defined, using Bayes theorem, credible sets of SNPs that were 95% likely, based on posterior probability, to contain the causal disease-associated SNPs. In 3 of the 14 regions, TCF7L2 (T2D), CTLA4 (Graves' disease) and CDKN2A-CDKN2B (T2D), much of the posterior probability rested on a single SNP, and, in 4 other regions (CDKN2A-CDKN2B (CAD) and CDKAL1, FTO and HHEX (T2D)), the 95% sets were small, thereby excluding most SNPs as potentially causal. Very few SNPs in our credible sets had annotated functions, illustrating the limitations in understanding the mechanisms underlying susceptibility to common diseases. Our results also show the value of more detailed mapping to target sequences for functional studies. © 2012 Nature America, Inc. All rights reserved.

Identifying vertebral end plate lesions (schmorl's nodes) using a semi-automatic method

INTRODUCTION There is a large range in the reported prevalence of end plate lesions (EPLs), sometimes referred to as Schmorl's nodes in the general population (3.8-76%). One possible reason for this large range is the differences in definitions used by authors. Previous research has suggested that EPLs may potentially be a primary disturbance of growth plates that leads to the onset of scoliosis. The aim of this study was to develop a technique to measure the size, prevalence and location of EPLs on Computed Tomography (CT) images of scoliosis patients in a consistent manner. METHODS A detection algorithm was developed and applied to measure EPLs for five adolescent females with idiopathic scoliosis (average age 15.1 years, average major Cobb 60°). In this algorithm, the EPL definition was based on the lesion depth, the distance from the edge of the vertebral body and the gradient of the lesion edge. Existing low-dose, CT scans of the patients' spines were segmented semi-automatically to extract 3D vertebral endplate morphology. Manual sectioning of any attachments between posterior elements of adjacent vertebrae and, if necessary, endplates was carried out before the automatic algorithm was used to determine the presence and position of EPLs. RESULTS EPLs were identified in 15 of the 170 (8.8%) endplates analysed with an average depth of 3.1mm. 73% of the EPLs were seen in the lumbar spines (11/15). A sensitivity study demonstrated that the algorithm was most sensitive to changes in the minimum gradient required at the lesion edge. CONCLUSION An imaging analysis technique for consistent measurement of the prevalence, location and size of EPLs on CT images has been developed. Although the technique was tested on scoliosis patients, it can be used to analyse other populations without observer errors in EPL definitions.

Morphometric analysis of the thoracic intervertebral foramen osseous anatomy in adolescent idiopathic scoliosis using low dose computerized tomography

Introduction. The dimensions of the thoracic intervertebral foramen in adolescent idiopathic scoliosis (AIS) have not previously been quantified. During posterior approach scoliosis correction surgery pedicle screws may occasionally breach into the foramen. Better understanding of the dimensions of the foramen may be useful in surgical planning. This study describes a reproducible method for measurement of the thoracic foramen in AIS using computerized tomography (CT). Methods. In 23 pre-operative female patients with Lenke 1 type AIS with right side convexity major curves confined to the thoracic spine the foraminal height (FH), foraminal width (FW), pedicle to superior articular process distance (P-SAP) and cross sectional foraminal area (FA) were measured using multiplanar reconstructed CT. Measurements were made at entrance, midpoint and exit of the thoracic foramina from T1/T2 to T11/T12. Results were correlated with potential dependent variables of major curve Cobb Angle measured on X-ray and CT, Age, Weight, Lenke classification subtype, Risser Grade and number of spinal levels in the major curve. Results. The FH, FW, P-SAP and FA dimensions and ratios are all significantly larger on the convexity of the major curve and maximal at or close to the apex. Mean thoracic foraminal dimensions change in a predictable manner relative to position on the major thoracic curve. There was no significant correlation with the measured foraminal dimensions or ratios and the potential dependent variables. The average ratio of convexity to concavity dimensions at the apex foramina for entrance, midpoint and exit respectively are FH (1.50, 1.38, 1.25), FW (1.28, 1.30, 0.98), FA (2.06, 1.84, 1.32), P-SAP (1.61, 1.47, 1.30). Conclusion. Foraminal dimensions of the thoracic spine are significantly affected by AIS. Foraminal dimensions have a predictable convexity to concavity ratio relative to the proximity to the major curve apex. Surgeons should be aware of these anatomical differences during scoliosis correction surgery.

Using low dose computerized tomography to morphometrically analyse the thoracic intervertebral foramen osseous anatomy in adolescent idiopathic scoliosis

INTRODUCTION The dimensions of the thoracic intervertebral foramen in adolescent idiopathic scoliosis (AIS) have not previously been quantified. During posterior approach scoliosis correction surgery pedicle screws may occasionally breach into the foramen. Better understanding of the dimensions of the foramen may be useful in surgical planning. This study describes a reproducible method for measurement of the thoracic foramen in AIS using computerized tomography (CT). METHODS In 23 pre-operative female patients with Lenke 1 type AIS with right side convexity major curves confined to the thoracic spine the foraminal height (FH), foraminal width (FW), pedicle to superior articular process distance (P-SAP) and cross sectional foraminal area (FA) were measured using multiplanar reconstructed CT. Measurements were made at entrance, midpoint and exit of the thoracic foramina from T1/T2 to T11/T12. Results were correlated with potential dependent variables of major curve Cobb Angle measured on X-ray and CT, Age, Weight, Lenke classification subtype, Risser Grade and number of spinal levels in the major curve. RESULTS The FH, FW, P-SAP and FA dimensions and ratios are all significantly larger on the convexity of the major curve and maximal at or close to the apex. Mean thoracic foraminal dimensions change in a predictable manner relative to position on the major thoracic curve. There was no significant correlation with the measured foraminal dimensions or ratios and the potential dependent variables. The average ratio of convexity to concavity dimensions at the apex foramina for entrance, midpoint and exit respectively are FH (1.50, 1.38, 1.25), FW (1.28, 1.30, 0.98), FA (2.06, 1.84, 1.32), P-SAP (1.61, 1.47, 1.30). CONCLUSION Foraminal dimensions of the thoracic spine are significantly affected by AIS. Foraminal dimensions have a predictable convexity to concavity ratio relative to the proximity to the major curve apex. Surgeons should be aware of these anatomical differences during scoliosis correction surgery.

Estimation of the time of a linear trend in monitoring survival time

Change point estimation is recognized as an essential tool of root cause analyses within quality control programs as it enables clinical experts to search for potential causes of change in hospital outcomes more effectively. In this paper, we consider estimation of the time when a linear trend disturbance has occurred in survival time following an in-control clinical intervention in the presence of variable patient mix. To model the process and change point, a linear trend in the survival time of patients who underwent cardiac surgery is formulated using hierarchical models in a Bayesian framework. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. We use Markov Chain Monte Carlo to obtain posterior distributions of the change point parameters including the location and the slope size of the trend and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time cumulative sum control chart (CUSUM) control charts for different trend scenarios. In comparison with the alternatives, step change point model and built-in CUSUM estimator, more accurate and precise estimates are obtained by the proposed Bayesian estimator over linear trends. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

Errors in the knee joint forces and moments during gait depending on the foot and knee prosthetic components

Background Previously studies showed that inverse dynamics based on motion analysis and force-plate is inaccurate compared to direct measurements for individuals with transfemoral amputation (TFA). Indeed, direct measurements can appropriately take into account the absorption at the prosthetic foot and the resistance at the prosthetic knee. [1-3] However, these studies involved only a passive prosthetic knee. Aim The objective of the present study was to investigate if different types of prosthetic feet and knees can exhibit different levels of error in the knee joint forces and moments. Method Three trials of walking at self-selected speed were analysed for 9 TFAs (7 males and 2 females, 47±9 years old, 1.76±0.1 m 79±17 kg) with a motion analysis system (Qualisys, Goteborg, Sweden), force plates (Kitsler, Winterthur, Switzerland) and a multi-axial transducer (JR3, Woodland, USA) mounted above the prosthetic knee [1-17]. TFAs were all fitted with an osseointegrated implant system. The prostheses included different type of foot (N=5) and knee (N=3) components. The root mean square errors (RMSE) between direct measurements and the knee joint forces and moments estimated by inverse dynamics were computed for stance and swing phases of gait and expressed as a percentage of the measured amplitudes. A one-way Kruskal-Wallis ANOVA was performed (Statgraphics, Levallois-Perret, France) to analyse the effects of the prosthetic components on the RMSEs. Cross-effects and post-hoc tests were not analysed in this study. Results A significant effect (*) was found for the type of prosthetic foot on anterior-posterior force during swing (p=0.016), lateral-medial force during stance (p=0.009), adduction-abduction moment during stance (p=0.038), internal-external rotation moment during stance (p=0.014) and during swing (p=0.006), and flexion-extension moment during stance (p = 0.035). A significant effect (#) was found for the type of prosthetic knee on anterior-posterior force during swing (p=0.018) and adduction-abduction moment during stance (p=0.035). Discussion & Conclusion The RMSEs were larger during swing than during stance. It is because the errors on accelerations (as derived from motion analysis) become substantial with respect to the external loads. Thus, inverse dynamics during swing should be analysed with caution because the mean RMSEs are close to 50%. Conversely, there were fewer effects of the prosthetic components on RMSE during swing than during stance and, accordingly, fewer effects due to knees than feet. Thus, inverse dynamics during stance should be used with caution for comparison of different prosthetic components.

Regional changes in choroidal thickness associated with accommodation

Purpose. To characterize the changes occurring in choroidal thickness (ChT) across the posterior pole during accommodation using enhanced-depth imaging optical coherence tomography (OCT). Methods. Forty participants (mean age 21 ± 2 years) had measures of ChT and ocular biometry taken during accommodation to 0, 3, and 6 diopter (D) stimuli, with the Spectralis OCT and Lenstar biometer. A Badal optometer and cold mirror system was mounted on both instruments, allowing measurement collection while subjects viewed an external fixation target at varying accommodative demands. Results. The choroid exhibited significant thinning during accommodation to the 6 D stimulus in both subfoveal (mean change, −5 ± 7 μm) and parafoveal regions (P < 0.001). The magnitude of these changes varied by parafoveal meridian, with the largest changes seen in the temporal (−9 ± 12 μm) and inferotemporal (−8 ± 8 μm) meridians (P < 0.001). Axial length increased with accommodation (mean change, +5 ± 11 μm at 3 D, +14 ± 13 μm at 6 D), and these changes were weakly negatively associated with the choroidal changes (r2 = 0.114, P < 0.05). Conclusions. A small, but significant thinning of the choroid was observed at the 6 D accommodation demand, which was greatest in the temporal and inferotemporal parafoveal choroid, and increased with increasing eccentricity from the fovea. The regional variation in the parafoveal thinning corresponds to the distribution of the nonvascular smooth muscle within the uvea, which may implicate these cells as the potential mechanism by which the choroid thins during accommodation.

Genetic studies of disorders of calcium crystal deposition

In summary, although many factors are likely to be involved in regulating calcification and ossification processes, studies of the causation of articular chondrocalcinosis and disorders of spinal ossification, such as DISH and OPLL, implicate control over inorganic pyrophosphate levels as being one of the most important factors in their aetiopathogenesis. The findings of these studies may prove relevant to other rheumatic diseases in which ectopic ossification occurs, such as AS.

A Bayesian Framework for the Assessment of Vision-based Weed and Fruit Detection and Classification Algorithms

This paper proposes new metrics and a performance-assessment framework for vision-based weed and fruit detection and classification algorithms. In order to compare algorithms, and make a decision on which one to use fora particular application, it is necessary to take into account that the performance obtained in a series of tests is subject to uncertainty. Such characterisation of uncertainty seems not to be captured by the performance metrics currently reported in the literature. Therefore, we pose the problem as a general problem of scientific inference, which arises out of incomplete information, and propose as a metric of performance the(posterior) predictive probabilities that the algorithms will provide a correct outcome for target and background detection. We detail the framework through which these predicted probabilities can be obtained, which is Bayesian in nature. As an illustration example, we apply the framework to the assessment of performance of four algorithms that could potentially be used in the detection of capsicums (peppers).

Tarsal tunnel syndrome: A narrative literature review

Background Tarsal tunnel syndrome is classified as a focal compressive neuropathy of the posterior tibial nerve or one of its associated branches individually or collectively. The tunnel courses deep to fascia, the flexor retinaculum and within the abductor hallucis muscle of the foot/ankle. The condition is rare and regularly under-diagnosed leading to a range of symptoms affecting the plantar margins of the foot. There are many intervention strategies for treating tarsal tunnel syndrome with limited robust evidence to guide the clinical management of this condition. The role of conservative versus surgical interventions at various stages of the disease process remains unclear, and there is a need for a structured, step-wise approach in treating patients with this syndrome based on derived empirical evidence. This narrative review attempts to scrutinize the literature to date by clarifying initial presentation, investigations and definitive treatment for the purpose of assisting future informed clinical decision and prospective research endeavours. Process The literature searches that have been incorporated in compiling a rigorous review of this condition have included: the Cochrane Neuromuscular Group's Specialized Register (Cochrane Library 2013), the databases of EMBASE, AMED, MEDLINE, CINAHL, Physiotherapy evidence database (PEDRO), Biomed Central, Science Direct and Trip Database (1972 to the present). Reference listings of located articles were also searched and scrutinized. Authors and experts within the field of lower-limb orthopaedics were contacted to discuss applicable data. Subject-specific criteria searches utilizing the following key terms were performed across all databases: tarsal tunnel syndrome, tibial neuralgia, compression neuropathy syndromes, tibial nerve impingement, tarsal tunnel neuropathy, entrapment tibial nerve, posterior tibial neuropathy. These search strategies were modified with differing databases, adopting specific sensitivity-searching tools and functions unique to each. This search strategy identified 88 journal articles of relevance for this narrative literature review. Findings This literature review has appraised the clinical significance of tarsal tunnel syndrome, whilst assessing varied management interventions (non-surgical and surgical) for the treatment of this condition in both adults and children. According to our review, there is limited high-level robust evidence to guide and refine the clinical management of tarsal tunnel syndrome. Requirements for small-scaled randomized controlled trials in groups with homogenous aetiology are needed to analyse the effectiveness of specific treatment modalities. Conclusions It is necessary that further research endeavours be pursued for the clinical understanding, assessment and treatment of tarsal tunnel syndrome. Accordingly, a structured approach to managing patients who have been correctly diagnosed with this condition should be formulated on the basis of empirical evidence where possible.

A simple Bayesian decision-theoretic design for dose-finding trials

A flexible and simple Bayesian decision-theoretic design for dose-finding trials is proposed in this paper. In order to reduce the computational burden, we adopt a working model with conjugate priors, which is flexible to fit all monotonic dose-toxicity curves and produces analytic posterior distributions. We also discuss how to use a proper utility function to reflect the interest of the trial. Patients are allocated based on not only the utility function but also the chosen dose selection rule. The most popular dose selection rule is the one-step-look-ahead (OSLA), which selects the best-so-far dose. A more complicated rule, such as the two-step-look-ahead, is theoretically more efficient than the OSLA only when the required distributional assumptions are met, which is, however, often not the case in practice. We carried out extensive simulation studies to evaluate these two dose selection rules and found that OSLA was often more efficient than two-step-look-ahead under the proposed Bayesian structure. Moreover, our simulation results show that the proposed Bayesian method's performance is superior to several popular Bayesian methods and that the negative impact of prior misspecification can be managed in the design stage.

Bayesian designs with frequentist and Bayesian error rate considerations

So far, most Phase II trials have been designed and analysed under a frequentist framework. Under this framework, a trial is designed so that the overall Type I and Type II errors of the trial are controlled at some desired levels. Recently, a number of articles have advocated the use of Bavesian designs in practice. Under a Bayesian framework, a trial is designed so that the trial stops when the posterior probability of treatment is within certain prespecified thresholds. In this article, we argue that trials under a Bayesian framework can also be designed to control frequentist error rates. We introduce a Bayesian version of Simon's well-known two-stage design to achieve this goal. We also consider two other errors, which are called Bayesian errors in this article because of their similarities to posterior probabilities. We show that our method can also control these Bayesian-type errors. We compare our method with other recent Bayesian designs in a numerical study and discuss implications of different designs on error rates. An example of a clinical trial for patients with nasopharyngeal carcinoma is used to illustrate differences of the different designs.